J. Phys. Chem. 1995, 99, 11-21
11
FEATURE ARTICLE Drift Tube Studies of Atomic Clusters Martin F. Jarrold Department of Chemistry, Northwestem University, 2145 Sheridan Road, Evanston, Illinois 60208 Received: September 30, 1994@
The injected ion drift tube technique permits studies of the chemistry, shapes, fragmentation, and annealing behavior of atomic clusters. Recent injected ion drift tube studies of the physical and chemical properties of silicon, germanium, and aluminum clusters are described. The most significant results to emerge from these studies are the observation of unusual geometries for medium-sized silicon and germanium clusters, the unexpectedly low chemical reactivity of silicon clusters toward a number of different reagents, and the observation of quantum size effects on the shapes of aluminum clusters.
Introduction
from theory can be used to assign the observed features to particular cluster geometries or isomers. While this approach Atomic clusters have been the object of an intense research does not provide detailed spectroscopic information about the effort over the past decade.’ The motivation for these studies geometries, it is currently the only approach that can provide is to understand what happens to the physical and chemical direct structural information for gas phase clusters containing properties of a bulk material as dimensions approach interatomic more than a few atoms. distances and to determine whether there are any special clusters Information about the geometries generated by the cluster with unique and potentially useful properties. Studies of atomic source is, however, only part of the story. A laser vaporization clusters are hindered by two factors: first, except for a few cluster source provides a nonequilibrium environment for cluster specific cases (for example, the fullerenes) it is currently difficult growth and may not generate the lowest-energy isomer.1o Thus, to generate macroscopic quantities of a cluster containing a to determine whether the clusters generated by the source are particular number of atoms; and second, naked clusters are in their lowest-energy geometry, it is necessary to anneal them. generally highly reactive, and specialized techniques must be Annealing can be accomplished by injecting the clusters into used to examine their properties. Studies of atomic clusters in the drift tube at elevated kinetic energies.’* As the clusters enter the gas phase or in an inert matrix probe the intrinsic properties the drift tube, they become excited by collisions with the buffer of the cluster. An alternative approach is to stabilize the cluster gas. After the clusters’ kinetic energy is thermalized, they are surface with ligands. While this approach clearly must change cooled by further collisions with the buffer gas. Thus, the the intrinsic properties of the cluster,* the principal advantage clusters experience a transient heating and cooling cycle as they is that macroscopic quantities can often be prepared and enter the drift tube. This occurs before the clusters penetrate a manipulated in air. significant distance into the drift tube, so the rest of the drift This article describes studies of the properties of gas phase tube can be used to probe the geometries of the annealed atomic clusters performed using injected ion drift tube techclusters. The degree of collisional heating that occurs as the niques. Drift tubes have been employed for many years to clusters enter the drift tube can be varied by adjusting the measure the mobilities of ions and examine their ~ h e m i s t r y , ~ , ~ injection energy, and at high injection energies the clusters can and this approach is ideally suited to examine the chemistry of be heated to the point where they fragment.’* An estimate of gas phase atomic cluster ions.5 The mobility of a cluster ion the activation energies for annealing and dissociation can be (how rapidly it travels through an inert buffer gas under the obtained from measurements performed as a function of influence of a weak electric field) can provide information about injection energy. This does not provide a rigorous measurement its geometry. The mobility depends on the average collision of these quantities because of the difficulty of determining the cross section, and the collision cross section depends on the fraction of the clusters’ injection energy that is converted into geometry. The dependence of mobility on ion structure was internal energy. By combining chemical reactivity studies with first examined using ion mobility spectrometry,6 and it was the mobility measurements, it is possible to determine which demonstrated using this approach that geometric isomers (of, of the isomers present are reactive, and when detailed kinetic for example, polycyclic aromatic hydrocarbons) could be studies are performed, reaction rate constants can be determined resolved on the basis of their different m~bilities.~Several for the individual isomers. Thus, the chemical reactivity of an groups have used mobility measurements to characterize the atomic cluster with a particular number of atoms in a specific size distribution of aerosols and small metal particles.8 More geometry can be examined. Such detailed infomation is recently, mobility measurements for carbon cluster ions showed unavailable from studies of the properties of neutral atomic that structural isomers of atomic clusters could also be separated clusters. by their different m~bilities.~ Comparison of measured mobilities with mobilities calculated for model geometries or structures In this article I will describe injected ion drift tube studies of clusters of the group 4 elements silicon and germanium, along with analogous studies of aluminum clusters. Bulk silicon and Abstract published in Advance ACS Abstracts, December 1, 1994. @
0022-365419512099-0011$09.0010
1995 American Chemical Society
Jarrold
12 J. Phys. Chem., Vol. 99, No. 1, 1995
Figure 1. Schematic diagram of the experimental apparatus.
germanium are semiconductors, while bulk aluminum is an almost ideal free electron metal. The methods outlined here have also been used to examine carbon clusters9J3 and metalcontaining carbon cluster^.'^ But this work will not be considered further here because carbon clusters are so different from typical atomic clusters.
synchronized with the vaporization laser. The drift time distribution (the distribution of times that it takes for clusters to travel across the drift tube) is determined from the arrival time distribution by subtracting off the flight time through the rest of the apparatus to the detector. (This is measured by removing the buffer gas from the drift tube.)
