Laser ablation of graphite is one of the methods ofcarbon nanoparticle production. A laser pulse, typ-ically lasting �10 ns, produces a power density suf-ficient to vaporize a small sample of the target. Thespectrum of the resultant plasma shows lines fromatomic carbon and its ion early in the lifetime of theplasma, and molecular spectra occur as the plasmacools. Analysis of spectra recorded from laser abla-tion plasmas has proved to been a useful diagnostictool.1–6
Highly excited molecular recombination spectraare also observed subsequent to laser-induced opticalbreakdown of gases. Specifically, optical breakdownplasma generated by nominal nanosecond-pulsed,Nd:YAG infrared laser radiation of 1–100 TW�cm2
irradiance focused in laboratory air shows well-demarcated progressions and sequences of molecularemission spectra. Such spectra can be readily re-corded by use of time-resolved laser spectroscopymethods some 10 to 100 �s after the laser spark,which will show spectroscopic temperatures of typi-
C. G. Parigger �[email protected]� and J. O. Hornkohl are withthe Center for Laser Applications, The University of TennesseeSpace Institute, 411 B. H. Goethert Parkway, Tullahoma, Tennes-see 37388. A. M. Keszler and L. Nemes are with Research Lab-oratory for Materials and Environmental Chemistry, ChemicalResearch Center, Hungarian Academy of Sciences, Pusztaszeri ut59-67, H-1025 Budapest, Hungary.
Received 20 January 2003; revised manuscript received 28 May2003.
cally 6000 K.7 Several orders of magnitude less-intense Nd:YAG radiation of some 10–100 GW�cm2,when it is focused on a solid target, also generateshighly excited molecular spectra in the plasma plumeemanating from the target. Detailed spectroscopicanalysis of selected diatomic molecules is accom-plished with the program BESP,8 which utilizes ac-curate line-strength files.
We report here the progress of the joint effort of ourlaboratories at the University of Tennessee SpaceInstitute and the Chemical Research Center of theHungarian Academy of Sciences, to use atomic anddiatomic spectra recorded from laser ablation plas-ma9 as diagnostic tools for studying nanoparticle pro-duction. We present details of the computation ofthe line-strength file for the Swan bands. Highlyexcited Swan spectra were previously measured andanalyzed10 following laser-induced optical break-down of gases.
2. Experimental Methods
Breakdown plasmas were produced by a QuantelBrilliant Nd:YAG laser giving 5-ns pulses at a 10-Hzrepetion rate. We obtained an irradiance in therange 100–300 GW�cm2 on the target by focusing thelaser beam. The laser pulse energy was monitoredby an Ophir Optronics NOVA laser power–energymonitor.
The focused laser irradiance is computed by use ofresults of Gaussian beam propagation.11 The focalspot diameter is d0 � 2f# �, where the f-number isdefined by f# � f�D, f is the focal length of the lens,and D is the diameter of the laser beam. The confocalparameter or depth of focus �2z � is given by 2z �
R R
6.28 �f#�2�, and the focal volume �area confocalparameter� is Vfocus � 19.2 �f#�4�3. The peak irradi-ance at the center of the focused spot is I0 � P0�2�f#��2, where P0 is the total power of the beam. ForGaussian temporal distribution, power P0 is given byP0 � 0.94 �energy�pulse��TFWHM,12 where TFWHM isthe full width at half-maximum.
The focal length of the lens that we used was f �13.5 cm, and the diameter of the beam was D � 0.5cm, yielding f# � 27, focal spot diameter of d0 � 57�m, depth of focus 2zR � 0.45 cm, and focal volumeVfocus � 105 cm3 for a Gaussian beam of 1-�m wave-length. However, because of multimode outputthe spot size was larger than d0 by a factor of 1.4�i.e., the so-called M factor� and M2 � 2, as inferredfrom the half-angle beam divergence of �0.3 mrad.For the fundamental Nd:YAG radiation ��1 � 1.064�m� we found a focal diameter d1 � 80 �m.
The peak irradiance for IR radiation of 300-mJpulse energy and 5-ns pulse width is I � I0�M2 � 1.9TW�cm2. In our experiments we used a cell with aflat glass at the Brewster angle and slightly rotatedthe graphite target to prevent backreflection into thelaser. Examinations with a stereo microscope ofsingle-laser-pulse-generated craters showed a craterdiameter of 200 �m for our optics. Consequently,we estimate a peak irradiance for the IR beam of I1 �300 GW�cm2. For the third-harmonic beam ��3 �0.355 �m� of 80-mJ pulse energy and 4-ns pulsewidth, we found that I3 � 100 GW�cm2 �again usingthe 200-�m spot diameter�. The peak electric fieldstrength, E, of the focused laser beam was calculat-ed13 from E � 27.4 I1�2, where E is given in volts percentimeter and the irradiance, I, is in watts persquare centimeter. Therefore we obtained for thepeak electric field strength E1 � 0.15 GV�cm for thefundamental wavelength and E3 � 0.085 GV�cm forthe third-harmonic wavelength. By way of compar-ison, the electric field strength that holds the hydro-gen atom together is �2.8 GV�cm.
