Observation of BeC2−n, a particularly abundant gaseous dianion

Observation of BeC2ÿn , a particularly abundant gaseous dianion

Je� Klein, Roy Middleton *

Department of Physics and Astronomy, University of Pennsylvania, 209 S, 33rd Street, Philadelphia, PA 19104-6396, USA

Received 21 November 1997; received in revised form 20 January 1999

Abstract

We describe two techniques for identifying double-negative molecular ions. In the ®rst, accelerator mass spec-

trometry (AMS) is used to identify and count the atomic fragments produced when a molecular dianion is destroyed at

the terminal of a tandem accelerator. This method can determine unequivocally the chemical composition of a mo-

lecular ion. It is most easily implemented for cluster ions with constituents that can be produced in states of identical

magnetic rigidity (e.g. clusters composed of several identical atoms). The other, Coulomb Explosion Imaging (CEI),

produces a ``picture'' of the dianion showing each atom. The diameter and length of the tracks are related to the Zs of

the particles producing them.

Using these techniques, we discovered a new class of gaseous dianions. These dianions are noteworthy because they

can be produced with intensities that are at least 10 times greater than the intensities achieved with any other known

double-negative ion. They are of the form BeC2ÿn , where n is even and greater than or equal to 4. The largest dianion

that we have observed is BeC2ÿ14 . A second weaker class of dianions of the form Be2C2ÿ

n has also been observed for n� 6

and 10. No dianions containing an odd number of carbon atoms were observed. A lower limit for the lifetimes for the

most abundant ions is at least 5 ls. Ó 1999 Published by Elsevier Science B.V. All rights reserved.

PACS: 36.40.ÿc; 36.40.Mr; 36.40.Qv; 36.40.Wa

Keywords: Dianion; Gaseous double-negative ion; Cluster ion; AMS; Lifetime; Beryllium

1. Introduction

Interest in multiply charged anions was stimu-lated not only by scienti®c curiosity but also by therealization that doubly charged negative ionswould provide a means of increasing the energyobtainable using a tandem accelerator without

increasing the voltage of the terminal. The initialdianion searches, begun more than 30 years ago,concentrated on atomic species because onlyatomic ions confer a practical advantage whenaccelerated. And, although there were some claimsof mass spectrometric evidence for doubly chargedatomic and diatomic anions (for example [1±4]),none of these observations were repeatable [5±9].With the burden of evidence against the existenceof dianions, interest in multiply charged smallanions languished for a decade until the discovery

Nuclear Instruments and Methods in Physics Research B 159 (1999) 8±21

www.elsevier.nl/locate/nimb

* Tel.: +1 215-898-8513, fax: +1 215-898-2010. e-mail:

[email protected]

0168-583X/99/$ - see front matter Ó 1999 Published by Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 8 - 5 8 3 X ( 9 9 ) 0 0 1 7 8 - 0

of small cluster dianions in 1990. Schauer et al.,[10] reported observing dianions composed ofcarbon atoms ± the smallest comprising sevencarbon atoms, and the most intense, 10. Eventhough, the carbon dianions are more than 106

times less intense than singly charged anion clus-ters with the same number of carbon atoms, theywere discovered because, they appear at half-in-tegral masses, whenever the total mass of themolecule is odd ± the case, when a 13C atom re-places a single 12C atom. Alerted by Schaueret al.Õs initial observation of these clusters, wecon®rmed their existence using accelerator massspectrometry (AMS) [11]. We developed a tech-nique able to analyze individual carbon atomscomposing a cluster following the clusterÕs break-up in the terminal of the accelerator ± countingfragments arriving in coincidence positivelyestablished that the ``half-integral'' masses ob-served by Schauer et al. are in fact double-nega-tive clusters of carbon ions. Subsequently,Calabrese et al. [12] published, further experi-mental veri®cation ± essentially repeating theoriginal experiment.

2. Discovery of BeC2ÿn

The discovery of the BeC2ÿn clusters was seren-

dipitous. We had just modi®ed our ion-source testfacility (see inset in Fig. 1), so that we couldmeasure more accurately the lifetimes of metasta-ble ions, particularly the lifetimes of carbon-clusteranions and dianions. We decided to check thecalibration of the setup using Beÿ, because Beÿ hasone of the most accurately known lifetimes (44 ls)[13±15] in the range 5 to 700 ls, the e�ectivemeasuring limits of our apparatus. Following thetests with Beÿ, we replaced the beryllium metalcathode with one containing graphite. In additionto the expected half-integral peaks at 48.5, 60.5,etc. due to carbon-cluster dianions of the form13C12C2ÿ

n , we saw two unexpected ones: a moder-ately strong peak at mass 52.5 and a very weakpeak at 64.5. We were astounded when we realizedthat these previously unobserved half-integralpeaks might be due to the dianions BeC2ÿ

8 andBeC2ÿ

10 . A surprising conclusion because, the only

source of Be was ``cross-talk'' from the previousberyllium metal cathode, used in the source of Beÿ

lifetime studies and generally, ``cross-talk'' in oursputter source is very low (typically <10ÿ3). Thesehalf-integral mass peaks suggested a new dianionthat was abundant enough to be formed from aconstituent that was being supplied only by ion-source ``memory.'' We subsequently, con®rmedthis startling conclusion by replacing the carboncathode with a cathode containing crushedgraphite mixed with an equal weight of ÿ200 meshBe metal. The intensity of these new half-integralspecies increased markedly, and a portion of aspectrum from such a cathode is shown in Fig. 2.In this ®gure, three di�erent classes of dianions arevisible: (1) At mass 60.5, 13C12C2ÿ

9 , an example ofthe previously known class of all-carbon clusters.(2) Examples of the most intense class of dianionswith the formula BeC2ÿ

n appear at masses 40.5,52.5 and 64.5, corresponding to BeC2ÿ

6 , BeC2ÿ8 and

BeC2ÿ10 , respectively. And, (3) at mass 45.5,

Be132 C12C2ÿ

5 represents another previously unre-ported class of dianions with the formula Be2C2ÿ

n .Anions with the structures, Cÿn , Beÿn , BeCÿn , andBe2Cÿn are also visible.