Experimental Aspects
General Considerations
A schematic diagram of the injected ion drift tube apparatus is shown in Figure 1. The clusters are generated by pulsed laser vaporization15 of a rotated and translated rod in a continuous flow of helium buffer gas. The source is similar to that employed by Riley and co-workers.16 A continuous flow of buffer gas is used (instead of a pulsed flow) so that high repetition rate pulsed lasers can be used to maximize the duty factor of the experiment. An excimer laser (operating at 308 nm and up to 200 Hz) is employed. The source can be cooled to enhance the clustering processes. Cooling the source also reduces contamination, simplifying the mass spectrum of the clusters generated by the source. Before the clusters exit the source, a high-energy electron beam may be injected into the buffer gas flow to enhance the relative abundance of charged clusters. Ionization does not occur by direct electron impact but results from charge transfer from He+ or Penning ionization by He*. Results presented below indicate that the cluster ions that leave the source are at a temperature which is close to that of the source block. There is no evidence for the formation of highly excited clusters which have been suggested to result from some sources using pulsed buffer gas f l 0 ~ s . l ~ After exiting the source, the cluster ions are focused into a quadrupole mass spectrometer. The mass spectrum of the ions leaving the source shows a broad distribution of cluster sizes, and the quadrupole mass spectrometer is used to select a cluster with a particular number of atoms. The size-selected clusters are then focused into a low-energy ion beam by a simple threeelement zoom lens and injected into the drift tube. The injection energy can be varied over a wide range (5-400 eV). The drift tube contains an inert buffer gas (usually He), and across the drift tube there is a weak electric field. After traveling across the drift tube some of the ions exit through a small aperture and are focused into a second quadrupole mass spectrometer. This mass spectrometer is used for chemical reactivity and fragmentation studies where the mass of the ions leaving the drift tube is expected to be different from the injected clusters. At the end of the second quadrupole mass spectrometer the ions are detected by an off-axis collision dynode and dual microchannel plates. Mobilities are measured by injecting a short pulse of sizeselected clusters into the drift tube and recording the arrival time distribution at the detector with a multichannel analyzer. The pulse of clusters is generated by an electrostatic shutter
Ions move across the drift tube at a drift velocity given by
vD = KE
(1)
where K is the mobility of the ion and E is the electric field. If only a single isomer is present, then under low field conditions (where the drift velocity is less than the average thermal velocity) the flux of ions leaving the drift tube as a function of time is given (for nonreacting ions) by3
')
-(L - VDt) exp(
4Dt
(2)
where ro is the radius of the entrance aperture, L is the length of the drift tube, P(tp) dtp is the distribution function of the pulse of ions entering the drift tube, C is a constant, and D is the diffusion constant which under low field conditions is given by KkBT/e. The expression for the drift time distribution given above contains no adjustable parameters, and drift time distributions calculated using this expression are generally in excellent agreement with the measured distributions. Thus, comparison of measured and calculated distributions can be used to ascertain whether a given peak in the drift time distribution consists of two or more components with similar mobilities. The ability to separate isomers with similar mobilities is limited by diffusion of the ion packet as it travels through the drift tube. The resolving power is given approximately by6
(3) Thus, to maximize the separation of isomers with similar mobilities, the drift tube should be long and operated with a large electric field. However, when the field is increased, the buffer gas pressure must be increased to keep the drift velocity in the low field limit. Thus, the maximum electric field that can be employed is limited by the maximum buffer gas pressure that can be used. The time resolution currently available is relatively low, which makes it difficult to separate isomers with similar geometries.
Feature Article
J. Phys. Chem., Vol. 99, No. I, 1995 13
Collisional heating of ions as they enter the drift tube is used to examine the annealing and fragmentation of atomic clusters. Around lo2- lo3 collisions with the buffer gas are required to thermalize the kinetic energy of the injected cluster ions, and because of the averaging inherent in this multicollision excitation process, a relatively narrow distribution of intemal energies is deposited into the injected clusters.12 It is not possible to rigorously determine the degree of collisional excitation that occurs as the ions enter the drift tube. However, an estimate can be obtained from a modified impulsive collision model.lZ According to this model, the fraction of the cluster's injection energy that is converted into intemal energy is given by
Fie= C
( n - 1)(1 - c) 2n
(4)
where n is the number of atoms in the cluster.
(5)
mc is the mass of an atom in the cluster, and mB is the mass of the buffer gas. Equation 4 is essentially the value of Fie predicted by an impulsive collision model, and C is an empirical correction factor which is determined by comparison of the measured injection energy threshold for dissociation with known dissociation energies. A value of around 0.4 appears to be valid for a wide range of different clusters and collision gases. However, activation energies for annealing (isomerization) or fragmentation determined from this type of analysis should clearly be treated as estimates. This method provides a quick and relatively easy way of getting an idea of the size of the activation energy; it does not provide a rigorous measurement. In addition to estimating the degree of collisional excitation that occurs in these experiments, it is also necessary to take into account the statistical name of the annealing or fragmentation process. This is done using the simple RRK (RiceRamsperger-Kassel) or more rigorous RRKM (Rice-Ramsperger-Kassel-Marcus) method.ls In general, there is insufficient information available about the fragmentation or annealing process to be able to perform accurate RRKM calculations, and many of the parameters required for these calculations must be estimated. Fortunately, dissociation rates are strongly dependent on the activation energy, and so the errors that can be introduced by the incomplete knowledge about the annealing or dissociation processes are not large. More reliable information about the size of the activation barriers can be obtained from studies performed as a function of the drift tube temperature, where the annealing or fragmentation processes are thermally activated.19 Unfortunately, this approach is limited to processes with relatively low activation energies and has not been used extensively for this reason. Annealing, in principle, converts the cluster to a lower-energy geometry. Higher-energy isomers may result from the specific growth processes that occur in the source, and when the clusters are annealed, the relative abundance of the higher-energy isomer should decrease. In some cases two isomers remain after the clusters are annealed, which generally indicates that these isomers have similar stabilities. In the collisional annealing experiments the clusters are rapidly heated to high temperatures where an equilibrium, X Y, between the different isomers is established." The equilibrium constant (for this microcanonical ensemble) is