For the indicated irradiance and electric fieldstrength there is plenty of optical radiation for laser-induced breakdown spectroscopy from plasma gener-ated at and near the graphite target. Although it isnot a metal but rather a semimetal14 for which thecarrier concentration is several orders of magnitudelower than the 1022�cm3 that is typical of ordinarymetals, graphite has an extremely short absorptionlength at all wavelengths and has good thermal con-ductivity. Plasma formation is always preceded bysurface vaporization,15 and absorption by electronsgenerated thermally in the vapor can occur. Thegrowth of electron density for wavelengths of � � 1�m, following laser-induced optical breakdown, oc-curs mainly by electron avalanche starting from a feworiginating electrons. For gases, multiphoton ion-ization can provide, at shorter wavelengths �� � 1�m�, enough seed electrons.15 Subsequently, theelectron–ion inverse bremsstrahlung process is theprimary determinant of the cascade-type electrongrowth. Also, at power densities of 10 GW�cm2 orgreater, above-threshold ionization13 including
quasi-free–free transitions can occur, and the result-ant above-threshold photoelectrons can be as largeas, or even larger than, those obtained from nonreso-nant or resonantly enhanced multiphoton ioniza-tion.13,15
We used a buffer gas in the cell and note thatparticularly strong C2 Swan emission was observedfrom plasmas produced in CO2 buffer gas. Temper-atures inferred by fitting of synthetic C2 Swan spec-tra temperature varied from 3500 to 9000 K invarious experimental conditions. Figure 1 shows atypical experimental spectrum, and Fig. 1 also showsthe fitted Swan spectra.
The graphite pellet was contained in a Pyrex cell�Fig. 2� that allowed ambient air to be removed or
Fig. 1. Top, recorded laser-induced breakdown spectra of the C2
Swan band �� � 1, 0, 1 progression. Bottom, from the syn-thetic C2 Swan spectrum, a temperature T � 6400 is inferred.The spectroscopic resolution �FWHM� is 0.27 nm.
replaced by He or CO2 buffer gas. Pellets were cutfrom a spectrally pure graphite rod placed in an evac-uated cuvette. Figure 2 also shows the laser spark.Use of f#�2 collection optics �focal length, 1 cm; lensdiameter, 0.5 cm� allowed us to image an area ofapproximately 0.2 cm 0.2 cm at a distance of 0.1–0.2 cm from the target focus. In other words, in ourspectroscopic studies we investigated a spatial aver-age of the plume.
An optical fiber or lens passed light from theplasma to the entrance slit of an Ophir OptronicsWaveStar-U spectrometer. The spectral range 350–630 nm is covered with a 2048-pixel CCD detector.Both the wavelength and the relative sensitivity cal-ibrations of this spectrometer are fixed at the time ofits manufacture. For detailed future studies includ-ing those of emissions from weaker plasmas, gatedmultichannel detection and a higher-throughputspectrometer are expected to allow us to map tempo-ral and spatial plume characteristics.
We also investigated the influence of using He as abuffer gas at a pressure of some 10–20 Torr. Both355-nm third-harmonic and fundamental 1064-nmwavelength Nd:YAG laser radiation was used. Weobtained spectroscopic temperatures by fitting syn-thetic and recorded C2 Swan spectra. Figures 3 and4 show the results for 355- and 1064-nm laser radi-ation, respectively. The recorded spectra show thetemporally integrated emissions �integrated over7.4 s, or 74 laser-plasma events� and also show spa-tially averaged results of the initial plume investiga-tions. Extensive time-resolved studies of expansiondynamics of the plasma plume6 show development intime of fast and slow components of C2 emissions.These components may indicate dissociative produc-tion �with long-duration C2 Swan emission, or a slowcomponent� and recombinational production �within
a narrow temporal window, or a fast component� ofC2. The dissociative component is expected to occurat low laser irradiance levels, at which graphite maybe ablated layer by layer to produce large particles�graphite shows a simple hexagonal Bravais lattice asopposed to the diamond lattice that consists of twointerpenetrating face-centered cubic Bravais lattices�and one of the fragments may be excited C2 mole-cules. And the recombinational component is ex-pected to occur at higher laser irradiance, resulting inthe presence of neutral and ionized carbon just out-side the target, and C2 emissions will occur followingrecombination. Double-peaked C2 emissions6 aremeasured 0.5 cm away from the target. For our ir-radiance levels of larger than 100 GW�cm2 and theindicated He buffer gas, double-peaked C2 emissionsshould also be measurable if gated detection wereused during the first few microseconds following laserablation.