A striking feature of Fig. 2 is the strength of theBeC2ÿ

n dianions: BeC2ÿ6 (the most intense dianion

of the form BeC2ÿn ) is 100 times stronger than

C139 C2ÿ (the most abundant C13

n C2ÿ ion). Allowingfor the isotopic abundance of 13C, BeC2ÿ

6 is stillnine times stronger than 12C2ÿ

10 . Another strikingfeature is the absence of BeC2ÿ

n peaks with oddvalues of n.

3. Veri®cation of the dianions

The data described above were taken using ourion source test facility schematically shown inFig. 1. Ions are produced by bombarding a solidcathode with an 8 keV Cs beam (further details ofthe source are given in Refs. [16,17]). Negative ionsare extracted through the center of the Cs ionizerand further accelerated by a potential that is ad-justable from 0 to 20 kV; typically we use an ex-tract voltage of 6 kV. Since, the emittance of thesource is only weakly a�ected by the magnitude ofthe extraction voltage, we can e�ciently produce

J. Klein, R. Middleton / Nucl. Instr. and Meth. in Phys. Res. B 159 (1999) 8±21 9

anions with energies that range between 8 and28 keV, and dianions with energies ranging from16 to 56 keV. Following acceleration, the ions aremass analyzed (M/DM�300) in a magnetic dipoleand either detected in a Faraday cup, or furtheranalyzed by a uniform-®eld electrostatic analyzer(EA) (E/DE�100), and detected by an electronmultiplier 1 (EM) operated with a gain of about200.

The spectrum shown in Fig. 2 was taken usingthe electron mulitiplier following the electrostatic

analyzer. The magnetic dipole selects ions with agiven magnetic rigidity, i.e. momentum to chargeratio (p/q). Combined with the EA, which selectsions with a ®xed energy to charge ratio (E/q), theanalysis system selects ions with a ®xed mass tocharge ratio (m/q). Use of the EA veri®es that thehalf-integral mass peaks are indeed dianions andare not fragments with lower energy (with coinci-dentally the correct p/q ratio) produced by thebreakup of heavier ions between the source andthe magnetic dipole.

We scanned the EA at ®xed magnetic rigidity toexamine the composition of the half-integralpeaks. A scan of BeC2ÿ

8 at mass 52.5 amu is shownin Fig. 3. Beam intensities are plotted against E/q

1 Obtained from an old helium leak detector (Veeco 12AB-R),

Veeco part number 0110-065-01.

Fig. 1. Schematic representation of ion-source test facility showing the location of ion source, 30 cm dipole magnet (M/DM� 300),

uniform-®eld electrostatic analyzer (EA) (E/DE� 100), Faraday cup and electron multiplier (EM). Spectra such as that shown in Fig. 2,

are taken with the input and output slits of the EA set to �0.25 mm, the EA set to the value appropriate to an ion produced in the ion

source, and the EM operating with a gain of �200´. Scanning the EA while keeping the dipole magnet constant enables the exam-

ination of the ions present at a particular ``mass'' setting (see Fig. 3). Lifetime measurements are made either with the setup shown in

the insert (used for decays with a ®nal state containing a neutral) or using the standard setup with the EA set for the appropriate value

of E/q for the decay product. The e�ective decay lengths for these two setups are 0.71 and 0.65 m, respectively.

10 J. Klein, R. Middleton / Nucl. Instr. and Meth. in Phys. Res. B 159 (1999) 8±21

normalized to unity for ions accelerated from thesource that do not charge exchange, breakup orlose energy between the ion source and analyzer.The spectrum is dominated by the peak with E/q� 1 corresponding to the dianion that has twicethe energy, and twice the charge of an anion fromthe source. It is more than one hundred times asintense as the next strongest peak. Peaks with E/q > 1 are produced only by dianions: speci®callywhen a dianion loses an electron after accelerationin the electric ®eld in the source. The peak with E/q� 2 is produced, when a BeC2ÿ

8 ion loses anelectron between the magnetic analyzer and theEA. The peak with E/q� 1.83 arises when a BeC2ÿ

8

ion loses a beryllium atom as well an electron be-tween the magnet and EA. The absence of a peakat E/q� 0.17 corresponding to Beÿ suggests thateither, the electron and beryllium atom are re-moved sequentially, or if Beÿ is formed, the Beÿ

loses its electron too rapidly to be detected.

The four remaining peaks (a,b,c,d) in Fig. 3 arenot related to the dianion, but are produced byions breaking up before the magnet. Peak a at E/q� 0.46 is produced, when a CsBe2Cÿ8 ion loses acesium atom forming Be2Cÿ8 . Although, this seemsan unlikely process, spectra similar to that in Fig. 2extended to mass 500, show that CsBeCÿn andCsBe2Cÿn are particularly intense anions. TheBe2Cÿ8 so produced happens to have the correctrigidity to pass around the magnet. It is sharplypeaked in the magnet and in the EA. Similarly,peak b at E/q� 0.73 and peak d at E/q� 0.87 areCÿ6 and Cÿ5 produced from Be3Cÿ6 and BeCÿ5 , re-spectively. Peak c at E/q� 0.84 is a little di�erent.It is produced when a BeCÿ4 ion disintegrates in-side the vacuum chamber of the magnet producing