where kx-y is the rate of isomerization of isomer X to isomer Y and ky-x is the rate of the reverse reaction. Using the RRKM theory,'* expressions for kx-y and ky-x yield
(7)
+
+
where Qx(E Ex) and eY(E EY) are the densities of states for isomers X and Y, EX and Ey are the activation energies for isomerization from isomers X and Y, respectively, and E is the energy above the activation barrier. Thus, the isomer distribution for the hot clusters is given by the ratio of the density of states. As the clusters cool, the equilibrium between the different structural isomers will be maintained as long as the isomerization rates kx-y and ky-x are larger than the cooling rate. As the cluster cools, the isomerization rates decrease, and when the isomerization rate drops below the cooling rate, the isomer populations are frozen. If the higher-energy isomer has significantly lower frequency vibrations, then the lowest-energy isomer will not have the largest density of states at high energies. Thus, if the isomer populations are frozen at relatively high energies, it is possible that the isomer that dominates after annealing is not the lowest-energy isomer. Studies of the chemical reactivity of the clusters are performed by adding a small partial pressure of gaseous reagent to the buffer gas. Cluster ions react as they travel across the drift tube. An estimate of the effective temperature increase due to the drift field can be obtained fromzo
6Te, = (mB/2kB)vD 2 From this expression the effective temperature increase typically amounts to less than 1 K with the conditions employed. Chemical reactions occurring in the drift tube follow pseudofirst-order kinetics given by
(9) where IO and Z are the initial and final reactant ion abundances, [A] is the number density of the neutral reagent, and f D is the reaction time (or drift time). The reaction kinetics can be followed by varying the drift field (to change the reaction time) or by varying the reagent pressure. Note that the rate constant, kz, determined in this way is a second-order rate constant. Many of the reactions of atomic clusters are association reactions :
M,'
+ A - M,Ai
These reactions probably occur in two steps: formation of an excited M,A+* complex (which is reversable) and removal of the excess energy from the excited complex
+ A =M,A+* M,A+* + B - M,A+ + B M,+
(1 1)
(12)
The effective overall second-order rate constant for these reactions is given by
where kd is the rate of dissociation of the M,,A+* complex, kf
Jarrold
14 J. Phys. Chem., Vol. 99, No. 1, 1995
TIME, p
zi
0.90
This procedure removes the changes in the mobility that are due to the change in the physical size of the cluster. There are clearly two families of isomers present in Figure 2. Starting at Silo+ the mobilities decrease sharply with increasing cluster size. At Si%+ a second isomer emerges with a larger mobility. As the cluster size increases, the relative abundance of the isomer with the smaller mobility (the slower moving isomer) decreases and the relative abundance of the other isomer increases. For clusters with more than -35 atoms only the faster moving isomer remains. Clearly, a structural transition occurs for silicon clusters with 24-35 atoms. Information about the shapes of atomic clusters can be deduced from the measured mobilities by comparing them to mobilities calculated for model geometries using a simple hard-sphere approximation.22 With the hardsphere approximation the reduced mobility is given by3
TIME, jcj
-
!
w 0.80-
f
K
PROLATE GROWTH
0.70 -
t
0.801 0
1
I
0
2
I
0
3
I
0
4
1
0
5
I
0
8
I
0
7
where m is the mass of the cluster and QHSis the average hardsphere collision cross section. Since the cluster is not, in general, spherical, QHSmust be determined by calculating the collision cross section for a particular orientation q(O,q5) and then averaging over all possible orientations
1 0
ATOMS IN CLUSTER
Figure 2. Mobilities of silicon cluster ions. The upper half of the figure shows drift time distributions recorded for Size+ and Siz+. The lower half shows the relative mobilities of Si,+ ( n = 10-60) plotted against cluster size.
is the rate of formation of the M,A+* complex, and ks is the rate of stabilization. If ks[B] > k d the reaction follows secondorder kinetics, but if ks[B] < k d the reaction follows third-order kinetics and the measured reaction rate depends on the buffer gas pressure. The reaction kinetics can be followed as a function of temperature by changing the temperature of the drift tube. A temperature range of 77-700 K can be achieved, and the high buffer gas pressure ensures that the reacting clusters are in thermal equilibrium. Studies performed as a function of temperature can provide useful information about the reaction mechanism. When the adduct formed in an association reaction is only weakly bound (< 1 eV), an equilibrium can be established as thermal desorption competes with the association reaction,
M,’
+A
M,A
+
(14)
The criterion for the establishment of equilibrium is that the ratio MnAm+lMnAm+l+ should be independent of the reaction time but proportional to [A]. If equilibrium constants are measured as a function of temperature, thermodynamic quantities such as A W and ASo can be obtained from a van’t Hoff plot of In Keq against 1/T.
Sicon Clusters Drift time distributions recorded for and Siz+ are shown in the upper half of Figure 2. For Si20+ there is a single component present in the drift time distribution, indicating that all Si*O+ clusters have similar shapes. For Si=+ there are two components resulting from two different isomers with significantly different shapes. The lower half of Figure 2 shows a plot of the relative mobilities of silicon clusters ions with 1060 atoms. The relative mobilities are obtained by dividing the measured mobilities by the mobility of a sphere with bulk density21 containing the same number of atoms as the cluster.
