J . Phys. Chem. 1991, 95,9181-9185
9181
Dissociation of Large Silicon Clusters: The Approach to Bulk Behavior Martin F.Jarrold* and Eric C. Honea AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (Received: June 10, 1991)
The dissociation of silicon cluster ions containing up to 70 atoms has been examined using a multicollision excitation method. Clusters with 19-35 atoms dissociate mainly by loss of Silospecies. Larger clusters fragment by Si6loss. For clusters with n > 60, loss of an individual Si atom (as occurs for bulk silicon) begins to become an important dissociation channel. These changes in the observed products can be attributed to changes in the clusters' cohesive energies. When highly excited, the large clusters dissociate by sequential loss of Si6units until they reach a size of -30 atoms. They then disintegrate into fragments containing 6-1 1 atoms. Dissociation energies have been estimated from the experimental results. Substantial variations in the dissociation energies are observed for clusters with up to 25 atoms. For clusters with n > 25 the dissociation energies increase smoothly.
Introduction Studies of the dissociation of atomic clusters can provide a wealth of useful information about these interesting species.'-I0 In particular, these studies can provide information on the relative or absolute stabilities of the clusters. A problem that is often encountered in these studies is that as the cluster size increases it takes more and more energy to cause dissociation on a reasonable experimental timescale. Large clusters have many internal degrees of freedom and a large amount of energy is required to heat them to a temperature where they start to dissociate. For example, a rough estimate shows that -41 eV is required to dissociate, on a microsecond time scale, a 70-atom cluster with a cohesive energy of 4 eV/atom. It is difficult to deposit this much energy into a cluster, or any polyatomic molecule, in a controlled fashion. In conventional collision-induced dissociation studies the ions generally undergo a single ~ o l l i $ i o n . ~The * ~ ~resulting ~ internal energy distribution is broad, ranging from zero up to the center of mass collision energy. Furthermore, only a relatively small fraction of the laboratory kinetic energy is converted into internal energy. In the work described in this paper we have taken a different approach. The ions are injected at various kinetic energies into a miniature drift tube containing a high pressure of an inert collision gas. As the ions enter the drift tube they undergo many collisions with the collision gas, each collision converting a fraction of the ions kinetic energy into internal energy. Eventually the ions are stopped (their kinetic energy in the laboratory frame is reduced to close to zero). The fragments and undissociated ions are then swept out of the drift tube by a weak electric field, mass analyzed, and detected. This multi-collision excitation process results in the conversion of a substantial fraction of the ions laboratory kinetic energy into internal energy. Furthermore, the resulting internal energy distribution is narrow because of the averaging that occurs in the multicollision excitation process. ( I ) Bloomfield, L. A,; Freeman, R. R.; Brown, W. L. Phys. Reu. Lett. 1985, 54, 2246. (2) Begemann, W.; Meiwes-Broer, K. 1986, 56, 2248.
H.; Lutz, H. 0. Phys. Rev. Lett.
(3) Hanley, L.; Anderson, S. L. J . Phys. Chem. 1987, 91, 5161. F. K.; Smalley, R. E. J .
(4) Zhang, Q.-L.; Liu, Y.; Curl, R. F.; Tittel, Chem. Phys. 1988,88, 1670.
( 5 ) Begemann, W.;Dreihofer, S.; Gantefor, G.; Siekmann, H. R.; Meiwcs-Btoer, K. H.; Lutz, H. 0. In Elemental and Molecular Clusters; Martin, T. P.. Ed.;Springer: Berlin, 1987, (6) Jarrold. M. F.; Bower, J. E. J . Phys. Chem. 1988, 92, 5702. (7) Loh, S. K.; Halcs, D. A.; Lian, L.; Armentrout, P. B. J . Chem. Phys.
.
1909. 90. 5466. . ..