Fig. 3. A spectrum obtained by varying the EA with the

magnet constant and set for mass 52.5 amu, i.e. for BeC2ÿ8

(105.0122 amu). The ®eld in the EA when bending BeC2ÿ8 is

7 kV/3.81 cm� 184 kV/m. In addition to the peak at E/q� 1

due to BeC2ÿ8 , there is a peak at E/q� 2 produced when a BeC2ÿ

8

loses an electron between the magnet and EA, and a peak at E/

q� 1.86, when a BeC2ÿ8 loses both an electron and a beryllium

atom. The lettered peaks are unrelated to the dianion. Peaks a,

b and d result from molecules breaking up before the magnet

into fragments that happen to have the correct magnetic rigidity

(see the text for details). In general, fragments with the correct

magnetic rigidity produced by molecules breaking up before the

magnet will have masses equal to M(E/q), and come from an-

ions with masses equal to M(E/q)2, where E/q is normalized to 1

for ions that experience no collisions or charge-exchange after

leaving the source, and M is the mass selected by the magnet.

Peak c is produced by a breakup in the ®eld of the bending

magnet. Though sharp in the EA, its intensity does not change

as the magnet is scanned over several mass units; it is produced

when a BeCÿ4 breaks up in the magnetÕs vacuum chamber

forming Cÿ4 .

Fig. 2. A portion of a spectrum measured on the ion-source test

facility (shown in Fig. 1) with a cathode containing approxi-

mately equal weights of powdered graphite and ÿ200 mesh

beryllium powder tamped into a 1.6 mm diameter hole in a

molybdenum cathode. The cesium sputter energy was 8 keV

and the energy of the negative ions leaving the ion source was

14 keV for singly charged ions and 28 keV for the dianions. The

currents were measured at the output of the electron multipler ±

true negative-ion currents are lower by �200´. Non-integral

mass peaks at 40.5, 52.5 and 64.5 were con®rmed to correspond

to BeC2ÿ6 , BeC2ÿ

8 , and BeC2ÿ10 , respectively. The weak peak at

45.5 is due to Be132 C12C2ÿ

5 and the somewhat stronger peak at

60.5 is 13C12C2ÿ9 .


a Cÿ4 ion. Since, the disintegration occurs insidethe magnet, the peak is comparatively insensitiveto the magnet setting, but the ion has a well-de-®ned energy (48/57 of the full energy), so it issharply peaked in the EA. The maximum intensi-ties for this peak occur with magnet settings of 57and 40.4 amu. The higher mass corresponds to theBeCÿ4 molecule breaking up after the magnet, inthe drift region between the magnet and EA. Thelower mass corresponds to breakup before themagnet, in the drift region between the source andthe magnet. In the latter case, the magnetic rigidityis 48/57.01 ´ 48� 40.4 amu.

Two arguments for the existence of the dianion,BeC2ÿ

8 , can be made from the evidence presented inFig. 3. First, the strong peak at E/q� 1 is obtainedwith the magnet set for a half-integral mass. Theonly ions with E/q� 1 at half-integral masses areodd-mass dianions. Second, the existence of peakswith E/q > 1. The only way to produce an ion withan E/q > 1 is by a reduction in the ionÕs charge be-tween the source and the EA, since it is not possibleto increase the energy of the ion. Consequently, adianion must have been formed at the source, an-alyzed by the magnet, and lost an electron betweenthe magnet and the electrostatic analyzer.

There is no peak at E/q� 0.50 that would ariseif Be2Cÿ16 dissociated into two equal mass frag-ments with one retaining its negative charge. BeCÿ8produced in this way would have the same mag-netic rigidity as BeC2ÿ

8 , and would be mistaken forthe dianion if only magnetic analysis were used. Itis worth noting that in our numerous studies of thedissociations of cluster ions, by far the most likelycharged product is an anion that has lost a singleatom ± certainly not the one that has ``®ssioned''into two equal-mass fragments.

4. Identi®cation of BeC2ÿn

We were able to verify the identi®cation ofthese clusters using a technique that we developedearlier to establish the identities of other unusualor uncertain negative ions including the dianionsof carbon [11], the dianions of the alkaline-earth¯uorides [18] and the anions Nÿ2 , COÿ and COÿ2[19]. The method uses AMSAMS to identify the atomic

fragments produced when a cluster disintegrates inthe tenuous gas stripper (N2 in our case), in theterminal of the tandem accelerator. The positivelycharged fragments thus produced are acceleratedback to ground potential, and following magneticanalysis, detected in an ion chamber. If the origi-nal cluster ion comprises many identical atomicconstituents, then multiple fragments from a singlecluster will sometimes arrive simultaneously in theion chamber. (Not always because not all ions,even of the same chemical species, leave the ter-minal in the same charge state, and the transmis-sion e�ciency from the terminal to the detector isless than 100%.) The ion chamber is able to de-termine the Z of an arriving ion from its charac-teristic energy loss at a particular energy (both aremeasured for each ion). The energy and energy-loss signals of events in which two or more ionsarrive simultaneously are linear combinations ofthe signals from single-particle events. Therefore,the number and type of atoms arriving simulta-neously in the ion chamber can be determinedfrom the total energy and energy-loss signals. Thetotal energy and energy-loss data are stored foreach event. The total number and type of atoms inthe original cluster can be determined by com-paring the frequencies of events with one, two orany number of ions arriving simultaneously, withthe expected frequencies assuming a binomialdistribution and a given number of atoms in theoriginal cluster. Since, we know the magnetic ri-gidity of the injected negative cluster ion, we canuniquely determine its charge after determining itscomposition (and therefore mass) from the anal-ysis of the positive-ion atomic fragments createdwhen the cluster was destroyed at the terminal ofthe accelerator. For a detailed description of themethod see Ref. [11].

