J . Phys. Chem. 1989, 93, 5012-5015
5012
-
set of coupled reactions of the form CCH3 D CCH2D
+ CCH2D + D CCHD,
+D
+H CCHD, + H
c*
CCD,
(5)
+H
Our samples are characterized by relatively large surface areas and small free volumes. At all temperatures the vast majority of H, D, and/or C atoms are confined to the surface. Therefore, the general theory of Bolder et al. for exchange reactions9 is applicable. Following their treatment we define the mean deuterium fraction, u, as u
= y3Cin,
for i = I , 2, 3
(6)
I
where the n, are the fractions of ethylidyne species containing i D atoms. They then show that u ( t ) is given by
41)
=
4m)
+ (40) - 4 m ) )
exp[-k(7')t/,(m)l
(7)
Equation 9 can therefore be used to derive k( 7') and thus E , and u. Using the data shown in Figures 3 and 4,such a treatment leads to the values E , = 14.3 f 2.5 kcal/mol and u = 4 X IO7*, s-l. Ogle and White6 have made measurements on hydrogen exchange of ethylidyne adsorbed on Pt ( 1 11) single crystals by SSIMS. They report E , = 7.2 f 0.3 kcal/mol. Figure 3 shows what the time course of our reaction would have been by using eq 5, their E,, and the preexponential factor u = 4 X IO2 s-I which we derive from their data. We also present the result of a similar calculation using our kinetic data. The large difference between their results and ours appears to be because Ogle and White neglect the possibility that in their low surface area samples the deuterium coverage varies with temperature. Christmann, Ertl, and Pignet l o have derived empirical constants that describe the variation in concentration of surface adsorbed hydrogen with temperature. Exploiting their analysis, we derive from the data of Ogle and White the kinetic factors E, = 11.8 kcal/mol and u = 7 X IO6 s-l, with which our N M R data agrees more closely.
where, in our case, u ( m ) = 1 / ( 1 a ) and a is the number of H atoms in the species undergoing exchange divided by the number of D atoms adsorbed on the surface ( a = 3 / 4 in our case). The NMR signal intensities S ( t ) are proportional to u(t). Considering a sequence of annealing steps of duration A, and defining u( T , ) and S(T,) as the values of u and S at the end of the ith annealing step of temperature TI,we can rewrite eq 7 in a form analogous to that of eq 2:
Conclusions We have demonstrated the application of deuterium NMR to the study of the reaction kinetics of ethylene on the surface of Pt. Kinetic parameters are simply derived from the measurement of the intensity of the deuterium signal arising from methyl groups in the ethylidyne species. The results of these experiments on highly dispersed catalytic samples provide kinetic parameters very similar to those derived from ultrahigh-vacuum studies on single-crystal surfaces.
or
Acknowledgment. The authors are grateful for an IBM postdoctoral fellowship awarded to D.B.Z. and also for an Exxon Foundation predoctoral fellowship awarded to C.A.K. We also acknowledge that this work has been supported through the University of Illinois Materials Research Laboratory by the Department of Energy, Division of Materials Research, under Contract DE-AC02-76ERO1198.
+
(9) Bolder, H.; Dallinga, G.; Kloosterziel, H. J . Cutul. 1964, 3, 312.
(10) Christmann, K.; Ertl, G.: Pignet, T. Surf. Sci. 1976, 54, 365
Unimolecular Decomposition of Sputtered Cs(CsI ), Evaporation Energetics
+
Clusters: Stabilities and
Hyun Jin Hwang, Dilip K. Sensharma, and Mostafa A. El-Sayed* Department of Chemistry and Biochemistry, University of California, Los Angeles, Los Angeles, California 90024 (Received: April 20, 1989)
The metastable decomposition of sputtered Cs(CsI),+ clusters of 1 5 n 5 17 is investigated in two different time windows by use of a double-focusing sector field mass spectrometer (reversed geometry). Cs(CsI),+ clusters are found to decompose mainly by evaporation of one or two Csl molecules in our time windows. Comparison of the evaporation probability with the evaporation energy predicted from the polarizable-ion model suggests that the two evaporation channels (the CsI monomer and dimer evaporation) are parallel and adiabatic with no reverse activation energy.
