Counting the Atoms: Some Applications in Chemistry G. S. Hurst Oak Ridge National Laboratory, Oak Ridge, TN 37830 We think of our world as a collection of atoms arranged in a variety of ways to form chemical compounds and all miterial substances. I t is, therefore, fitting that we should learn to actually count the individual atoms and molecules. To learn how to take matter apart atom-hy-atom and to count each atom according tc, iw~type,regardless of its initial chemlcal or physical state. is prcsumallly a worthy aspiration of the analvtical chemist. The advent of the laser has created real hope that these aspirations will be realized. The counting of atoms is not merelv an intellectual exercise set aoart from real-world applicacons. On the contrary, even tiough the canabilitv is scarcelv more than five vears old.. oractical an. plications have been made in many fields of chemistry, physics, the environment, and industry. Why does the modern laser make it possible to count atoms? To beein to answer this auestion. we need to think about how photons interact with atoms 'and what are the conseauences of such interactions. Basicallv, it has been knownsince the Bohr theory that when are absorbed bv an atom electrons are promoted either to excited states in hbund-bound transitionsbr to the ionization continuum. The production of excited states reauires photons of particular wavelengths, depending on thetype of atom, whereas continuum ionization can occur a t any photon frequency ahove a threshold. Thus, if lasers are used to fire photons intoatoms we can expect to see reemissionof light from theexcited state (fluorescence) or the appearance ofelectrical charge (photoionization). These are the two consequences of photon absorptions in atoms, and both of them have been used for the sensitive detection of atoms. In hoth cases sensitivity is derived from the fact that with lasers a very large number of photons can be fired into the atom, while only a few interactions need to occur to enable an observation since hoth vhoton and ionization detection are very sensitive. I t is readily understood whv the fluorescence method is selective to a tvpe of atom. In the photoionization method selectivity can come about onlv when one or more bound-bound (or resonance) transitionprecedes the final ionization step. Sensitive and selective detection of atoms is but one of the applications of laser spectroscopy, a subject developed especially by Arthur Schawlow who received a Nobel award for his work in 1981. Another recipient of the 1981 award was Nicolaas Bloemhergen whose work in nonlinear optics forms the basis for generating a wide variety of radiation wavelengths with la*-,... .". Early work nn laser fluorescence was aimed mainly at the determination of very low concentrations of atoms in a cell rather than the countineof individual atoms. Thus. Fairbank et al. ( I ) were able to measure as low as 100Na atoks per cm3 of volume hv a resonance fluorescence techniaue. Another fluorescence"technique (2) takes advantage of bonresonant nhoton emission from an excited atom. which helvs to reduce hackgrounds caused by resonance sratterlng fr(;m the laser beam itselL Aaaln, such methods are usuallv d ~ r w t r dtoward the detection i f s&all concentrations of atoms rather than the
Research sponsored by the Officeof Health and Environmental Research, US. Depanment of Enerqy under conbact W-7405eng26 w th the Union carbide Corporation..
counting of atoms. In this brief review we concentrate on methods for actually counting atoms based primarily on a photoionization process which we call Resonance Ionization Spectroscopy (RB), but we make reference again to additional fluorescence methods which can also be used to count atoms in special circumstances. Resonance Ionization Spectroscopy
Resonance ionization spectroscopy originated early in 1974 as a new form of atomic and molecular spectroscopy in which wavelength-tunable light sources are used to remove electrons from (i.e., to ionize) a given kind of atom or molecule. At the Oak Ridge National Laboratory (ORNL), laser-based RIS techniques have been developed and used with ionization detectors such as the proportional counter to show that single atoms can be counted. When an atom (or molecule) is subjected to a light source s an annular freauencv w . these ohothat provides ~ h o t o n of tons can he ahsorbed by the at& if the photon energy (h is Planck's cmstant divided by 2n)is almost eractls the difference in energy between an atom in its normal or ground state and some excited state. Suppose, as in scheme 1of Figure 1,that a light source is tuned to a frequency which excites a given kind of atom, A. If the light source is a tunable, pulsed laser of very narrow bandwidth, it is highly unlikely that any other kind of atom will be excited. But the atoms which are in an excited state can he further excited to the ionization continuum where electrons are set free, provided that the ionization potential of the atoms is less than 2hol. While the final ionization step can occur with photons of any energy ahove a threshold, the entire processis a resonanceprocess. In sharp contrast with other iunization means-for example, X-ravs or radioactive sources-RIS is a selective orocesi in whi& only those atoms that are in resonance wit< thelight source are ionized. Modern oulsed lasers are excellent tunahle sources for RIS; furtherm&e, they provide enough light in a single vulse to remove one electron from each atom of the selected type. A laser that provides 100 mJ of photons in a single pulse of l0W-sec duration can be tuned to ionize nearly all of the atoms of a given type that may happen t o be contained in avirtual test tube whose diameter is 1cm and whose ~
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@ RIS SCHEMES
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Figure 1. Various laser schemes used in MS. With only five basic schemes,all of the known elements except He and Ne can be ionized. Familiar nuclear physics notation is used to classify Me RIS processes. Volume 59 Number 11 November 1982
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Figure 2. Classification of RIS schemes for Me elements.