where 8 is the angle between a cluster fixed axis and an axis fixed in space and q5 is the angle of rotation about the cluster fixed axis. For simple model geometries the averaging can be performed analytically, but in general numerical integration is required. The dashed lines in the lower half of Figure 2 show the predictions of what are probably the two simplest models for cluster growth: one-dimensional (prolate) and twodimensional (oblate) growth. For the prolate model we start with a roughly cylindrical cluster (with the length of the cylinder, 1, equal to its diameter, d) and assume that the cluster grows by addition of atoms along the axis (d remains fixed, 1 increases). Thus, the cluster grows to look like a sausage. In the second idealized growth model we assume that atoms add to the outside of the cylinder so that I is fixed and d increases, and the cluster grows to look like a pancake. The predicted change in the mobility for the one-dimensional (prolate) growth model clearly fits the change in the measured mobilities for the smaller silicon clusters, suggesting that small silicon clusters follow a onedimensional growth sequence and adopt “sausage”-shaped geometries. The geometry change that occurs for clusters with 24-35 atoms appears to result from a reconstruction to a more spherical geometry. Figure 3 shows the results of annealing experiments for Si,+. At low injection energies both isomers are observed (“sausage” and “sphere”), but at high injection energies the slow moving isomer (“sausage”) disappears. No fragmentation is observed at the relatively low injection energies where the first isomer disappears: so clearly the “sausage” converts into the faster moving “sphere”. When the clusters are annealed, the “sausage” form vanishes for all clusters with more than 30 atoms, and the structural transition (“sausage” to “sphere”) appears to occur for clusters with around 27 atoms. The nature of the two types of isomers and the origin of the structural transformation has been addressed in several theoretical s t ~ d i e s . ~For ~ - ~small ~ silicon clusters, the large number of dangling bonds that exist for bulk fragment geometries is known to drive a reconstruction to more compact and more
Feature Article
J. Phys. Chem., Vol. 99, No. 1, 1995 15 1.21
I
INJECTION ENERGY. eV
n
II \
1000
1500
S‘,+
ANNEALED
2000
2500
3000
TIME, ps
Figure 3. Annealing of Si32+. At low injection energies (upper plot) both the “sausage” and “sphere” form of Si32+ are observed. As the injection energy is raised, the “sausage” disappears as it anneals into the “sphere” (lower plot).
highly coordinated structure^.^^*^' Why clusters with 10-27 atoms adopt prolate geometries is not completely understood, but it appears to be related to the difficulty in accommodating internal atoms in these smaller clusters (the internal atoms tend to be over~oordinated).~~ For larger clusters, calculations using the Car and Parrinello method28find geometries which consist of two shells of atoms, with the outer shell buckled so that the inner atoms are not over~oordinated.~~ The abrupt change in the structure at -27 atoms (inferred from the mobility measurements) is presumably due to the transition between these two very different types of geometry. Unlike metal clusters that almost always fragment by evaporating individual silicon clusters fragment by loss of stable units such as Si6 and Si10.30,31Si6+ and Silo+ occur as “magic number” (particularly abundant) clusters in the mass spectra of clusters generated by pulsed laser vaporization. Studies of the fragmentation of silicon clusters induced by multicollision excitation at the drift tube entrance show that loss of Silo is the dominant fragmentation pathway for clusters with 19-35 atoms.12 For clusters with more than 35 atoms loss of Si6 dominates. When heated, bulk silicon evaporates individual atoms. So for large clusters loss of individual atoms should become the lowest-energy fragmentation pathway. The cluster size where this transformation occurs has not yet been determined, but there are indications that it begins to occur for clusters with just over 70 atoms. The change in the fragmentation processes from loss of Silo Si6 Si can be understood in terms of thermodynamic arguments. Si6 and Silo are strongly bound with dissociation energies which are close to the bulk cohesive energy. The cohesive energy is the total binding energy divided by the number of atoms; it increases with increasing cluster size to approach the bulk value. The cohesive energy of Silo is larger than that for Si6, and it is energetically favorable for small clusters to fragment by loss of Silo rather than by loss of Si6 or Si.32 As the cluster size increases and the cluster’s cohesive energy increases, it becomes energetically cheaper to loose Si6 (even though Si6 is less strongly bound than Silo) because fewer strongly bound atoms need to be removed from the cluster. As the cluster’s cohesive energy
- -
t-
w w n 0 10 20 30 40 50 60
.% 0
Cluster Size Figure 4. Dissociation of silicon clusters. The upper plot shows the injection energy threshold measured for the dissociation of S48+. The points are the experimental data, and the line is a simulation to estimate
the dissociation energy. The lower plot shows the dissociation energies estimated from the injection energy thresholds for clusters with up to 50 atoms. continues to increase, it ultimately becomes energetically cheaper to loose an individual atom. The upper half of Figure 4 shows the injection energy threshold measured for the fragmentation of SL+g+. The threshold is relatively sharp, which indicates that a relatively narrow distribution of internal energies is generated in the multicollision excitation process. The points are the experimental data, and the line is a simulation to determine the dissociation energy using the approach described above. As noted above, the dissociation energy obtained from this simulation should be regarded as an estimate because of the difficulty in determining the fraction of the clusters injection energy that is converted into internal energy. Dissociation energies obtained from studies with He, Ne, and Ar buffer gases are nearly identical. The dissociation energies are plotted in the lower half of Figure 4. There are significant size-dependent variations in the dissociation energies of the smaller clusters. A substantial decrease in the dissociation energies occurs for clusters with 12 atoms, and for clusters with more than around 26 atoms the dissociation energies