Here are the speci®cs, regarding the applicationof this method to the investigation of the BeC2ÿ

ndianions. The negative-ion beams are produced ina sputter source identical to the one on our testfacility and accelerated through a total potential of28 kV before injection into the tandem. Selectionof the negative-ion beam is accomplished with amagnet (radius� 30 cm) whose resolution can bevaried by adjustment of input and output slits.Unlike the test facility, the tandemÕs injector is not


equipped with an electrostatic analyzer. Althoughan EA is clearly desirable, it is apparent from Fig.3 that its absence in the present case, is not criticaleither for the study of BeC2ÿ

8 or BeC2ÿ6 (where the

EA scan looks very similar).With the voltage of the accelerator set to 7 MV,

an injected beam of Cÿ3 was stripped to C3�at theterminal. The 23.333 MeV 12C3�ions were used toadjust the magnetic quadrupole lenses, the ana-lyzing magnet and switching magnet to optimizethe current in a Faraday cup, located immediatelybefore the ionization detector. After very consid-erable attenuation, this beam was used to calibratethe energy (E) and energy-loss (DE) signals of themulti-anode detector that was used to analyzethe fragments from the dianions. We studied thedianions by changing the terminal voltage of theaccelerator, so that atom fragments of interest(usually carbon, but occasionally beryllium) hadthe same magnetic rigidity (and in the case ofcarbon, the same energy) as our pilot beam. Theterminal voltage of the accelerator is monitoredwith a generating voltmeter that has a precisionand reproducibility of 1 kV. The reproducibility ofthe terminal voltage (1/7000) is well within theacceptance of the analyzing magnet (the most se-lective element of the positive-ion transport sys-tem), which had a resolution of DM/M� 5 ´ 10ÿ4

with the settings employed in this experiment. Weconsidered using C4� instead of C3�, so that wecould simultaneously analyze C4� and Be3� fromthe breakup of a dianion cluster, applying theprinciple that all ions with the same m/q aretransported together if they are fragments of thesame injected molecule. But, the yield of the 4+charge state for C was low and the mass of Be is9.0122, so the magnetic rigidities of Be3� and C4�

ions di�er enough (0.068%) that transmission ofone can be had only at the expense of the other.Consequently, most measurements were madewith C3� after tuning the beam transport as de-scribed above. Typical transmission through theaccelerator (from the ion source to the detector)with a gas stripper (used to minimize the angulardivergence of the atomic fragments) was 12% forCÿ3 ions, but only 5.4% for BeC2ÿ

6 . The di�erencein transmission may have several causes, but themost likely are: (1) Loss of the fragile dianion in

the residual vacuum. Fig. 4 shows the attenuationof the BeC2ÿ

8 current as a function of the pressurein the 65 cm long ¯ight path between the analyzingmagnet, and the EA on the test facility. On thetandem, the dianions have to travel about 6 mbetween the low-energy cup position and the ter-minal. Since all measurements were made using agas stripper, the average pressure was higher thanusual and probably approached 10ÿ6 Torr. Thus,collisional losses alone could account for the ob-served low transmission. (2) In order to obtainmeasurable positive ion currents of several pico-amps (necessary because of the large leakage cur-rents of the tandemÕs high-energy Faraday cup),the input and exit slits of the injection magnet wereopened beyond their optimal values. The conse-quent reduction in resolution of the injector mayhave resulted in the dianion currents being over-estimated because of contaminant beams.

Fig. 5A is a two-parameter (DE vs. E) repre-sentation of the C3� fragments detected from thebreakup of BeC2ÿ

6 . Peaks from the arrival of asingle C3�, two ions in coincidence, and the arrivalof up to six ions simultaneously from the breakupof a single cluster negative ion are apparent. Fig.5B is a projection of the two-parameter plot ontothe energy axis to make it easier to see the relativeintensities of the various coincidences.

Fig. 4. The dependence of the BeC2ÿ8 current (measured by the

EM) is shown as a function of pressure. The current decreases

by more than a factor of two when the pressure between the

magnet and EA on the test bench is raised from 2 ´ 10ÿ7 to

3 ´ 10ÿ5 Torr. It is clear, comparing this ®gure and Fig. 10, that

most of the loss of BeC2ÿ8 is to neutrals ± not to BeCÿ8 or Cÿ8 .


The probability of observing an m-fold coinci-dence is given by:

n!P m�1ÿ P�nÿm

�nÿ m�!m!; �1�

where n is the number of 12C atoms in the clusterand P is the probability that a carbon ion from the

cluster will be ionized into the 3+ charge state anddetected in the ion chamber. Fig. 6A and B showcomparisons between the observed counts of C3�

Fig. 6. Observed C3� coincidences arising from the injection of

BeC2ÿ6 (A) and BeC2ÿ

8 (B) are shown as histograms and calcu-

lated values from Eq. (1) as black circles. Error bars are the

one-sigma uncertainties for the calculated values. `Àccidental''

pileup (calculated from the count rate and assuming Poisson

statistics) has been subtracted before plotting the data. Typi-

cally `àccidental'' pileup corrections were less than 1% of the

main peaks, and only a few counts (<10) for the higher order

coincidences. There are two counts corresponding to the coin-

cident arrival of seven carbon atoms in the spectrum for BeC2ÿ6 .

These counts are the result of the coincident arrival of frag-

ments from two separate dianions, and illustrate the uncer-

tainties in pileup subtraction. As mentioned in the text, the only

adjustable parameter in Eq. (1) is P (the transmission), and the

best ®t was obtained with a value of 25.4% for BeC2ÿ6 and 19.6%

for BeC2ÿ8 . The transmission is higher for BeC2ÿ

6 than BeC2ÿ8 ,

because the velocity of the BeC2ÿ6 at the terminal is very close to

the optimum for stripping into the 3+ charge state, whereas the

velocity of BeC2ÿ8 is signi®cantly lower.