length can he very long (even meters), if the divergence of the laser beam is low. Many laser schemes can be used in the RIS process as shown in Figure 1. In this figure the notation A(wl,wle-)A+ is used for the two-step process described above. On the other hand, the frequrncy ;fa laser can bedouhled to 2wl,so that scheme 2 requires only one laser, while schemes 3,4, and 5 involve two lasers to generate photons at frequencies oi wl and w?. For further discussion of laser schemes for HIS,see reference 0). With these five schemes only, it is now possible to ionize selectively every known element in the periodic table except two of the noble gases, He and Ne (see Fig. 2). One-Atom Detectlon Roth the high selectivity and theextraordinary sensitivity a laser directly throueh of HIS were drmonstrated bv. oulsine . a proportional counter (see Fig. 3). It was shown 11y Curran et al. ( 4 ) in 1919 that the improved versionof the 1908Rutherford-Geiger electrical counkr (now known as a proportional counter) can be used to count single electrons at thermal energy. Therefore, if lasers are used to remove one electron from all of the atoms of a selected type, one-atom detection is possible. Proportional counters are normally filled with gases like Ar (90%)and CH4 (10%).But, for example, a pulsed laser tuned to 4555 A can ionize with unit efficiency each atom of Cs without producing background ionization of the counting eas. In the original demonstration (5) of one-atom detection it ORNL it w& proven that one atom of Cs could be selected out of 1019 atoms of the counting gas (Ar and CH4). Another important form of atom counting involves the time-resolved detection of a single daughter atom in flight following the decay of a parent atom. Thus, it was shown ( 6 ) that an individual atom of Cs could be counted from the fission decay of an individual atom of the isotope 252Cf. The energv released in the fission process generated a sianal in a charged particle detector thattriggereb the laser used to accomplish the RIS process Cs(w~,w,e-)Cs+.The experiment that daughter atoms c& be counted in coincidence with the decay of parent atoms. Such techniques could 896
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Figure 3. Schematic of an experiment conducted to prove lhat RiS can be used to detect a single atom.
eventually work for most of the daughter atoms associated with radioactive decay and could uossiblv be used to reduce backgrounds greatly in low-level counting facilities. Claslcal Chemlcal Physics Applications The capability for detecting a population of just a few atoms has made it possible to investigate some problems in classical chemical physics which previously were difficult or impossible. Precision measurements of the diffusion of free atoms among other atoms and molecules have been made in sufficient detail to test the basic diffusion equation in both time and space domains. The determination of rates of reactions of extremely reactive species (such as alkali atoms) with other atoms or molecules is now possible. Since only a few of these reactive atoms need to be produced, several problems concerning corrosion of the apparatus and the production of complicated chemical by-products are avoided. Study of a population of a few atoms (e.g., 10) to observe their statistical behavior has been made.