start to systematically increase. This systematic increase appears to begin in the cluster size regime where the structural transition occurs in the mobility measurements. Note that for the larger clusters there are no significant size-dependent variations in the dissociation energies, indicating that none of the larger clusters show enhanced stability. The chemistry of silicon clusters has been examined by several groups. Early work was limited to small c l ~ s t e r s , ~ ~ ~ ~ ~ while more recent work has focused on the larger ones. For reasons that are not entirely clear, the reactions of Si,+ with C2& are particularly sensitive to the detailed geometry of the cluster (this result suggests that the reaction with C2& occurs at a special type of site on the cluster’s surface).35 The only product observed results from adsorption of one or more C2H4 molecules onto the cluster. The upper half of Figure 5 shows kinetic data for Si29+ which indicates the presence of two isomers which react at significantly different rates. The lower half of Figure 5 shows drift time distributions measured for Si29+ in pure helium and in helium with a trace of CZ& (to react away the more reactive isomer). These results show that the
Jarrold
16 J. Phys. Chem., Vol. 99, No. I, 1995
’r
Si29+
+ C2H4
-*
PRODUCTS Si’,
-1O
2
:-2
+ 02
-
PRODUCTS
296K
1’
k
+
\
10-‘50 10
20
30
40
50
60
70 I
lo-”
10-15
Si(lll)- (7x7) 353K
F-0
10 20 30 40 50 60 NUMBER OF ATOMS IN CLUSTER
4
40-2
E
70
Figure 6. Bimolecular rate constants measured for the reaction of silicon cluster ions with 0 2 and DzO. The scale on the right shows a WITH C2H4
A X ’ O ~
1400
1800
2200 TIME, ps
2600
3000
Figure 5. Chemical reactivity of Si2sf isomers with C2H4. The upper half of the figure shows kinetic data which indicate the presence of two isomers which react at significantly different rates. The lower half
shows drift time distributions measured in (a) pure helium (showing the “sausage” and “sphere”) and (b) helium with a trace of C& (to react away the more reactive isomer). These results show that the “sausage” is the unreactive isomer. “sausage” isomer is the unreactive isomer. When Si29+ is annealed, the relative abundance of the “sausage” isomer decreases, suggesting that it is less stable than the “sphere”. But the results in Figure 5 show that the “sausage” isomer is less reactive than the “sphere”. Apparently, the more stable isomer is the more reactive. Similar results are observed for some of the other clusters.” Clearly, there is not a strong correlation between chemical reactivity and thermodynamic stability for these clusters. This is reasonable because thennodynamic stability is a property of the whole cluster, while chemical reactivity presumably occurs at a specific site on the cluster. The good correlation between the Si29+ isomers found in the mobility measurements and those inferred from reactivity studies with C2H4 is not observed for all clusters. For example, for Si26+, the “sausage” form is again unreactive, but only around 50% of the “sphere” reacts rapidly with C2H4. So for Si26+ there must be at least three different isomers: an unreactive “sausage” and reactive and unreactive “spheres”. Kinetic data for the C2H4 reactions of the larger clusters (n > 35) indicate that isomers (which react at significantly different rates) are present for the larger clusters as well, even after annealing.”
sticking probability scale, and the dashed lines represent the sticking probability on Si(lll)-(7x7). The drift time distributions for these larger clusters only show a single component. But the width of this component is broader than predicted by eq 2, which suggests that there are a number of isomers present with similar mobilities. Recent theoretical studies for the larger silicon clusters also suggest that many, almost energetically degenerate, isomers exist.25 Clearly, the presence of these isomers makes it difficult to characterize the properties of these clusters. The other reagents that have been examined in detail ( O Z , ~ ~ H20,37and NH338*39) do not show the strong sensitivity to cluster structure that was observed for C2H4. With 0 2 the nature of the product observed depends on the cluster size. For n 30 the dominant reaction is34
Si,+
+ 0, - Si,_,+ + 2 ~ i 0
while for larger clusters the
Si,+
0 2
+ 0,
adsorbs: .-+
Si,O,S
This behavior can be easily understood: oxidation of the silicon clusters is highly exothermic, and the smaller clusters with fewer degrees of freedom are heated to a higher temperature and evaporate S i 0 molecules before they can be cooled by collisions with the buffer gas in the drift tube. The basic chemistry observed here is identical to that observed on bulk silicon surfaces. 0 2 dissociatively chemisorbs on clean silicon surfaces, and when the oxidized surface is heated S i 0 desorbs.4o Rate constants measured for the reaction of Si,” with 0 2 are shown plotted against cluster size in Figure 6 . Substantial sizedependent variations in the reaction rates are observed for the smaller clusters, but the larger clusters (n > 30) a l l react at similar rates. Unlike the reactions with 02, water (D2O) chemisorbs on all but the smallest clusters (n = 1-3)34 to form a series of Si,(D20),+ product^:^'
Feature Article Si,(D20),+
-
+ D20
J. Phys. Chem., Vol. 99, No. 1, 1995 17 Sin(D20)m+l +
(19)
Water dissociatively chemisorbs on bulk silicon surfaces to yield H and OH bound to the surface.41 Indirect evidence37suggests that a similar dissociative chemisorption process occurs on the larger silicon clusters. As can be seen from Figure 6, rate constants for the reactions of the silicon clusters with water show the same general trends as those found for the reactions with 0 2 : substantial size-dependent variations in the reactivity of the smaller clusters which diminish with increasing cluster size. As can be seen from Figure 6, some of the smaller clusters are less reactive than their neighbors with both reagents. Si13+ is the least reactive cluster with 0 2 , D20, and C2&. This result has been interpreted as indicating that Sil3+ is i c o ~ a h e d r a l . ~ ~ However, according to Rothlisberger et ~ 1 . : ~the icosahedron is a relatively high-energy geometry for (neutral) Si13. Several low-energy isomers were found for Si13 with geometries based on capped trigonal prisms and antiprisms. However, there appears to be nothing particularly special about these geometries that might provide an explanation for the low reactivity for Si13+. Besides its low reactivity, Sil3+ does not