Fig. 5. (A) A two-parameter (DE vs. E) representation of the

C3� ions, when BeC2ÿ6 ions are injected into our tandem at

terminal voltage of 7 MV. (B) A projection of the two-param-

eter plot onto the energy axis. The peaks labeled C, 2C, 3C, etc.,

correspond to the arrival of single C3� ions, two C3� ions in

coincidence, three C3� ions in coincidence, etc. arising from the

dissociation of a single BeC2ÿ6 ion. Although pileup rejection

was used, the count rate was rather high (2 kHz) making some

pileup inevitable. The contribution from pileup for most peaks

was negligible, but pileup is responsible for the two counts at

124 MeV.


and those predicted using Eq. (1), when BeC2ÿ6 and

BeC2ÿ8 are injected into the accelerator. The ®t

requires the adjustment of a single parameter, thepositive-ion transmission (from the terminal to thedetector), which was found to be 25.4% for BeC2ÿ

6

and 19.6% for BeC2ÿ8 . Note that these values are

much higher than the overall transmission (fromion source to detector) of 5.4% measured forBeC2ÿ

6 . The high transmission for the positive ionsformed in the breakup of BeC2ÿ

6 suggests that thelower source-to-detector transmission for BeC2ÿ

6

compared to Cÿ3 (noted above) occurs during ac-celeration of the negative ion, and not after strip-ping at the terminal.

Using the accelerator and our six-anode ion-ization detector, we searched for and successfullydetected BeC2ÿ

4 , but its intensity was over twoorders of magnitude less than that of BeC2ÿ

6 . Wewere just barely able to detect it using our ion-source test facility. Using both the test facility andthe accelerator, we searched unsuccessfully forBeC2ÿ

3 and BeC2ÿ7 , and conclude that if BeC2ÿ

7

exists at all, its intensity is <10ÿ4 that of BeC2ÿ6 .

We guessed that the very weak peak at mass45.5 was Be13

2 C12C2ÿ5 , and con®rmed this identi®-

cation on the accelerator by observing the ®vepeaks due to C4�, and then by dropping the ter-minal voltage of the accelerator by 10 kV, the twoBe3� peaks. A second peak at mass 57.5 was sim-ilarly con®rmed to be Be13

2 C12C2ÿ7 .

5. Further con®rmation

Initially, we hoped that we could determine themolecular structure of the BeC2ÿ

n ions from Cou-lomb Explosion Images (CEI) obtained at theterminal of the tandem. The details of the ap-proach are described in Ref. [11]. Here we sum-marize the technique.

To produce a visible track in an appropriatematerial, an ion must have su�cient energy ±usually a few 100 keV/amu. If one hopes, as wedid, to glean structural information, even moreenergy (�1 MeV/amu) is necessary to reduce theunwanted e�ects of multiple scattering. For heavyions, obtaining these energies requires the use of anuclear-physics type accelerator such as our FN

accelerator. Since the dianions are destroyed at thetandemÕs central terminal, imaging must occurthere. The procedure was as follows: A dozenCoulomb explosion ``cameras'' were prepared (seeFig. 9 in Ref. [19]) and mounted on our standardstripper-foil frames. These ``cameras'' consist of a1 lg/cm2 thick carbon foil supported on an electro-formed 90% transmission Ni mesh separated by adistance of 840 � 75 lm from a 0.25 mm thickpolycarbonate plastic sheet manufactured to beespecially sensitive to track formation. Theseframes were loaded into the stripper-foil carrousel,which holds sixty frames). The carrousel allowedus to raise and lower the frames out of and into thenegative-ion beam while the accelerator was op-erating.

Technically, this approach o�ers several chal-lenges. The greatest inconvenience is that the ac-celeratorÕs pressure vessel has to be pumped outand the accelerator-tube vacuum broken both be-fore and after the experiment to install and removethe foils. Another major di�culty is estimating theproper `èxposure'' for the Coulomb explosion®lms. For the BeC2ÿ

n dianions, especially with theslits closed as tightly as they were to reduce thecount rate at the terminal of the tandem, the in-jected beam was almost entirely composed of thedianions despite the lack of an electrostatic ana-lyzer (see Section 3 and Fig. 3). Because of thepurity of the injected beam, we were able to esti-mate fairly accurately the exposure at the terminalfrom the count rate of C3� at the detector and theestimated transmission of the positive ions. Weadjusted the slits of the negative-ion magnet toyield about 20 events per mm2 in the plastic.

Examples of the results obtained for BeC2ÿ4 ,

BeC2ÿ6 , and BeC2ÿ

8 are shown in Fig. 7. The ®guresare dominated by the dianions, especially in thecases of BeC2ÿ

6 and BeC2ÿ8 where few other ions are

visible. In all of the ®gures, the smaller size of thetrack made by the Be atom makes it distinguish-able from the C atoms, but for clarity, in the lowertwo frames, the positions of the Be atoms are in-dicated by arrows. Each pane is a reproduction ofa single photographic frame ± not a composite ofseparate photographs. There is more backgroundin the BeC2ÿ

4 images because, BeC2ÿ4 is nearly two

orders of magnitude weaker than either BeC2ÿ6 or


BeC2ÿ8 , and the neighboring peaks at mass 28 and

mass 27 are quite strong (28Siÿ and Beÿ3 , respec-tively).

Although these ®gures present convincing sup-port for the identi®cation of the dianions, they

make it clear how di�cult it is to extract structuralinformation from CEIs of even moderately small(5 atom) molecules.