Introduction The physical and chemical properties of small gas-phase clusters have been subjects of great interest in recent years. Stabilities of clusters are one of the main concerns in this growing field because they are essential to deduce structural information and to understand the form of interactions among constituents of clusters. In particular, alkali-metal halide ( M X ) clusters of the form M( MX),' have been widely investigated concerning this matter both theoretically and experimentally. They are theoretically attractive because of their elementary electronic and
ionic-bonding nature'v2 and experimentally because they are easily formed by the sputtering of alkali-metal halide surface with fast -~ stabilities of this type of atom or ion b ~ m b a r d m e n t . ~Relative ( I ) Martin, T. P. Phys. Rep. 1983, 95, 167.
(2) Welch, D. 0.;Lazareth, 0. W.; Dienes, G. J.; Hatcher, R. D. J . Chem. Phys. 1976, 64, 835; 1978, 68, 2159. (3) Honda, F.; Lancaster, G. M.; Fukuda, Y.; Rabalais, J. W . J. Chem. Phys. 1978, 69, 493 1. (4) Dunlap, B. 1.; Campana, J. E.; Green, B. N.; Bateman. R. H. J . Vac. Sei. Technol. 1983, A l , 432.
0022-3654/89/2093-5012$01.50/00 1989 American Chemical Society
Letters clusters have been implied from strong variation of cluster yields observed in a sector field mass spectrometer."-* Cs(CsI),+ clusters have been most extensively studied because they are most emissive in the sputtering process and also show pronounced anomalies in the cluster yield distribution. I n the earlier studies, attempts were made to interpret the anomalies as due to the formation process using a crystal-cleavage5 or bond-breakingg model. However, from the time-of-flight measurements by Ens et a1.,I0 it was shown that there was no preferential formation of specific clusters at the time of formation. The cluster yield distribution of Cs(CsI),+ clusters right after their formation showedI0 a smooth quasi-exponential decrease with increasing n, in agreement with the random-bond-breaking modeL4 Moreover, this study showed that metastable decomposition was the main reason for the cluster yield anomalies. Diefenbach and Martin" have recently used a rigid-ion model potential and a polarizable-ion model potential to calculate the minimum energies for small Cs(CsI),+ clusters. The rigid-ion model predicted clusters of lower energies at n = 1, 4, 6, 9, and 13 while the polarizable-ion model predicted these at n = 1, 3, 6, 9, and 13. Previous mass spectra5-',* showed relatively strong peaks at masses corresponding to n = 6, 9, and 13. I n the present work, we report direct measurements on the metastable decomposition of sputtered Cs(CsI),+ clusters, focusing our attention on the relative stabilities and the evaporation energetics of these clusters. The Cs(CsI),+ clusters are found to decompose mainly by evaporating one or two CsI molecules. The formation probabilities of daughter cluster ions Cs(CsI),+ made by evaporation of one or more CsI molecules from selected parent cluster ions Cs(Csl),+ are measured in two different time windows, by which different ranges of internal energy distributions of the clusters can be selected. The results suggest that the evaporation of one or more Csl molecules leading to the formation of clusters with n = I , 3, 6, 9, and 13 have higher probabilities, supporting the polarizable-ion model fqr the relative stabilities of these clusters. The branching ratios between the two dominant evaporation channels, the evaporation of one or two CsI molecules, are compared with the adiabatic evaporation energies predicted from the polarizable-ion model. Our results are consistent with the predictions made from the polarizable-ion model in most cases, suggesting that the two evaporation channels are parallel and the evaporation is adiabatic with no reverse activation energy.
Experimental Section Results were obtained by use of a VG Analytical ZAB-SE mass spectrometer (reversed geometry) fitted with a fast atom bombardment gun (Model F A B l l N , Ion Tech Ltd., Teddington, Middlesex, UK). The general features of the reversed geometry mass spectrometer are described elsewhere.'* Briefly, cluster ions are produced by 7-keV Xe atom bombardment of CsI target prepared by evaporating aqueous salt solution on Ni foil. After passing the source region (between the target and the source exit slit) over a distance of about 0.5 mm, positively charged ions are accelerated to 8.1 keV through two-stage acceleration plates, analyzed by a 66-cm-radius 35' magnetic sector or in conjunction with a following 38-cm-radius 81' electric sector, and then detected by a conversion dynode followed by a CuBe electron multiplier. A slightly higher potential, compared to the target, was applied to the source exit slit (typically about 5 V higher) to focus the ions into the detection axis. ( 5 ) Campana, J. E.; Barlak, T. M.; Colton, R. J.; DeCorpo, J. J.; Wyatt, J. R.; Dunlap, B. 1. Phys. Reu. L e f f .1981, 47, 1046.