( 8 ) Brechignac, C.; Cahuzac, Ph.; Leygnier, L.; Weiner, J. J . Chem. Phys. 1989. 90. .- ., . - , 1492. - .- -. (9) Radi, P. P.; Rincon, M. E.; Hsu. M. T.; Brodbelt-Lustig, J.; Kemper, P.; Bowers. M. T. J . Phys. Chem. 1989, 93, 8414. (IO) Beck, R. D.; St. John, P.; Homer, M. L.; Whetten, R. L. ImpactInduced Cleaving and Melting of Alkali-Halide Nanocrystals. Science, in press.
There have been several previous studies of the dissociation of silicon cluster ions. In 1985 Bloomfield, Freeman, and Brown' showed that Si6+and Silo+ were favored products from the photodissociation of small silicon clusters ( n up to 12). Subsequently, Smalley and co-workers extended these photodissociation studies to clusters containing up to 60 atomse4They found that clusters with 12-30 atoms dissociate mainly by loss of 6, 7, and 10 atom species, but larger clusters completely disintegrated to yield fragments with 6-1 1 atoms. Jarrold and Bowefl investigated the collision-induced dissociation of silicon cluster ions containing up to 26 atoms and found similar fragmentation patterns to those found in the photodissociation experiments: clusters with 12-1 8 atoms dissociate mainly by loss of 6 or 7 atom species, and clusters with 19-26 atoms fragment predominently by ejecting Silounits. This behavior is very different from that observed with bulk silicon. If bulk silicon is heated, individual atoms evaporate from the surface. Raghavachari and Rohlfing" have shown that the products observed in the fragmentation of silicon clusters containing up to 17 atoms can be accounted for simply on the basis of their thermodynamic stability. Si,, Si,, and Silo(and their ions) are particularly stable species.'* However, this does not explain the mysterious disintegration of the larger clusters observed by Smalley and co-workers. How many atoms are required before the silicon clusters start to behave like the bulk material and evaporate individual atoms? In this paper we report a study of the collision-induced dissociation of silicon cluster ions containing up to 70 atoms using the multicollision excitation methods outlined above. Experimental Methods A schematic diagram of the experimental apparatus is shown in Figure ] . I 3 Silicon cluster ions, generated by pulsed laser vaporization of a silicon rod in a continuous flow of helium buffer gas, were focused into a quadrupole mass spectrometer where a particular cluster size is selected. The size-selected clusters were then focused into an ion beam and injected at various energies into a miniature drift tube.I4 The collision gas pressure in the drift tube was directly measured using a capacitance manometer. Most of the experiments were performed using neon at a pressure of 0.8 Torr. A few studies were performed with helium and argon, ( I 1) Raghavachari, K.; Rohlfing, C. M. Chem. Phys. Lett. 1988,143,428. (12) Raghavachari, K.; Logovinsky, V. Phys. Rev. Left. 1985.55, 2853. Raghavachari, K. J . Chem. Phys. 1986, 84, 5672. Raghavachari, K.; Rohlfing, C. M. J . Chem. Phys. 1988,89.2219. Raghavachari, K. Z . Phys. D. 1989, 12, 61. Raghavachari, K. Phase Trans. 1990, 24-26, 61. (13) Jarrold, M. F.; Bower, J. E.; Creegan, K. M. J . Chem. Phys. 1989, 90,3615. Creegan, K. M.; Jarrold, M. F. J. Am. Chem. Soc. 1990,112,3768. Jarrold, M. F.; Ray, U.; Creegan, K. M. J. Chem. Phys. 1990,93,224. Ray, U.; Jarrold, M. F. J . Chem. Phys. 1990, 93, 5709. Ray, U.;Jarrold, M. F. J . Chem. Phys. 1991, 94, 2631. Jarrold, M. F.; Ijiri, Y.; Ray, U. J . Chem. Phys. 1991, 94, 3607. (14) McDaniel, E. W.; Mason, E. A. The Mobility and Diffusion of Ions in Gases; Wiley: New York, 1973.