appear to be unique in any other regard. The dissociation energy of Sil3+ is not particularly large. Studies of the buffer gas pressure dependence of the silicon cluster ion reactions show that the measured rate constants are independent of the buffer gas pressure, suggesting that these reactions are in the second-order limit. So the measured rate constants reflect the sticking probability of the reagent on the cluster surface. Sticking probabilities can be deduced by dividing the measured rate constant by the collision rate, and sticking probability scales are shown on the right of Figure 6. These sticking probabilities can be compared with the sticking probabilities for bulk silicon surfaces. Sticking probabilities are shown in Figure 6 for Si( 111)-(7 x7), which is the lowestenergy surface of bulk silicon. Clearly, the cluster sticking probabilities are substantially lower than for the bulk surface. Recent studies of silicon surface chemistry have indicated that dangling bonds play a critical role in promoting surface reactions. So a reasonable interpretation of the low reactivity of the silicon clusters is that they have a lower density of dangling bonds than bulk silicon surfaces. In other words, the clusters have done a better job of reconstructing than the bulk surface. This is not unreasonable. Most of the atoms in these silicon clusters are surface atoms, and the cluster is free to optimize its surface, possibly even at the expense of slightly higher energy internal atoms. On the other hand for bulk silicon, most of the atoms are bulk atoms, and the surface must fit over the template provided by the lowest-energy bulk configuration. It is worth noting that there is not a substantial change in the reactivity of the clusters at the structural transition that occurs around 27 atoms. As noted above, the dissociation energies appear to start systematically increasing at the structural transition. And recent measurements have shown that the ionization energies& and polarizabilitie~~~ of Si, also change abruptly at n = 20-30. So it is surprising that the structural transition does not have a larger impact on the chemistry. Unlike the reactions with 02 and H20 where dissociative chemisorption appears to occur, with NH3 molecular adsorption dominates, at least close to room t e m ~ e r a t u r e . This ~ ~ is in striking contrast to bulk silicon surfaces where dissociative chemisorption occurs with a sticking probability close to 1.O at room temperature.& The evidence that indicates molecular adsorption occurs on the clusters is as follows. At room temperature, in the high-pressure environment of the drift tube, all the clusters react with NH3 at the collision rate to yield a
'O-gl
(0-44
t
Y 110-5
40-~;b io
loloioo';
10-6
NUMBER OF ATOMS IN CLUSTER
Figure 7. Bimolecular rate constants for the reactions of silicon cluster ions with MI3at 700 K. The dashed line shows the sticking probability of NHs on Si(111)-(7x7) at 700 K.
range of Sin(NIWmfproducts. However, at temperatures above 370 K an equilibrium Si,(NH3),+
+ NH3
Si,(NH3),+1+
(20)
can be established: the Si,(NH3),+1+/Sin(NH3),+ ratio is independent of time but proportional to NH3 pressure. A W and ASo were deduced from equilibrium constants measured as a function of temperature. A W for binding the first NH3 molecule is around 1.0 eV for all clusters. This can be compared to the value of 3.0 eV expected for dissociative chemisorption. Thus, these results indicate that molecular adsorption occurs at room temperature and slightly above. As the temperature is raised further, the product resulting from molecular adsorption diminishes rapidly as the equilibrium in eq 20 is pushed to the left (and any NH3 that does molecularly adsorb rapidly desorbs). Under these conditions a second process is observed: a slow bimolecular reaction yielding NH3 strongly bound to the cluster surface. This process is presumably dissociative chemisorption. The measured rate constants for this process at 700 K are shown plotted in Figure 7. Note that the rate constants are exceedingly small; the sticking probabilities are in the range. This is much smaller than the value of 0.1 for the initial sticking probability of NH3 on Si(ll1)-(7 x7) at 700 K.46 The results described above differ significantly from those obtained by Smalley and co-workers using the FT-ICR (Fourier transform ion cyclotron resonance) technique. They have reported that all of the larger clusters react slowly with NH3 (sticking probability around and that several clusters, for example Si39+ and Si45+, are several orders of magnitude less reactive than their neighbors. Note that Si45+ is somewhat less reactive than its neighbors in Figure 7, but we have not been able to reproduce the large variations in reactivity reported by Smalley and co-workers. The lower reaction rates observed in the FT-ICR experiment probably result from the low pressures employed in these experiments. At these low pressures the reactions of all the clusters may not follow true second-order kinetics.
Germanium Clusters Germanium is directly below silicon in the periodic table, and the properties of bulk germanium are very similar to those of bulk silicon. The clusters, however, show significant
Jarrold
18 J. Phys. Chem., Vol. 99, No. 1, 1995
>
-
i
5,
I
I
I
.E f 0
n 0
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i
30 40 50 60 Cluster Size Figure 8. Dissociation energies of germanium cluster ions estimated 0 from the injection energy thresholds. The solid points show the results Cluster Size of previous measurements for Gen4* Figure 9. Relative mobilities of germanium clusters. The open points differences. As noted above, medium-sized silicon clusters (n are the mobilities of Ge,+, and the filled points are for Gen2+.The A = 19-35) dissociate by loss of a 10-atom fragment. Mediumshows the mobility of the new isomer that emerges for Gea+ when the clusters are annealed. sized germanium clusters fragment in the same way. However, with silicon the fragmentation pattern changes with increasing the relative mobilities remain approximately constant. A scale cluster size from loss of Silo Si6 Si. No such change is on observed for germanium clusters: they continue to loose G e ~ o . ~ ~ the right in Figure 9 shows aspect ratios determined assuming that the clusters adopt prolate geometries. The aspect ratio for As described above, the changes in the silicon cluster fragmenclusters with 50-60 atoms is around four (assuming a prolate tation pattern can be ascribed to the increase in the cohesive