(6) Barlak, T. M.; Campana, J. E.; Colton, R. J.; DeCorpo, J. J.; Wyatt, J. R. J. Phys. Chem. 1981, 85, 3840. (7) Barlak, T. M.; Wyatt, J. R.; Colton, R. J.; DeCorp, J. J.; Campana, J. E. J. Am. Chem. SOC.1982, 104, 1212. (8) Barlak, T. M.; Campana, J. E.; Wyatt, J . R.; Colton, R. J. J . Phys. Chem. 1983, 87, 3441, (9) Dunlap, B. 1. Surf.Sei. 1982, I21, 260. ( I O ) Ens, W.; Beavis, R.; Standing, K. G. Phys. Reo. Left. 1983, 50, 27. ( 1 I ) Diefenbach, J.; Martin, T. P. J . Chem. Phys. 1985, 83, 4585. (12) Morgan, R. P.; Beynon, J. H.; Bateman, R. H.; Green, B. N. In?. J. Mass Spectrom. Ion Phys. 1978, 28, 17 1 .
The Journal of Physical Chemistry, V O ~ 93, . NO. 13, 1989 5013 TABLE I: Formation Probabilities (in %) of the Daughter Cluster Ions Formed by Evaporation of One or More CsI Molecules from the Sputtered Cs(CsI),' Clusters in the First and the Second Field-Free Region second field-free regionb
first field-free region'
n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
n-1 0 1.5 0.13 6.3 1.1 2.9 19.2 4.7 10.6 26.1 7.2 17.4 13.6 88.4 7.8 21.3 37.4
n-2
0 1.6 0 3.4 3.5 0.89 12.3 3.4 5.1 22.6 8.5 5.6 4.1 71.7 5.2 9.2
n-3
0 0 0 0 0 0 0 0 0 0 0 0 0 11.0 0
n-4
0 1.7 0 0 0 0 0 0 0 0 0 0 0 0
n-1 0 0 0 0.052 0 0.019 0.75 0.027 0.25 1.62 0.16 0.78 0.45
n-2
0 0 0 0.013 0.011
0 0.065 0.013 0.067 0.45 0.094 0.053
"These values are reproducible within f7%. bThese values are reproducible within f 4 0 % .
A metastable decay of a mass-selected (or mass-identified) parent ion ml+ into a specified ion m2+ either in the first field-free region (between the acceleration region and the magnetic sector, drift length 120 cm) or in the second field-free region (between the magnetic sector and the electric sector, drift length 150 cm) can be detected as f01lows.'~ In the first field-free region, the magnetic sector field is tuned to the apparent mass m* = m 2 / m l and the ion signal is detected at the focal point of the magnetic sector (the sirigle-focus mode). In the second field-free region, this is done by tuning the magnetic sector field to m l + and the electric sector field to m 2 / m l and detecting at the focal point of the electric sector (the double-focus mode). These procedures uniquely identify the unimolecular decay of the mass-selected cluster ions into defined fragment ions in the corresponding field-free region. In the present experiments, spectra of parent and daughter ions were obtained (1) in the single-focus mode by scanning the acceleration voltage after tuning the magnetic sector field to the mass of corresponding ions and ( 2 ) in the double-focus mode by scanning the electric sector field after selecting a parent ion by tuning the magnetic sector field. During the experiments, the pressure is kept at - 2 X lod Torr in the acceleration region and at -5 X lo-* Torr in the analyzer region. At this analyzer pressure, no collision-induced dissociations contaminate the unimolecular decomposition of the sputtered clusters. The experimental time windows are estimated to be, for to = 1.0 ps and At = 57.1 ps in the first C S ( C S I ) ~clusters, ~+ field-free region and to = 77.3 ps and At = 71.3 ps in the second one, where to is the time needed to reach the corresponding field-free region and At the residence time in the field-free region. In this experimental condition, decomposition of the cluster ions is effectively detected if the lifetime of the cluster ions is in the range 10-5-104 s in the first field-free region and 104-10-5 s in the second one.l4
Results and Discussion All possible unimolecular decomposition channels were examined as described above for 1 In I17 in the first field-free region and for 1 In I13 in the second field-free region, and loss of one or more CsI molecules was observed. Table I gives the formation probabilities P,,, of daughter cluster ions Cs(CsI),+ from selected parent cluster ions Cs(CsI),+, which can be determined as (13) Cooks, R. G.; Beynon, J. H.; Caprioli, R. M.; Lester, G. R. Merosfable Ions; Elsevier: Amsterdam, 1973. (14) Klots, C. E. J . Chem. Phys. 1973, 58, 5364.