6. Relative abundance of BeC2ÿn ions

The structure of the Cÿn spectrum has beendiscussed in a number of Refs. [10,11]. Here wewill consider only the features of clusters con-taining both C and Be. Fig. 8 shows the relativeintensities of various Be±C cluster anions (circles)and dianions (triangles). As is the case with carbonclusters [10], the BeCÿn clusters, show a strongeven±odd e�ect, with the clusters containing aneven number of carbon atoms more than an orderof magnitude more intense than the clusters with

Fig. 8. The relative intensities of the anions BeCÿn and Be2Cÿnand the dianions BeC2ÿ

n and Be2C2ÿn are plotted as a function of

the number of carbon atoms. Note the extremely pronounced

(>four orders of magnitude) odd±even behavior for BeC2ÿn , the

much weaker odd±even behavior for BeCÿn (approximately one

order of magnitude), and the almost non-existent odd±even e�ects

in Be2Cÿn . The Be2C2ÿn currents are about two-and-a-half orders of

magnitude weaker than the corresponding BeC2ÿn currents.

Fig. 7. Single-frame microphotographs of the tracks produced

in polycarbonate plastic following the Coulomb explosion of 15

MeV BeC2ÿ4 , BeC2ÿ

6 , and BeC2ÿ8 ions in a 1 lg/cm2 carbon foil.

The upper frame was obtained while injecting mass 28.5 (i.e.

BeC2ÿ4 ) and shows ®ve BeC2ÿ

4 clusters that are circled for clarity.

Several tracks and clusters of tracks arise from the injection of

impurity negative ions, notably 28Siÿ and 9Beÿ3 . The tracks

corresponding to Be, C and Si are clearly distinguishable from

one another by their diameters. Tracks from impurities are

nearly completely absent when injecting BeC2ÿ6 and BeC2ÿ

8

(shown in the lower two panels). The Be atom in each cluster is

identi®ed by an arrow. The central frame was obtained while

injecting an extremely attenuated mass 40.5 beam for 2 s. The

lower frame is a 1-s exposure while injecting mass 52.5.


an odd number. The intensities of the clustersdecrease with increasing mass, becoming about afactor of two hundred less intense with the addi-tion of each carbon atom. The anion clusterscontaining two beryllium atoms show only a slightodd±even e�ect, with clusters containing an oddnumber of carbon atoms slightly favored (but byless than a factor of 2) over even clusters. In gen-eral, the Be2Cÿn clusters are 20 to 100 times lessintense than the BeCÿn clusters with the samenumber of carbon atoms.

The smallest BeC2ÿn cluster that we saw clearly

on the test bench contains six carbon atoms, al-though the cluster containing four carbons wasdetected during the experiments on the accelerator.The dianion clusters show an extreme even±odde�ect ± clusters containing an odd number ofcarbon atoms were not observed at all, setting anupper limit for their abundance at four orders ofmagnitude lower than the dianions with an evennumber of carbon atoms. The dianions containingtwo beryllium atoms are considerably weaker thanthose containing a single beryllium atom. Theobserved ratio of BeC2ÿ

6 to Be2C2ÿ6 (measured as

Be132 C12C2ÿ

5 because, only ``half-integral'' massdianions can be positively identi®ed on the testbench) is 630:1, but allowing for the isotopicabundance of 13C, this ratio is �40:1. We wereonly able to observe the di-beryllium dianions atmasses 45.5 and 69.5; BeCÿ4 at mass 57, presum-ably obscured the peak at 57.5 (Be13

2 C12C2ÿ7 ). For

these ions as well, no clusters containing an oddnumber of carbons were observed.

7. Structure of BeC2ÿn

We are able to extract disappointingly littleinformation about the molecular structure ofBeC2ÿ

n from the CEIs, examples of which areshown in Fig. 7. However, based on the completeabsence of any experimental evidence for BeC2ÿ

nions with n odd, and based on the steric limitationsof forming small rings with Be and C, we proposethe two structures shown in Fig. 9. Needless to say,nearly identical additional structures are alsopossible with the Be atom in intermediate positionsbetween the extremes shown in the ®gure.

We suggest that an unbranched linear structurewith alternating single and triple bonds couldstabilize the dianion and would explain the lack ofdianion clusters containing odd numbers of car-bon atoms. The position of the Be atom within themolecule is not known. Conjugation and chargeseparation are both greater in the structure thathas the Be atom located at a terminus of the car-bon chain; two reasons why this con®guration maybe more stable than the structures with the Beatom within the carbon chain. On the other hand,Be is slightly less competent than C in stabilizingan extra charge, and dividing the conjugationsystem into two would also reduce the coulombrepulsion between the two extra charges. If theberyllium plays a role in separating the two extracharges, it would provide a reason why BeC2ÿ

ndianions are more stable than C2ÿ

n dianions.

Fig. 9. Two possible structures for the BeC2ÿn ions are shown.

Note that the structure in (B) is linear and rigid, while the

structure in (A) consists of two rigid linear carbon chains joined

at an angle >100°. For both structures, a dipole moment would

be expected that would cause the molecule to be accelerated

with the Be atom trailing. Although the Coulomb explosion

images provide little evidence in favor of one structure over the

other, we prefer (B) based on the presence of Cÿ8 in the EA

spectra of the breakup products of BeC2ÿ8 obtained on the test

facility.


Linear unbranched structures with alternatingsingle and triple bonds could explain the absenceof BeC2ÿ

n ions with odd numbers of carbon atomssince an odd number of carbon atoms cannot bebuilt with alternating single and triple bonds. Adianion with an odd number of carbon atomswould require the beryllium atom to be at one endof the molecule double bonded to a carbon atomthat (formally) is the location of one of the extraelectrons. This carbon atom would be singlebonded to a chain of carbon atoms bound by al-ternating single and triple bonds, and the otherextra electron would formally sit on the end car-bon. Resonance is also possible in this structure,but charge separation would be smaller and theenergy penalty for having a double-bonded beryl-lium would be large.