geometry). Clearly, an important issue here is whether the energy (the total binding energy divided by the number of clusters are in their lowest-energy geometry. For the silicon atoms) associated with the increase in cluster size. So the clusters the prolate growth sequence persisted to larger cluster absence of such a change for germanium clusters is an indication sizes for unannealed clusters. However, annealing the germathat the cohesive energies are not increasing at the same rate. nium clusters causes a significant change in the drift time Figure 8 shows dissociation energies estimated from the distribution for only one cluster: Gea+. When Ge40+ is injection energy thresholds for germanium cluster fragmentaannealed, a second component emerges in the drift time t i ~ n (The . ~ ~filled points show the results of previous measuredistribution with a relative mobility which puts it close to the ments of the dissociation energies of small Ge,.48) The line for prolate growth (A in Figure 9). But it appears that all dissociation energies of the smaller germanium clusters (n the other clusters are already in their lowest-energy geometries. 25) closely follow the silicon cluster dissociation energies. Even As can be seen from Figure 9, germanium clusters with more the small variations in the dissociation energies, such as the than around 45 atoms appear to retain approximately the same small local maxima at 19 and 23 atoms, are reproduced. The aspect ratio until 64 atoms where a second isomer with a more dissociation energies for germanium clusters, in this size regime, compact geometry suddenly emerges. The two isomers coexist are somewhat smaller than for the corresponding silicon clusters, up to 78 atoms; for clusters with more than 78 atoms only the but this difference may simply reflect the differences in the bulk more compact isomer remains. cohesive energies (3.85 eV for germanium vs 4.68 eV for The large dissociation energies of the small germanium silicon). For clusters with more than 25 atoms, however, a clusters (n 12) suggest that, like small silicon clusters, the major difference begins to emerge. Twenty-five atoms is small germanium clusters reconstruct to more highly coordinated around the size regime where silicon clusters undergo a geometries. The small dissociation energies for clusters with structural transformation, and at this point the silicon cluster n > 11 suggest that these clusters might be considered as a dissociation energies start to increase smoothly. No such loose assembly of small strongly bound fragments (such as Ge7 increase is observed for the germanium clusters; the dissociation and Gelo). This behavior will arise if the reconstruction of the energies of the larger germanium clusters remain at 1.0-1.5 small germanium clusters has been very successful so that eV up to at least 56 atoms. (Germanium is substantially heavier conversion of a loosely bound GeloGelO+ cluster, for example, than silicon, and the mass range of the quadrupole mass to a compact Gezo+ geometry is energetically unfavorable. The spectrometers limits the largest singly charged germanium extended prolate growth sequence observed for the larger cluster that can be studied to Ge56+.) These results clearly germanium clusters can be understood in terms of geometries suggest that the germanium clusters do not undergo the structural consisting of a stack of these small strongly bound fragments. transition observed for medium-sized silicon clusters. (The special behavior of Gem+ could then be explained in terms Relative mobilities for germanium clusters are shown in of a stack of four Gel0 units.) The cohesive energy of a loose Figure 9. The open points show the mobilities for Gen+clusters, assembly of small stable fragments only increases slowly with and the filled points are for Gen2+. (These were measured to increasing cluster size. (The cohesive energy of these geomextend the cluster size range to n > 56.) For clusters with up etries is essentially the cohesive energy of the small stable to 35 atoms the mobilities decrease sharply with increasing fragments.) On the other hand, the cohesive energy of a cluster size and closely follow the predictions of the onespherical cluster with bulklike bonding is expected to follow dimensional growth model (solid line in Figure 9). So the smaller germanium clusters appear to follow the same growth pattern as the smaller silicon clusters. However, there is no evidence for the structural transition that occurs for silicon clusters with around 27 atoms. Instead, the mobilities of Gen+ where Ecoh(-) is the bulk cohesive energy, V, is the bulk atomic continue to decrease. For Gen+ with n > 35 the relative volume, and y is the bulk surface energy. According to this mobilities begin to depart from the predictions of the oneexpression, the cohesive energy of a cluster with bulklike dimensional growth model, and for clusters with n > 45 atoms bonding increases as n-lm. Thus, with increasing cluster size 10
20
- -
Feature Article the cohesive energy of the loose assembly will drop below that of a bulklike cluster, and when this occurs, the loose assembly should reconstruct to the bulklike geometry. Using the simple models described above, this transition is predicted to occur at -65 atoms. Thus, the structural transition observed at -70 atoms in the mobilities could result from a fundamental change in the chemical bonding in the cluster. Geometries based on a stack of small stable fragments have been proposed for medium-sized silicon The silicon cluster dissociation energies (Figure 4) show a minimum in the 12-25-atom size range; however, the dissociation energies remain relatively large and provide less support for a geometry based on a loose assembly of small stable fragments. On the other hand, the mobilities and the dissociation energies of small silicon and germanium clusters show similar trends, suggesting that they adopt similar geometries. If the geometries of these smaller clusters are similar, why should silicon clusters reconstruct at -27 atoms while germanium requires -70 atoms? The answer to this question is not clear at this time.
J. Phys. Chem., Vol. 99, No. I, 1995 19
0.75 6
1
0
20
40
60 80 100 120 NUMBER OF ATOMS
140
160
Figure 10. Relative mobilities of AI,' (n = 5-73) (dashed line) and (n = 20-142) (solid line). The arrows show the locations of
Aluminum Clusters
the electronic shell closings. The numbers associated with the arrows give the number of valence electrons required to completely fill the shell.