5014
The Journal of Physical Chemistry, Vol. 93, No. 13, 1989
where I , is the integrated intensity of the selected parent Cs(CsI),+ peak and I , , or I,,, are those of the daughter cluster ion peaks formed by evaporation of CsI molecules from the selected Cs(Csl),' clusters. As shown in Table I, the evaporation probability (or the formation probability of the daughter ions) is much smaller in the second field-free region than in the first one. This is a reflection of the change in the average temperature of the cluster distribution as time lapses. The "hotter" clusters evaporate faster (e.g., in the first field-free region) leaving behind the "colder" clusters which evaporate slower ( e g , in the second field-free region). Table I also shows that the loss of one or two CsI molecules is the dominant evaporation channel and the loss of more than two CsI molecules is observed only in the first field-free region and for only a few cases. As will be discussed in detail in a forthcoming paper,I5 the evaporation of two or more CsI molecules seems to occur via a direct fission process. In short, the loss of two or more CsI molecules represents relatively high decay probabilities in both field-free regions compared to the total decomposition probabilities even for very small clusters, e.g., n = 3 cluster in the first field-free region. For some cases, they are even more dominant than the monomer loss, e.g., for n = 3, 5, 6, 8, 1 I , and 15 in the first field-free region. This tendency is almost retained in the second field-free region. If these processes occur via sequential loss of CsI molecules, the loss of two or more Csl molecules should occur much less probably than the monomer loss for most of the clusters in the first field-free region and would be dramatically reduced in the second field-free region where colder clusters are examined. In Figure 1, the total decomposition probabilities of Cs(CsI),+ clusters in both the first and second field-free regions are compared to the corresponding cluster yields measured in the double-focus mode. The total decomposition probability can be determined as the sum of the formation probabilities for all the daughter cluster ions resulting from decomposition of a selected parent cluster ion. The decay probabilities are dramatically reduced in the second field-free region compared to the first field-free region, reflecting the strong cooling of the clusters resulting from the evaporation process over a longer period of time. It is thus expected that the kinetics of the evaporation will be highly nonexponential and the temperature of the clusters will depend on the time lapse after their formation. (Hotter clusters will decay faster than colder clusters within a given internal energy distribution.) As shown in Figure 1, variation in the decay probability exhibits qualitatively a mirror image of cluster yield distribution, implying that the metastable decay, not the formation process, is the main reason for the appearance of clusters with magic numbers. This is in agreement with conclusions made from a different type of experiments by Ens et a1.I0 While enhanced cluster yields are observed at n = 6, 9, 13, and also slightly at n = 3, the decay probabilities of corresponding clusters are relatively reduced, especially compared to the next larger clusters, Le., clusters of n = 4, 7 , IO, and 14. From this observation, it is obvious that enhanced cluster yields at n = 3, 6, 9, and 13 are mainly due to instabilities of the next larger clusters due to the evaporation. In other words, clusters of n = 3, 6, 9, and 13 are relatively stable to the evaporation processes. Since more than one evaporation process is involved in this observation, one cannot correlate these relative stabilities to well-defined thermodynamic quantities of a specific evaporation process. For this purpose, it is necessary to follow the loss of one or two CsI molecules independently. I n Figure 2, a and b, the formation probabilities in the first and the second field-free region, respectively, are plotted as a function of the daughter cluster ion size. As in the total decay probability (Figure I ) , strong variation is superimposed on the general increasing tendency with increasing cluster size. A striking ( I 5 ) Hwang. H. J.; Sensharma, D. K.; El-Sayed, M. A. Chem. Phys. Left., submitted for publication.