These measurements of the diffusion, chemical reaction, and statistical fluctuation of atoms are best made by starting with a chemically inert source such as an alkali-halide molecule. Upon photodissociation of CsI (for example) with a pulsed laser in the UV region, a well-defined source of Cs atoms is produced along the narrow laser beam a t some time, say t = 0. At any time t > 0 another laser can be pulsed to detect Cs atoms if they exist as free atoms in the path of this detector laser. One geometry for carrying out these experiments is illustrated in Figure 4. For the geometry of Figure 4 the appropriate diffusion equation is
where p is the distance hetween source and detector, t is the time. U is thediffusion coefficient.and Bis the rate constant for loss due to chemical reactions; hes solution for the concentration of free atoms n(p,t) is
for a line source of A atoms per unit length created at t = 0 and located in an infinite medium. The source and detector can
Figure 4. Schematic of method used to study dinusion, chemical reactions, and statistical fi~ctuationsof atoms.
he assumed to be well separated from any surfares since atoms are both liberated and delected with pulsed laser beams. The data shown in Figure 5 can be analyzed to obtain Band D. We note that thequantity n(o,,t)/n(pdJ is independent of 3 hut contains D ;thus, pr&ision measurement of U can he made even when the chemically reactive medium has a large 3. In other words, if experiments are done at two different separations between the source and detector lasers, chemical effects can be cancelled in the ratio n(pl,t)ln(p2,t). These methods have been used to ohtain the diffusion coefficient for Cs atoms and for Li atoms in several eases or gas mixtures. Besides providing more accurate measurements of the diffusion roeifirients for theye difficult chemical environments. the method has possible fundamentalvalue. Since both time and space resolution are inherent in the method, it provides a very detailed test of the validity of the diffusion equation itself (7). studies have also been made to obtain the reaction constant 0 in various chemical environments. Thw, Grossman et al. (8) studied the reaction of Cs with 0 2 in various atmospheres of both He and AT.Similar experiments have been reported hy Kramer et al. (9)for Li atom reactions with 0 2 in He and Ar. These were slightly more complex laser experiments since one laser at 2950 A was used to detect Li in the RIS scheme Li(q,wz,e-)Li+ with ol corresponding to 6708 A and w2 corresponding to 6104 A. The source laser and the detector lasers .all overlapped in space, this being the geometry in which chemical effects are most easily separated from diffusion losses. One interesting result from the Li experiment is shown in Fieure 6 where it is seen that B s the nressure for . d e.~ e n don h o t h ~ eand Ar. These complex pressure-dep;ndent data sueeest that the reaction of 1.i with 0, to make stable LiO? both by energy transfer from intermediates like (LiO?)*and 01 reactions with intermediates like LiAr. .4 particularly interesting experiment in statistical mechanics has just been completed in our lahuratory I 10). Einstein ( I 1 ) d~scusseda Gedanken experiment to test the ergodic hvr~othesisfor the case of freely diffusing atoms. Essentially, the geometry in Figure 4 is tlie one ~ o ~ s i d e r ehyd in stein except he virualized an infinite plane Rourre and infinite plane detector. In any case, two tests uf the solution to the diifusion equation could he visualized. In one casea large number of atoms would be released at t = 0 and the detector would essentially measure the density function n(p,t) on each trial for a particular p and t. This method was called a space summation method. Einstein's time summation method was visualized as a process where a small number of atoms would be released a t t = 0,such that the detector a t p and t would count a single atom and with low probability; thus, a series of trials are required so that probabilities are involved in esti-
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Figure6. Data on the rate constam for Li reaction with O2 in atmaspheres of He or Ar.
Volume 59 Number 11 November 1982
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Figure 7. Experiments data obtained on Einstein's "Gedanken" experimentto illustrate the ergodic hypothesis.