0022-365419 1 12095-918 1%02.50/0 , . 0 1991 American Chemical Society I
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Jarrold and Honea
9182 The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 ibJ
BUFFER + REACTANT
LASER
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Figure 1. Schematic diagram of the experimental apparatus.
also at 0.8 Torr. A drit't field of 1.O V/cm was employed in all of the experiments. At the end of the drift tube the product ions and undissociated cluster ions exit through a small aperture and are subsequently mass analyzed by a second quadrupole mass spectrometer. The ions were then detected by an off-axis collision dynode and dual microchannel plates. Mass discrimination is an issue in these experiments where the product and parent masses can differ by a large amount. There should be no mass discrimination in the drift tube because the transmission efficiency is not mass d e ~ e n d e n t . ' ~I n order to minimize mass discrimination in the second quadrupole mass spectrometer all measurements were performed with low mass resolution so that the peaks in the mass spectrum were approximately flat topped. When ions were injected into the drift tube at sufficiently high energies that a substantial fraction of the clusters dissociated into small fragments, the total ion signal appeared to drop. This drop in the total ion signal probably arises from clusters dissociating, just outside the drift tube, into small fragments which then have insufficient energy to make it into the drift tube.
Results Figure 2 shows mass spectra recorded as a function of injection energy for clusters containing 21, 33, 38,48, and 67 atoms. Si2,+ cleanly fragments by loss of a Silospecies to give Sil,+. The fragmentation patterns observed for the smaller clusters in these experiments are similar to those observed in previous photodis~ociation'*~ and collision-induced dissociation studies., Clusters with 12-1 8 atoms dissociate by loss of Si, and Si, species, and clusters with 19-26 atoms fragment predominantly by ejection of Silounits. Clusters with 27-35 atoms behave in a similar way, at least at low injection energies. The results for Sij3+shown in Figure 2 are representative of clusters in this size regime. Loss of Sil! is the only product observed at low energies but at higher energies loss of Si, (and Si7) becomes an important dissociation pathway. As shown in the figure, with even higher injection energies Si33+fragments to give predominantly product ions with 6-1 1 atoms. For clusters larger than Sijj+a fundamental change occurs. With increasing cluster size the relative abundance of the Siloloss channel quickly diminishes, and loss of a Si, species dominates at the lowest injection energies. Clearly for these larger clusters loss of a Si, species has become the lowest energy dissociation pathway. The results shown for Sij8+in Figure 2 are typical for clusters in this size regime. At low energies only loss of Si6(and Si7) occurs with significant abundance. At the higher energies Sij8+dissociates to give mainly product ions with 6-1 1 atoms. Note that very few products are observed in the 15-30-atom size range. It appears that after losing a single Si, unit the cluster disintegrates to yield much smaller product ions. This behavior continues for larger clusters as shown by the results for Si48+in Figure 2. For Si48+the lowest energy dissociation pathway is also loss of Si,. but for this larger cluster three sequential losses of Si6 can be identified as the energy increases. Again, essentially no products are observed in the 15-20-atom size range, suggesting that after the cluster has reached a size of around 30 atoms it disintegrates to give fragment ions with 10 or 11 atoms. At even higher energies the dominant charged products are in the 6-1 1atom size regime as observed for Si38+.Loss of Si4becomes an important fragmentation channel for these larger clusters at the higher energies. Like clusters with 6 , 7, and 10 atoms, Si4is also a relatively stable species according to the theoretical calculations
0
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Figure 2. Mass spectra recorded for the collision-induced dissociation of silicon clusters with (a) 21, (b) 33, (c) 38, (d) 48, and (e) 67 atoms. Note that the intensities are shown on a logarithmic scale.