How might we distinguish between these alter-native structures? As shown in Fig. 9, the moleculewith Be on the end would be linear; a molecule withBe located elsewhere would be bent. We see nomanifestation of a linear structure in the CEIs, butnor are we likely to. Regardless of where the Be islocated, the BeC2ÿ

n dianion would have an electricdipole moment that would result in the ion beingpreferentially oriented in the electric ®eld of theaccelerator. A linear ion would arrive ``head ®rst''at the stripper foil, and in this orientation it wouldproduce CEIs very similar to the bent structurescontaining Be within the chain. Surprisingly, someindication of molecular structure was obtainedfrom the studies on the test bench. In Fig. 3, it waspointed out that the peak at E/q� 1.83 is due to theloss of a beryllium atom and an electron from aBeC2ÿ

8 ion. Such a loss can only occur if the be-ryllium atom is at one of the termini of the mole-cule. Of course, there is nothing to say that onlyone structure of BeC2ÿ

8 is stable, or that if multiplestructures exist that they would have identicallifetimes. But the results of the test bench indicatethat, at least some of the BeC2ÿ

8 ions formed withlifetimes greater than a few microseconds have theBe atom at one of the termini of the molecule.

The proposed structures also provide a quali-tative argument for why the dianion containingtwo Be atoms is less stable than the dianion withonly one. If the Be atoms are located at the terminiof the molecule, the Be2C2ÿ

n dianion would be less

stable than the BeC2ÿn dianion because now both

extra electrons would now be concentrated on Beatoms. If the Be atoms are located within thechain, the additional Be atom will further decreasethe conjugation of the alternating single and triplecarbon bonds, and consequently the sizes of the``boxes'' containing the extra charges. The exis-tence of the di-beryllium dianions probably isfurther evidence for the Be ions being located atthe termini of the ions.

8. Lifetimes of the BeC2ÿn ions

On the ion-source test facility, we were able tomeasure the ``lifetimes'' of the two most intenseBe±C cluster dianions. We use the term lifetime inquotes because the lifetime of a molecular ion ispoorly de®ned due to the multitude of initial statesof varying levels of vibrational and rotational ex-citation, and the plethora of ®nal states into whicha molecular ion can decay. Since, we make no ef-fort to ``cool'' the ions produced by the sputtersource, the lifetimes we measure are a combinationof the lifetimes of various excited states. We expectthat the lifetime of every excited (vibrational orrotational) state is shorter than the lifetime of thegroundstate, so from this standpoint, the lifetimethat we measure is a lower limit for the lifetime ofthe groundstate of the molecule. In general, for aninitial state composed of a number of states, Si,each decaying with a rate ri, the overall decay rateis given by:

r �X

i

firi; �2�

where fi is the fraction of the initial state in stateSi. The e�ective ``lifetime'' of the ion is the inverseof the total decay rate. But by de®ning it so, thelifetime is not time invariant, because the relativeproportions of the states change with time. As timegoes on, the states with the shortest lifetimes aredepleted and the lifetime of the ion increases.Therefore, a decay-rate measurement at a singletime is not su�cient to determine the lifetime ofany individual state if more than one state ispopulated. But, it does allow certain limits to beset. A lifetime measured at any time will always be


an upper limit for the shortest lifetime. A lowerlimit for the lifetime contributing to the decay atsome particular time can be set if there is a boundon the abundance of the ion at t� 0.

From a practical standpoint, the lifetime wemeasure is very useful. It accurately re¯ects thesurvivability of ions produced in a sputter source(the only e�cient means we know of producingdianions), a question of utmost importance to thestudy of these ions in a mass spectrometer.

The question of decay mode is also trouble-some. In the case of singly charged negative ions, aneutral fragment is always a product when the iondecays. When a dianion decays, a neutral does nothave to be produced. Fission into two chargedfragments, autodetachment of an electron orbreakup into multiple fragments are all possible.The apparatus we constructed (inset of Fig. 1) canbe used to search for ®nal states containing aneutral fragment or for ®nal states with onlycharged fragments. With the test bench set up as inthe inset, we determine the rate of neutral forma-tion from the ratio of the current in the electronmultiplier with the electrostatic de¯ecting plates onto the current with them o�. Only when a neutralfragment is produced in the drift region betweenthe EA and the de¯ecting plates is there a currentwith the electrostatic de¯ecting plates on. Decayinto (negatively) charged ®nal states is measuredby scanning the EA. The E/q of a decay productalways di�ers from that of its parent.

Decays can also be induced by collisions withresidual gas molecules. The vacuum in the testbench is typically �2 ´ 10ÿ7 Torr. Assuming acollision cross section of about 1 ´ 10ÿ15 cm2

(probably an over estimate), the collision rate isexpected to be �4 ´ 10ÿ4 over the e�ective inter-action length (65 cm for charged-product studies,71 cm for neutral-product measurements). In somecases, we have determined the dependence of decayrates on pressure over a pressure range of over twoorders of magnitude. Such a study is shown in Fig.10, where we varied the pressure between themagnet and EA from 2 ´ 10ÿ7 to 3 ´ 10ÿ5 Torr. Atlow pressures, the Cÿ8 current goes to zero imply-ing that it is formed (primarily, exclusively?)through collisions with residual gas molecules. Weestimate the cross section for this process to be

8 ´ 10ÿ16 cm2. The cross section for the productionof BeCÿ8 from collisions is smaller, 1.4 ´ 10ÿ16 cm2.A smaller cross section for the loss of a singleelectron makes sense ± negative ions are known tobe fragile and loss of only one electron from adianion is not likely to be the most probable out-come of a collision. In fact, comparing Figs. 10and 4 it is clear that neutralization of the dianion isthe most likely result of a collision with a residualgas molecule. An extrapolation of the BeCÿ8 cur-rent to zero pressure does not go through zerosuggesting that the dianion is not stable againstautodetachment. An estimate of the lifetime withrespect to this branch is 410 ls. Similar measure-ments of BeC2ÿ

6 yield an autodetachment lifetimeof 100 ls, and cross sections of 5 ´ 10ÿ16 cm2 forthe loss of an electron and 6.3 ´ 10ÿ16 cm2 for theloss of a beryllium atom and electron.