only lasers for selective ionization and proportional counters for sensitive detection is the development by Mayo et al. (16) a t the National Bureau of Standards (NBS). They have developed Laser Ablation and Resonance Ionization Spectrosconv (LARIS). as shown in Fieure 8 for the analvsis of a few .impurity atoms in a solid samile. With LARIS aiaser is used to ablate atoms from a solid. followed with a laser for RIS of the neutral atoms. Using a proportional counter as an electron detector. the NBS eroun was able to detect down to 5 X 10" Na atomdcm3 of el&tronics grade Si, or 1atom of Na in 10" atoms of Si. Since one electronic device in modern VLSI technology has only 5 X 1O"atoms of Si, the NRS sensitivity for Na was such that less than 1 atom of Na per device could he detected. The combination of a RIS ionization source and a mass spectrometer provides the best features of two methods. Essentiallv, a RIS source for a mass spectrometer provides selelctivitjon Z and the mass analyz& provides selectivity on A. With hoth Z and A selectivity, many interferences associated with electron ionization can he eliminated and isobars can he distinguished. A particularly interesting example of the combination of RIS with mass spectrometers has been proposed (17,18) for isotopically selective counting of nohle gas atoms. Essentially, Maxwell's sorting demon can he made' to work with the intelligence to recognize even an isotope of an atom and with the memory capacity to store and count each atom. .A
mating n(p,t).If the space summation method and the time summation method agree, the system is ergodic. Our results of an actual experiment are shown in Figure 7. In basic terms, the Gedanken experiment visualized by Einstein could actually he done in the laboratory because we can now count individual atoms. Furthermore, the experiment was actually convenient because of a special property of the proportional counter-namely, it is a good digital device for counting one electron (thus one atom. assumine saturated RIS) and apood analog d&ce for summhg many llectrons (thus many at&) created hy one laser pulse. Analytical Chemistry Applications Lasers are making a major impact on the field of analytical chemistry. Some aspects are described by other papers in this conference. Even if we restrict ourselves in this paper to fluorescence and ionization, the scope would he unmanageable. However, a few more remarks i n fluorescence maybe appropriate. Fluorescence techniaues most often use cw lasers indsuch use provides good seniitivity enhanced by a longer duty cycle. This means, however, that what can be measured is a low average concentration over the duration of the measurement-in contrast to the actual counting of an individual atom. However, in special applications (llrwhere a beam of atoms can be directed through a cw laser beam, some of the atoms will scatter enough photons to enable detection of individual atoms, even with time resolution. Other applications of the "photon burst" method have been made to measure the velocity of an individual atom (12). A similar photon burst method, but using two detectors in coincidence counting, has been used by Balykin e t al. (13). However. the real Dower of the fluorescence methods mav ultimately reside in'their simplicity for analytical i n s t i mentation. Strav light backerounds have to be overcome: the nonresonance m&d by ~elbwachset al. (2) is an impre&ive step in the right direction. Another major advantage to fluorescence methods is their utilization in hostile environments to determine the concentration of a species in, for example, a plasma where ionization measurements are difficult. A major limitation yet to he overcome with fluorescence methods is their lack of generality due to the fact that cw laser sources cannot provide photons at as many wavelengths as the pulsed lasers. The use of RIS in analytical chemistry has been reviewed by Young et al. (14) and by Hurst (15). The essential advantages of RIS to any analytical system are selectivity, sensitivity, and generality to nearly all of the elements. An example of an analytical application of RIS that requires 898
Journal of Chemical Education
Weak Interaction Physics One-atom detection makes it feasible to detect extremely rare events. Measurements of neutrinos from the sun are crucial to testing hoth solar models and neutrino physics (19). Prolonged exposure to the solar neutrino flux mav nroduce on the order of 100 atoms of a particular type in a;& large tank (100,000 gallons). Previouslv, targets have been rich in 37CI SO that neutrino capture would brod;ce 37.41, a radioactive atom which can he counted bv the standard methods of radioactivity (20). Resonance ionization spectroscopy and one-atom detection (3) are making possible a much wider variety of neutrino targets. For example, an experiment under consideration involves Br-rich targets where the neutrino capture produces S1Kr. Radioactive S1Kr could be counted directly (before it decays), a technique made possible by RIS. Studies of double beta (p@)decay involving lifetimes of about loz0 years are also made possible by the counting of nohle gas atoms. Radiochemical experiments on processes such as
are especially attractive since a few kilograms of the parent
atom produces measurable numbers of noble gas atoms in a few days. Such experiments can help to determine the validity of lepton number conservation, the nature of the neutrino (whether a Maiorana or a Dirac particle), and the mass of the neutrino . ... -....(211 ~--,
modern pulsed laser, is providing direct methods for counting atoms that are well suited to these and other rare-event situations. Literature Cited
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decay are well known exSolar neutrino physics, and amples of weak interaction physics in which it is essential to have methods for rare-event detection. But there are other examples. Grand unified theories leave room for the production of stable super-heavy atoms in the "big hang." It has been ~ o i n t e dout recentlv bv Cahn and Glashow (22) that there is iittle hope for the production of the super-heavy atoms with accelerators; thus, we should spend more of our effort in looking for heavy atoms and other species as primordial particles. ..