of Raghavachari and co-workers.12 When bulk silicon is heated, individual silicon atoms evaporate from the surface. Loss of a single silicon atom is observed at high energies for Si48+,though the relative abundance of this product channel is small, for this cluster. With increasing cluster size the relative abundance of the Si atom loss channel increases, and the product is observable at lower energies relative to the other products. This is apparent from the results shown in Figure 2 for Si6,+. While loss of Si6is still the lowest energy dissociation pathway for this cluster, the Si atom loss channel is now much more important. The influence of the Si atom loss channel can clearly be seen at high energies where the pattern of sequential loss of Si, units observed for the smaller clusters is now essentially washed out and the products have a broad distribution of cluster sizes. With increasing cluster size we expect that the trends outlined above will continue and Si atom loss will eventually become the lowest energy dissociation pathway. With the current instrumentation the largest cluster we can examine is and it appears that a somewhat larger cluster is required for loss of a Si atom to become the lowest energy product. It seems from the results shown in Figure 2 that relatively sharp injection energy thresholds are associated with the dissociation of the clusters. Figure 3 shows a plot of the fraction of Si4*+ clusters that are dissociated against injection energy. There is a threshold for the dissociation of this cluster at 180 eV. These thresholds contain information about the relative stabilities of the clusters, and the fraction of the clusters' injection energy that is converted to internal energy as they enter the drift tube. Before any information can be extracted from the dissociation thresholds it is necessary to account for the statistical nature of the dissociation process. The fraction of clusters which dissociate within a time t is given by
-
where E, is the vibrational energy initially in the clusters (which are assumed to be at room temperature), Ei is the extra internal energy added as the clusters are injected into the drift tube, QV is the vibrational partition function, p,(E,) is the vibrational density
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9183
Dissociation of Large Silicon Clusters
2
6.0,
I
BULK ;’.yo
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I
z 0
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Figure 3. Results for the dissociation of Sil8+. The upper half of the figure shows a plot of the fraction of Sia+ clusters which dissociate against injection energy. There is a sharp threshold at 180 eV. The points are the experimental data and the lines are the results of simulations described in the text. The lower half of the figure shows the internal energy distribution deduced from the simulations for an injection energy of 182.8 eV.
-
+
of states, and k(Ei E,) is the rate constant for dissociation. Since little is known about the vibrational frequencies or the nature of the transition states p,(E,) and Q, were evaluated using a classical density of states and the Debye frequen~y,’~ and k(Ei E,) was determined from quantum RRK theory.I6 If dissociation energies were available for any of the silicon clusters it would be relatively straightforward to evaluate the fraction of the injection energy converted into internal energy (Fie). But dissociation energies have not yet been measured and the only information available is from theoretical calculations. Comparison of the measured injection energy thresholds with the thresholds predicted using the models described above and employing Raghavachari and coworkers’I2 scaled dissociation energies for the silicon clusters shows that Fieis -0.1 50 with neon as the collision gas. This comparison can only be made for small clusters (n < 11) because reliable calculations of the dissociation energies are not available for the larger ones. A limited number of experiments were performed with helium and argon collision gases. With helium Fiewas -0.046 and with argon it was -0.225. Comparable values for Fie have been obtained by Cooks and coworkers” in their studies of collisional activation of molecular ions. The values for Fie obtained above can be compared with the predictions of a simple impulsive collision model. This model, which is described in detail in the Appendix, predicts that Fieis given by
+
Fie
( n - 1)(1 2n
70
2n
I
,
*:*.-A
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gas but significantly overestimates Fie(which is expected for an impulsive collision model). In what follows we have assumed that Fieis given by (n - 1)(1 - c ) Fie C (4)
*
; , , ’,
20 30 40 50 NUMBER OF ATOMS IN CLUSTER
Figure 4. Plot of dissociation energies estimated from the measured dissociation thresholds.
1
INJECTION I ENERGY=~~~.~~V
10
- c) (2)
in which (3)
and mg is the mass of the collision gas. The impulsive collision model suggests that Fieis only slightly dependent on cluster size for the size range examined in this work. This model predicts, almost exactly, the variation of Fie with the mass of the collision ~~
( I 5 ) Kittel, C. Introduction to Solid State Physics; Wiley: New York, I 986.