We measured the production of neutrals fromBeC2ÿ

6 and BeC2ÿ8 8.6 and 9.8 ls after their pro-

duction in the ion source. BeC2ÿ6 decayed with a

rate implying that the decays were dominated by astate with a lifetime between 1.5 and 413 ls, andBeC2ÿ

8 with a rate indicating a state with a lifetimeof 1.1 to 471 ls. The lower limits are set by as-suming that the current of BeC2ÿ

6 leaving the ion

Fig. 10. The pressure dependence of the detachment of BeCÿ8and Cÿ8 from BeC2ÿ

8 is shown. Two observations are worth

making. BeCÿ8 increases more slowly with pressure than Cÿ8 ,

suggesting a larger collisional cross section for the latter. And,

the current of Cÿ8 extrapolates to zero current at zero pressure,

while the current of BeCÿ8 does not, suggesting that Cÿ8 is

produced only through collisions, whereas BeCÿ8 is formed both

through collisions and by the autodetachment of an electron

from BeC2ÿ8 . See text for details.


source is equal to the current of BeC2ÿ6 produced

under identical conditions (�30 times larger thanthe current of BeC2ÿ

6 measured at the electronmultiplier). A similar limit for the maximum cur-rent for BeC2ÿ

8 was taken to be that of BeCÿ8 .These lower bounds are extremely generous: it isunlikely that BeC2ÿ

n and BeCÿn form with equalprobability. If the dianion current leaving thesource is not too much smaller than the currentmeasured in the electron multiplier (as we believeis likely), the actual lifetime will be close to theupper limit.

The transit time from the source to the terminalis �5 ls, so that if the lower transmission of theBeC2ÿ

n clusters (compared to Cÿn=2) is to be ex-plained by decay, the lifetime of the BeC2ÿ

n clusterswould have to be �3.1 ls. Our lifetime measure-ments do not fully exclude this possibility, al-though it would require the lifetime of the state tobe at the lower end of the allowed range.

9. Discussion

The experimental observation of this new classof multiply charged anions has stimulated theo-rists to recalculate electron a�nities of negativeions, and in a recent article in Science, Schelleret al. [20] summarize the state of knowledge of thestability of gas-phase multiply charged anions.Experimental evidence has already been shown tobe at odds with the present calculations in severalsigni®cant ways. For instance, calculations yieldtwo general characteristics for carbon clusters: (1)stability increases with size, (2) even clusters aremore stable than odd clusters. However, withoutad hoc assumptions about geometry, calculationsdo not correctly predict that C2ÿ

7 is the ®rst stablecluster (calculations for a linear Cÿ7 predict that asecond electron would be unbound by 2 eV) and infact predict that the ®rst stable dianion of carbonshould be C2ÿ

10 . Even with the improved geometricassumptions of Sommerfeld et al. [21,22] that re-sult in C2ÿ

7 being bound, additional problems arisebecause with these geometric assumptions, C2ÿ

7 ispredicted to be more stable than C2ÿ

8 , and C2ÿ9

more stable than C2ÿ10 , both at odds with experi-

mental evidence. Experimentally, C2ÿ10 is the most

abundant carbon dianion; calculations predict in-creasing stability at least through C2ÿ

16 . In defenceof theory on this last point, the apparent peak instability of C2ÿ

10 might be due to the sputter processand the decreasing probabilities of ejecting largerand larger multi-atom clusters and not becauseC2ÿ

10 is the most stable cluster dianion. Theorypredicts that C2ÿ

10 is bound by only 0.5 eV and thatmore stable cluster dianions with electron a�nitiesgreater than 3.6 eV can be built on alkali-metal oralkaline-earth halides. We have looked for dian-ions of lithium, beryllium and magnesium ¯uoride,[18] and although we ®nd dianions of the alkalineearths (BeF2ÿ

4 and MgF2ÿ4 ), we observe none from

lithium and ¯uorine (LiF2ÿ3 and Li2F2ÿ

4 ) althoughthe alkali-metal halides are predicted to be themost stable. Yields of alkaline-earth halide dian-ions are considerably smaller than carbon-clusterdianions suggesting that the electron a�nities ofthe carbon clusters are actually greater than thoseof the alkaline-earth halide clusters.

Clusters of the form BeCn are the most proli®cgaseous dianions yet discovered. On our tandeminjector which has larger slit openings than our testfacility, we have observed up to 1 nA of BeC2ÿ

6

ions. BeC2ÿ4 is the lightest dianion yet observed.

These ions have not to our knowledge receivedtheoretical consideration.

Acknowledgements

This work was supported by a grant from theNSF (Phys 9417364) that has enabled us tomaintain our FN tandem in operable condition.We also wish to express our thanks to Mr. HarryWhite who assisted in all phases of this work. Wewould also like to thank Ted Litherland whoprovided many constructive criticisms in his reviewof this paper.

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Observation of BeC2−n, a particularly abundant gaseous dianion

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