Earth and planetary scientists and environmental scientists h a w already developed magnificent tools for the detection of rare even&; foremost of these have been decay counting and mass spectroscopy. These investigators are increasingly looking to the laser for increasing the sensitivity of their tools. Improved instrumentation will find immediate applications in oceanography, groundwater dating, polar ice cap dating, and in radioactive waste management. For instance, 39Ar with a half-life of 270 years occurs naturally in the atmosphere and would be ideal as a tracer for ocean water circulation studies; similarly, 85Kr with a half-life of 2 X 1 0 5 years is ideal for groundwater circulation studies and for polar ice cap dating. In these examoles where the half-life is so long, we must develop direct comting (as opposed to decay cou&ng) methods. Resonance ionization spectroscopy, made possible by the
(1) Fsirbank,Jr., W.M.,H&nseh,T. W.andSchawlow,A. L . , J Opt. Sm.Amer.65.199 (1975). (2) Gelbwachs, J.A.,Klein,C. F.,and Wesse1.J. E.,Appi.Phys. ktf.,30,489 (19771. 13) For s summary and review of theearly hisfmy of RIS, see Hunt. G. S., Pame, M. 6.. Kramer, S.D.,andYoung, J. P.,RPu, Mvd.Phys.51.767 (19791. (4) Curran, S. C., Coekroft, A. L., and Angus, J., Phil. MW, 40,929 (1949). (51 Hurst, G. S.. Nayfeh, M. H., and Young, J. P., Appl. Phys. Lett., 30, 229 (1977). (6) Kmmer. S. D., Bemia, Jr., C. E., Young, J. P.. and Hurst, G . S.. Opt. Loll.. 3, 16 11978). (71 Hunt. G. S., AUmsn. S. L., P a n e , M. G..and Whi1aker.T. J., Chem Phye. Lelt.. 60,
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(9) ~ ~ a m S. ~ D., ; . ~ e h m a n n ,E., ~ .Hum, G. 8.. Payne, M. G.. andYoung,J. P.. J. Chom. P h M , 76(7) 3614 (1982). (10) Iturbe, Jscinto,Allmsn, S.L..Hurst.G.S.,andPayne,M. G. (tobepubliahedl. 1111 o f the~ Bmwnian ,--,F.mrtsin. ~ A..''lnvestieationson ~ ~ ~ t h e,T h w. ~ , Mowment" (Editor: FWh. R.),Dover, New ~ b r k1956. , (12) Groen1oea.O. W.,Clark, 0.L., K a " f m u f , S . L . , L , J. H.,Opl. Comm.,23,236(1977). (131 Bahkin.V. I..Lctokhov, V. S.,Mishin,V. I.,andSemchishen,V. A., JETPLett.26, 357 (1977). (14) Youna,J.P..Humt,G.S.,Krsmer,S.D.,andPayne,M.G.,Anolyl Chem .S1,1050A (19%). (15) Hurst, G.S.,Anolyt. Chem., 53,1448A(1981). (16) Mayo, S., Lucatorto,T. B., and Luther, G. G., Anal. Cham. 54 [3l, 553 11982). (17) H m f , G . S.,Payne,M.G.,Kramer,S, D.,andChen,C. H.,Phya. Todw33.No.9.24-29 (1980). E.,md . Kramer, S. (18) Hursl. G. S.,Payne, M. G.,Chen.C.H., W i I l i , R . D D , L e h m ~ n , B D., in "Laser Speclraseopy V (Editors: McKeUlu. A. R. W.. Oka. T., and Stoieheff, ~. B. P.), Springer-Vorlsg. New YorkiBerlin. 1 9 8 1 , ~5966. (19) Bahcall. J. N.,Rau. Mod. Phys.,50,881 (1978). 1201 Davis. Jr.. R..and Evans. J. M.. in Proceediws 13fhlnfernalionol CoamicRodiolion ~~~
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,211 Korcn, S P.and I'r#mahnff H . i n ,\Ipha. Bets indCammdRa) Sparfr.dopy" ~ l a , r . rS e ~ n a h nK. S r r h Holland Puh.lrhlndl'o ,.+mrurddn.. 1965. d? Cal.r~.l(.lr. . n r l U h r h ~ u j l..Sr~enc.. ? l J . i i 19b1,
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