(16) Robinson, P. J.; Holbrook, K. A. Unimokcular Reactions; Wiley: London, 1972. Font. W.Theory of UnimoleculorReactions;Academic: New
York,1973. (1 7) Kenttamaa, H. 1.; Cooks,R.G. Inr. J . Mass Spectrom. Ion Processes 1985, 64. 79.
where C is an empirical correction factor. The dashed line in the upper half of Figure 3 shows the results of a simulation of the dissociation threshold for Sia+ using the models described above. The calculated threshold is considerably narrower than the measured one. The origin of this difference is that a distribution of internal energies results when the clusters are injected into the drift tube. The solid line in the upper half of Figure 3 shows the result of the simulations including a distribution of internal energies characterized by a normal distribution function. The width of the normal distribution was adjusted to fit the experimental data. The lower half of Figure 3 shows the internal energy distribution which results, according to the simulations, when the clusters are injected into the drift tube with an injection energy of 182.8 eV. The distribution is narrow (-23% wide at the half-maximum). The internal energy distribution is narrow because of the averaging that occurs in the multicollision excitation process. The origin of this narrow internal energy distribution can be qualitatively understood by considering just two different types of collision event: a head-on collision and a glancing collision. In the head-on collision a significant amount of the ions’ kinetic energy is converted into internal energy and kinetic energy of the collision gas. In the glancing collision a much smaller fraction of the ions kinetic energy is lost. Thus, although the ion which experienced the head-on collision has more internal energy, the one that experienced the glancing collision retains a larger fraction of its initial kinetic energy. Figure 4 shows a plot of the dissociation energies obtained from the measured dissociation thresholds using the methods described above. These values should be considered estimates because critical assumptions used to derive the results shown in Figure 4 cannot be independently tested. However, a number of observations described below suggest that these estimates are reliable. As can be seen from Figure 4 the dissociation energies drop between Sill+ and Sil2+,and again at Sil6+.Clusters with 19, 22, and 23 atoms have high dissociation energies relative to their neighbors. For clusters with n > 25 there are no significant variations in the dissociation energies with cluster size, and the dissociation energies just gradually increase with size.
Discussion With increasing cluster size the main product channel switches from loss of Si,, to loss of Si6 to loss of an individual atom. According to the theoretical calculations of Raghavachari and co-workers12the scaled cohesive energies of Si6and Siloare 3.60 and 3.82 eV/atom, respectively. Silois more strongly bound than Si6, so it is not immediately obvious why there should be a switch from loss of Silo to loss of Si6 with increasing cluster size. However, as we describe below this switch can be accounted for simply on the basis of energetics. Figure 5 shows a plot of the dissociation energy associated with the loss of a particular fragment (Silo,Si6, and Si) against the cohesive energy of the cluster. If the cluster is only relatively weakly bound (say a cohesive energy of 4 eV/atom) loss of Silo is the lowest energy dissociation
Jarrold and Honea
9184 The Journal of Physical Chemistry, Vol. 95, No. 23, 199' I -10
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20
30
50
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Figure 6. Plot of the cohesive energies of the silicon cluster ions. The dashed line shows the predictions of a simple model based on the bulk cohesive energy and the bulk surface energy.'* 36
38
40
42
4 4
46
COHESIVE ENERGY, eV
Figure 5. Plot of the dissociation energy associated with the loss of Silo, Si,, and a Si atom against cluster cohesive energy. With increasing cohesive energy the lowest energy dissociation pathway switches from loss of Siloto loss of Si6 to loss of an individual atom.