Letters feature is that strong enhancement of the formation probability is correlated with the formation of certain daughter cluster ions Cs(CsI),+ when evaporation channels associated with the same size of a neutral fragment are compared. Strong enhancement is seen when m = I , 3 , 6, 9, and 13 in the first field-free region (Figure 2a) and when m = 3, 6, and 9 in the second field-free region (Figure 2b). The CsI monomer and dimer evaporation channels show enhanced probabilities to form these clusters (having magic numbers) in both field-free regions. Two trimer and tetramer Csl evaporation channels observed in the first field-free region also correspond to production of one of these fragment cluster ions, Le., CS(CSI),~+to CS(CSI),~+and Cs(CsI),+ to Cs(Csl)+. Note that most of these magic numbers were also observed in the cluster yields and the total decay probabilities shown in Figure I . All of the results described above seems to be attributed to enhanced stabilities of Cs(CsI),+ clusters of n = 1, 3, 6, 9, and 13. At the time of formation, clusters are formed in a wellthermalized condition, and thus the average internal energy of clusters is roughly proportional to the number of atoms in the cluster. On the other hand, as was seen in the time dependence of the total decomposition probabilities (see Figure l), the strong cooling which accompanies evaporation of CsI molecules will wash out the initial internal energy distribution from the high-energy tail of the distribution, depending on the kinetics of each cluster. If the experimental time window is narrow enough, this trend would be observed showing an increase in the decay probability with increasing cluster size. If some specific clusters have enhanced stabilities, they will decompose with lower probabilities and will be observed as having magic numbers. Furthermore, the decay will be more pronounced when the decomposition channels produce stable daughter cluster ions (Le., with m = 1, 3, 6, 9, and 13) since they will represent in general lower evaporation barriers. Diefenbach and Martin" have performed total energy calculations for Cs(CsI),+ clusters based on a simple shell model in which size-independent two-body interaction potentials were used. The most stable structures and corresponding binding energies of Cs(CsI),+ clusters have been determined for 1 5 n 5 18, using two different model potentials, the rigid-ion and polarizable-ion models. While the former potential was expressed only with the electrostatic Coulombic and the repulsive Born-Mayer interaction terms, the latter included interactions due to the polarization of the ions. From this calculation, it was predicted that the sizes of relatively stable Cs(CsI),+ clusters were n = 1, 4, 6, 9, and 13 in the rigid-ion model and n = 1, 3, 6, 9, and 13 in the polarizable-ion model. The latter model agrees qualitatively well with our results. Considering this good agreement, it is tempting to compare the evaporation probabilities with the evaporation energies calculated from the polarizable-ion model. In Figure 3, it is shown how the energies of evaporation play a controlling role in the decay probabilities when two competitive evaporation channels coexist. Figure 3a shows the branching ratios of the monomer (R",,) and evaporation as a function of parent cluster ion the dimer (Rfldlm) size n. For a given cluster of size n, the branching ratios can be determined from the evaporation probabilities into two channels, P,,n-l for the monomer evaporation and Pn,-*for the dimer evaporation:
and (3) Rndim= I - R",,, The solid line represents the values determined in the first field-free region and the dashed line in the second field-free region. If the condensation process has no barrier, the branching ratio will be determined mainly by the internal energy distribution of the parent cluster and the evaporation energies for the loss of the CsI monomer and dimer, AEflmonand hE"dim,respectively. Since the two channels arise from the same internal energy distribution of the parent for each cluster, the variation in branching ratio thus
The Journal of Physical Chemistry, Vol. 93, No. 13, 1989 5015
Letters
O
>-
-
0.
fa
80-
0.
t
m 0
E
z 9 t v)
8
1".
1.
s
C
-
j.,i 0.4
E
K
60 -
to*.' ,E
O. 0.
1.0
(b)
40-
8 Y
20-
w a
c
-1.0
0 0
6
3
12
9
15
18
n Figure 1. Size dependence of the total decomposition probability (0, in the first field-free region; X, in the second field-free region) and the relative cluster yield (A, measured in the double-focus mode) of the sputtered Cs(CsI),+ clusters.