While bulk silicon and germanium are semiconductors, bulk aluminum is a free electron metal. The bonding in metals is less directional than the covalent bonding in the semiconductors, so metal clusters are expected to adopt roughly spherical shapes. As we will see below, this simple picture is essentially true, but the shapes of small aluminum clusters are modulated by quantum size effects. The electronic shell model accounts for many of the physical properties of clusters of free electron metals such as sodium and al~minum.4~ In the electronic shell model the valence electrons are assumed to move in a uniformly positively charged background, and the electronic energy levels are quantized by angular momentum restrictions (in much the same way that atomic energy levels are quantized). Particularly stable clusters result when a shell or subshell is filled, and there is a significant energy gap to the next available level. The locations of the shell closings is somewhat dependent on the nature of the potential employed. For a square well potential the f i s t few shell closings occur at 2, 8, 18, (20), 34, (40), 58, 92, 138, and 198 electrons. (The minor shell closings with smaller gaps are shown in parentheses.) The electronic shell model is based on the nuclear shell model developed in the late 1940s. One of the refinements of the nuclear shell model was to allow distorsion from spherical symmetry. Within the framework of the electronic shell model, if a cluster is allowed to undergo an ellipsoidal distorsion, degeneracies are lifted and some of the electronic energy levels rise and some fall. For clusters with a closed shell the total electronic energy increases; thus, filled shell clusters retain spherical symmetry. However, for a partially filled shell it is often possible to lower the total electronic energy by distorting. So clusters at the shell closings should be spherical while those between the shell closings should distort. Figure 10 shows relative mobilities measured for Ala+ (n = 5-73) and Aln2+ (n = 20-142).19350 The mobilities of the singly- and doubly-charged clusters are almost identical, which suggests that the charge does not significantly perturb the shape of the clusters. There are a series of local maxima in the relative mobilities which indicate that the clusters adopt more spherical geometries. The m o w s in the figure show the location of the electronic shell closings from the spherical jellium model calculations of Persson et aLS1 Though the agreement between the maxima in the relative mobilities and the predicted shell closings is not perfect, it is quite compelling and demonstrates how the number of valence electrons modulates the shape of
these metal clusters. Close inspection of the relative mobilities for the singly- and doubly-charged clusters shows that local maxima for the doubly-charged clusters appear in general to be shifted to slightly larger cluster sizes; thus, it is the number of valence electrons and not the number of atoms which controls the shape of these clusters. The oscillations in the mobilities appear to diminish with increasing cluster size. This behavior can also be understood within the framework of the electronic shell model. The total electronic energy of filled shells increases when the clusters are distorted; it is only the highest partially filled shell that is able to lower its energy. So larger clusters with several lower-lying filled shells are essentially stiffer and more resistant to distorsion. Structural isomers were observed in the drift time distributions for several of the aluminum clusters. The structural isomers found for n = 45 and 46 are particularly interesting because these isomers appear to be associated with the shell closing with 138 electrons. The upper half of Figure 11 shows the drift time distribution measured for &+ with the drift tube at 77 K. There are two poorly resolved components present. However, the drift time distribution measured at room temperature only shows a single component (the faster moving one). Clearly, these isomers interconvert below room temperature. (Note that the source was cooled to around 180 K for these studies.) The lower half of Figure 11 shows the measured fwhm of the A46+ drift time distribution divided by that calculated using eq 2 plotted against drift tube temperature. The sharp transition at around 275 K indicates the annealing temperature of &+. A rigorous analysis of this annealing threshold is possible and yields an activation energy of 0.55 eV. Isomers were also observed for A45+. But for this cluster only a single isomer is observed at low temperature, and a different isomer is observed at higher temperatures. The annealing temperature for these isomers is thus the temperature where both isomers coexist, which is given by the maximum in Figure 11 at around 345 K. The activation energy for annealing of A 4 5 + is 0.71 eV. The shell closing with 138 electrons occurs around A46+, and according to the shell model the geometries should smoothly become spherical as a shell closing is approached. The abrupt change in the geometry that occurs for 4 5 ' and is inconsistent with the shell model and suggests that the electronic structure of the cluster departs from the shell model predictions between the shell closings but follows the shell model close to shell closings where additional stabilization is available from adopting a
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20 J. Phys. Chem., Vol. 99, No. 1, 1995
studies of complex cluster systems where a single measurement is often insufficient to provide much information. It is not possible to fully understand the properties of atomic clusters without knowledge of their structure, and structure remains the most difficult physical property to determine. The mobility measurements described above provide some information about the cluster's shape. But detailed spectroscopic information is still required to more completely characterize the geometry. Such information remains exceedingly difficult to obtain. Despite a substantial effort, progress has been slow, and there is still no detailed structural information available for an atomic cluster containing more than 10 atoms (except for the fullerenes). In order to make much progress in this area, it seems that new experimental techniques must be developed.
TIME, ps
2.5 i
Acknowledgment. The work described here was made possible by my collaborators, in particular Eric Bower, Eric Honea, Unni Ray, and Kathleen Creegan at AT&T Bell Laboratories and Joanna Hunter and Jim Fye at Northwestern. Some of the research described in this paper was partially supported by the National Science Foundation (Grant CHE9306900).
A& ANNEALING TEMPERATURE A
I
4
5
ANNEALING
1.0
4 0
References and Notes 1
100
200 300 TEMPERATURE, K
400
500
Figure 11. Thermal annealing of aluminum clusters. The upper plot shows the drift time distribution measured for &+ at 77 K which shows two poorly resolved components. The lower plot shows the fwhm of the drift time distributions for &5+ and &+ divided by that calculated from eq 2 plotted against drift tube temperature. anneals at 345 K and &+ anneals at 275 K.
&5+
closed-shell configuration. For A4s2+ spherical and distorted isomers are also observed, but the two isomers coexist after annealing, suggesting that they have similar stabilities. For A45+ the more spherical isomer is the more stable, so it seems that adding a single electron to A452+ is enough to stabilize the more spherical geometry.
The Future The results described above illustrate some of the progress that has been made in recent years in the study of atomic clusters. As is often the case, the first studies raise more questions than they answer. So while the results presented above indicate that small silicon and germanium clusters adopt unusual and unexpected geometries, the factors responsible for this behavior remain poorly understood. On the other hand, understanding this behavior will clearly provide a deeper understanding of the chemical bonding in these materials. Another unexpected result to come from these studies is the low chemical reactivity of the silicon clusters. This can be rationalized by extensive reconstruction of the cluster surface which reduces the density of dangling bonds. The size regime where silicon clusters begin to display bulklike chemical properties is not yet known. There is clearly great interest in determining where this transition occurs and whether it occurs abruptly or gradually over a range of cluster sizes. As the results presented here show, the injected ion drift tube technique provides a powerful tool to examine the physical and chemical properties of gas phase atomic cluster ions. The greatest strength of this approach is its flexibility, which allows studies of the chemistry, shape, fragmentation, and annealing of atomic clusters in a single instrument. This flexibility is needed in
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