pathway. With a cohesive energy of 4 eV/atom it requires 40 eV to remove IO atoms from the cluster. The cohesive energy of Siloaccording to the theoretical calculations of Raghavachari and co-workers, is 3.82 eV/atom. So 38.2 eV of the 40 eV is recovered and the overall dissociation energy is 1.8 eV. Similarly the energy required to remove an Si, unit is (6 X 4.0 eV) - (6 X 3.6 eV) = 2.4 eV. So we obtain the expected result that loss of Silois lower energy than loss of Si,. However, as the cohesive energy of the cluster increases it becomes energetically cheaper to lose fewer atoms in the form of a less strongly bound Si, species. For a cohesive energy of 4.4 eV/atom, loss of Silorequires 5.8 eV but loss of Si, requires only 4.8 eV. So loss of Si6is now lower energy than loss of Silo. However, loss of Si, is not the lowest energy dissociation pathway for a cohesive energy of 4.4 eV/atom; the lowest energy dissociation pathway is loss of an atom. From the data shown in Figure 5 it appears that the switch in the products from Siloloss to Si, loss to Si atom loss is expected from simple energetics considerations as the cohesive energy (and cluster size) increases. Note that loss of a Si atom is not expected to become the lowest energy dissociation pathway until the dissociation energy is 4.3 eV, or almost 94% of the bulk cohesive energy. We have not considered the possibility that activation barriers may be associated with these dissociation processes. It is not yet known whether activation energies exist for these reactions. As mentioned above, Raghavachari and Rohlfing" have shown that the products observed in the dissociation of silicon clusters containing up to 17 atoms can be accounted for on the basis of their thermodynamic stability. It appears that a first-order understanding of the observed dissociation processes of the larger clusters can also be obtained from energetic considerations alone. The plot shown in Figure 5 can also provide approximate limits on the dissociation energies of the clusters. The switch from Silo loss to Si, loss is expected when the cluster's dissociation energy is -3.5 eV and the switch from loss of Si, to loss of a Si atom is expected when the dissociation energy is -4.3 eV. These limits are shown on Figure 4 by the arrows, and they are in good agreement with the estimated dissociation energies. The limit obtained for the switch from Siloto Si, loss (3.5 eV) is very sensitive to the cohesive energies of Si, and Si,, so the good agreement with the estimated dissociation energies, in this case, may be fortuitous. There are substantial variations in the dissociation energies as the cluster size increases above n = 1 1. The dissociation energies have relatively drop significantly at Sil2+and Sil6+.Sil9+and Si23+ high dissociation energies. Cluster ions with 15 and 19 atoms (and also those with 22 and 23 atoms) often stand-out amongst the products from the dissociation of larger clusters, suggesting that these may be particularly stable species. However, clusters which have a large dissociation energy need not necessarily be particularly
stable. A good example is provided by Sil2+.The dissociation energy of Sil2+is significantly smaller than that of Sill+.However, Sil2+dissociates into Si6+and Si6,both of which are particularly stable.I2 So the low dissociation energy obtained for Sil2+may reflect the high stability of the products rather than the low stability of Silz+.A measure of the intrinsic stability of the clusters can be obtained by converting the dissociation energies into cohesive energies. Figure 6 shows a plot of the cohesive energies against cluster size. The large variations in the dissociation energies of clusters with 11-25 atoms have now vanished, showing that these variations mainly reflected product stability. Sharp increases in the cohesive energies occur at Si6+and Silo+.The cohesive energies than gradually increase with cluster size. The dashed line in Figure 6 shows the predictions of a simple model for cluster cohesive energies which employs the bulk cohesive energy and bulk surface energy.I8 Previously we have shown that this model accurately predicts the cohesive energies of aluminum clusters containing as few as 7 atoms.I9 The model is clearly much less successful for silicon. This can be attributed to the silicon clusters adopting compact high coordination number structures with considerably lower surface energy than the bulk. For clusters containing up to 30 atoms the products observed in these and previous, collision-induced dissociation experiments are similar to those found in photodissociation ~tudies.l+~ However, for larger clusters a striking difference emerges. Smalley and co-workers have shown that photodissociation of silicon cluster ions containing 30-60 atoms results in complete disintegration of the cluster into product ions containing 6-1 1 atoms.4 In the collision-induced dissociation experiments described here we found that the larger clusters fragment by sequential loss of Si6species until they reach a size of -30 atoms, they then disintegrate to give products with 6-11 atoms. The disintegration after the clusters have reached a size of -30 atoms can be understood quite easily from the dissociation energies shown in Figure 5 . When the cluster size is reduced to -30 atoms the dissociation energies drop significantly. Thus if fragments with -30 atoms contain enough energy to dissociate further, they often contain enough energy to undergo two sequential dissociation processes because the dissociation energy associated with the second step is considerably smaller than for the first. We have reproduced this behavior in simulations of these sequential dissociation processes using the dissociation energies shown in Figure 5 . Some typical results are shown in Figure 7 for Si48+.We assumed that Si4*+ dissociates in the following way: Sid8+ Si42+ Si?,+ Si3o+ Si2o+ Silo+ Si6+. The calculated fragmentation patterns clearly reproduce the main features of the experimental results shown in Figure 2. The difference between the collision-induced dissociation and photodissociation results for these large silicon clusters thus appears to be that the intermediate steps are not observed in the photodissociation experiments. According to the simulations we have
- - -
-
-+
+
(18) Miedema, A. R. Faraday Symp. Chem. Soc. 1980, 14, 136. Miedema, A. R.; Gingerich, K. A. J . Phys. B 1979, 12, 2081. (19) Ray, U.:Jarrold, M. F.: Bower, J. E.; Kraus, J. S. J . Chent. Phys. 1989, 91. 2912.