R
I
c
2 1.5 9 1.0 a
0. 5
0. 0 0
3
6
m
9
1
2
1
5
Figure 2. Size dependence of the formation probabilities of the daughter cluster ions CS(CSI),,,~ formed by evaporation of one (0)or two ( X ) CsI molecules from the sputtered Cs(CsI),+ clusters in thc first (a) and second (b) field-free regions.
reflects the variation in the difference of the evaporation energies for the monomer and the dimer evaporation. In Figure 3b, &?dim - AEnmon is plotted against n. These values were calculated by using the theoretical formation energies" of Cs(CsI),+ clusters (E,) and those2 of the CsI monomer (Emon)and dimer (Edim) predicted from the polarizable-ion model. For a given cluster of size n, they are given by From this relation, the change in this difference with n reflects only the variation in the stabilities of the daughter ion clusters resulting from the evaporation of the dimer and the monomer from a parent ion cluster with n CsI molecules. As shown in Figure 3a,b, the branching ratios seem to correlate well with the theoretical predictions in their patterns (except for n = 9). The general trends in both figures are the same. In Figure 3a, it is clear that the branching ratio favors the evaporation of the dimer for n = 3, 5 , 8, 11, and 15. For these clusters, &"dim - AE",,, shown in Figure 3b is negative; Le., it takes less energy to evaporate the dimer than to evaporate the monomer. On the
j , , , , , , , , , , 0 3 6 9 n
1
, , , A, , , 12
15
18
Figure 3. Comparison between the size dependence of the branching ratio of the monomer and the dimer evaporation in the first (0)and second ( X ) field-free regions (a) and the calculated**"difference of the evaporation energies between the two evaporation channels (b).
other hand, for the clusters with n = 2, 4, 7, 10, and 14, the branching ratio in Figure 3a favors the monomer evaporation. As shown in Figure 3b, hE"d, - AE",,, is positive for these clusters, suggesting that it takes more energy to evaporate the dimer than to evaporate the monomer. These observations are consistent with the previous conclusions that clusters with n = 1, 3, 6,9, and 13 are exceptionally stable. The generally good correlation shown in Figure 3 itself supports several assumptions made in this comparison. First, the polarizable-ion model calculation seems to be very good in predicting the formation energies of the Cs(CsI),+ clusters since the fluctuation of the energy difference between the two channels in the range of 2 In I13 is very small, yet the expected correlation remains very good. Second, the evaporation is probably adiabatic as assumed with no or negligible reverse activation energies for the two evaporation channels. Moreover, it also supports the assumption of two parallel and competitive evaporation channels as was concluded from a different type of study that involves results on the kinetic energy re1ea~e.I~ In summary, one reaches a number of conclusions regarding the stabilities and the evaporation dynamics of the CS(CSI),,~ clusters from the above study. Our results support the results of previous studies, that magic numbers appear as a result of the stabilities of "magic" clusters to evaporation in the time window used for most of the mass spectrometric experiments and are not due to faster rates of their formation. The observed clusters with the lower probabilities of evaporation are also those which are formed readily by evaporating one or two CsI molecules from those clusters having one or two more CsI molecules. The fact that one can explain the observed branching ratios for the evaporation of one vs two CsI molecules for these clusters (except for n = 9) with the corresponding calculated evaporation energies based on the polarizable-ion mode12J1suggests (a) the correctness of the theoretical model, (b) the absence of reverse activation energy, and (c) the loss of two CsI molecules is a result of fission of a dimer rather than a sequential evaporation. The latter conclusions are also supported by our studies of the kinetic energy release in these evaporation processes.I5 It is noteworthy that the most stable structures of Cs(CsI),+ clusters predicted from the polarizable-ion model for n = 3, 6, and 9 are basically distorted six-atom hexagonal rings with an extra Cs+ ion embedded in these structures." This is to be contrasted with cubelike structures found for the larger clusters with magic numbers (n = 13 and higher). Acknowledgment. The authors thank the Office of Naval Research for the financial support. The UCLA Chemistry Department is acknowledged for allowing us to use the VG Analytical ZAB-SE mass spectrometer for this study.