The Journal of Physical Chemistry, Vol. 95, No. 23, 1991 9185
Dissociation of Large Silicon Clusters Si&
100
I I
I
I
I
I
151 eV ,
I
4
loo 10 100 7
181 eV
1
loo 10
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I
I
100 7
I 0
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20 30 40 ATOMS IN CLUSTER
I 210eV 50
Figure 7. Calculated product distributions for the dissociation of Siut. The calculations were performed using the dissociation energies shown in Figure 5 and assuming that Siut dissociates in the following way: Si4+ Sil2+-.,Si36+ Si3o+ Si,+ Silot Si6+. Note that the Si,+ product is not observed because SiM+undergoes two sequential Silo
-
+
- - -
assumptions used to derive the dissociation energies from the experimental results cannot be independently tested, the dissociation energies should be considered estimates. Substantial variations in the dissociation energies were found for clusters containing up to 25 atoms. However, the variations observed for clusters with 12-25 atoms appear to be mainly due to variations in the stabilities of the products (clusters with 6-1 1 atoms). The dissociation energies of the larger clusters increase smoothly with size and there is no indication that any of these larger clusters are more stable than their neighbors.
Appendix Here we describe a simple impulsive collision model to estimate the fraction of the clusters' injection energy that is converted into internal energy as the clusters enter the drift tube. This model is similar to that recently discussed by Uggerud and Derrick." We assume that the collision occurs between a neon atom and a single silicon atom of the cluster. After the collision the internal energy of the cluster is obtained from the kinetic energy of the silicon atom involved in the collision relative to the rest of the cluster. For a collinear collision geometry, conserving energy and momentum, the internal energy of the cluster, the kinetic energy of the neon atom, and the final kinetic energy of the cluster are given by
losses.
performed it takes -30 eV to remove the first Si6 unit from a 48-atom cluster but only an additional 9 eV is required to reduce this cluster to fragments in the 6-1 I-atom size regime. While only a relatively small amount of additional energy is required to disintegrate these clusters this still does not explain why the intermediate steps are not observed in the photodissociation experiments. The most likely explanation is that after the first couple of photons are absorbed the cross section for absorbing a photon increases significantly. Thus it is difficult to stop the photon absorption sequence at intermediate internal energies and the clusters disintegrate.
where m represents mass,p reduced mass, u velocity, and E energy. The fraction of the cluster's kinetic energy which is converted into internal energy is thus
Conclusions The products observed from the dissociation of silicon cluster ions undergo several changes as the cluster size increases. Medium sized clusters (19-35 atoms) dissociate mainly by loss of a Silo species. si6 loss is the lowest energy dissociation pathway for clusters with n > 35. For clusters with more than 60 atoms loss of an individual atom (as occurs with bulk silicon) begins to become an important dissociation channel. Silois more strongly bound than Si,. However, the switch from loss of Siloto Si, loss can be accounted for simply by energetics, because as the cluster cohesive energy increases it becomes energetically cheaper to lose fewer atoms in a less strongly bound Si, unit. Dissociation energies were obtained from the thresholds for collision-induced dissociation of the clusters. Because critical
where C =
msi - "e msi +
(A51
and the double prime and prime refer to before and after the collision, respectively. If the assumption of a collinear collision geometry is relaxed then the values of Ei: and ESi,'change but the ratio Fieremains constant. (20) Uggerud, E.; Derrick, P. J. J . Phys. Chem. 1991, 95, 1430.