Singly and doubly ionized carbon atomic lines werealso recorded, at 427 and 570 nm, respectively. Thisallowed us to estimate and characterize some laser-generated plasma parameters. The electron densi-ties and electron kinetic temperatures are estimatedby use of the Saha–Boltzmann ionization equilibriumrelationships together with tabulated Stark broaden-ing coefficients.16 We typically find well over1-order-of-magnitude larger electron number densi-ties �5 1017 cm3� when we use third-harmonicNd:YAG radiation than the electron number densi-ties when we use IR radiation. The electron numberdensity is inversely proportional to the distance fromthe sample surface, and rapid decay within the first300 ns has been reported.6 This report would indi-cate that spatially and temporally resolved data aredesirable for better characterizing the plasma plume.The results of our initial plasma characterization
Fig. 3. �a� Measured emission spectrum for an ambient He pres-sure of 20 Torr; the Nd:YAG third harmonic 355-nm was used forplasma generation. �b� Fitted Swan spectrum, showing temper-ature T � 4790 K.
Fig. 4. �a� Measured emission spectrum for an ambient He pres-sure of 10 Torr; 1064-nm Nd:YAG laser radiation was used forplasma generation. �b� Fitted Swan spectrum, showing temper-ature T � 6920 K.
from average spectra are summarized in Table 1,which also shows the C2 Swan temperature inferredfrom fitting of the molecular emission spectra.
3. Synthesizing the C2 Swan Spectrum
The analysis of molecular spectra is based on usingso-called line-strength data. All quantum-mechanical information required for synthesis of aspectrum is contained in a line-strength file. A dif-ferent line-strength file is required for each diatomicmolecule–isotomer, but the programs for computa-tion of a theoretical spectrum are unchanged whenone’s interest moves to different diatomic molecules.Accurate synthesis of C2 spectra, in particular the d3�g 7 a 3�u spectrum of 12C2, is the topic of thissection. First, we elaborate on the details of di-atomic molecular spectroscopy and illustrate the de-gree of accuracy of our line-strength data bycomparing expanded spectra from different carbonatoms. Second, we discuss the computation of line-strength data, including Honl–London, Franck–Condon, and electronic transition factors, and showexcerpts of our line-strength data. And third, wesummarize application of our line-strength data forinferring spectroscopic temperature.
The d 3�7 a 3� spectra of the terrestrially abun-dant 12C2 and the isotopes 12C13C and 13C2 of astro-physical interest have a long and continuing historyin pure and applied spectroscopy. Comparison ofisotopically related Swan spectra �Fig. 5�, rather con-
vincingly shows that �1� Swan spectra are diatomic,�2� the total electronic spin is 1, �3� some of the iso-topic forms are homonuclear and others are hetero-nuclear, and �4� the nuclear spin of the terrestriallyabundant isotope 12C is 0, whereas the nuclear spin of13C is 1�2. The ability to fit the wavelengths accu-rately in a Swan spectrum to the differences of eig-envalues of two numerically Hamiltonian matrices,computed on the basis of Hund’s case a, demonstratesthe validity of the diatomic model. The appearanceof triplet structure and again the ability to fit it witha diatomic model in which the total electronic spin is1 proves the second conclusion. Whether the twonuclei are identical is determined by the missing halfof each � doublet in the 12C2 spectrum �nuclear spin,0�, the 3:1 alternation in the 13C2 spectrum �nuclearspin, 1�2�, and the appearance of both halves of the �doublets with the same intensities in the 12C13C spec-trum.
Almost all the complexity of an electric dipole spec-trum is contained in the line strength. One who hasan electronic file of the upper- and lower-term valuesand the line strength for each line in the spectrumhas all the information, except for the populationdensities, required for accurate synthesis of the spec-trum produced, for example, by free spontaneousemission:
I� �64�4c�4
3�4�ε0�S�n�v�J�, n�v�J�� N�n�v�J��. (1)
The set of single-primed quantum numbers n�, v�,and J� is associated with the electronic, vibrational,and rotational levels, respectively; the double-primedquantum numbers describe the lower level. Transi-tion wave number � is given by the term-value dif-ference F�n�v�J�� F�n�v�J��. The transitionstrength is factorized and written as the product ofelectronic transition strength Se�n�v�, n�v��, Franck–Condon factor q�v�,v��, and Honl–London factor S�J�,J��:
S�n�v�J�, n�v�J�� � Se�n�v�, n�v��
� q�v�, v��S� J�, J��. (2)
Calculation of an accurate line strength beginswith accurately recorded line positions. Startingwith trial values for the molecular parameters, oneiteratively improves the parameters by numericallydiagonalizing Hamiltonian matrices for the upperand lower states and computing corrections to theparameters by comparing eigenvalue differenceswith measured line wave numbers. The processconcludes when the computed corrections to the lat-est parameter values have become negligibly small.The result is a set of molecular parameters and amodel Hamiltonian that accurately predict the linepositions. Accurate angular-momentum eigenfunc-tions are also obtained as a finite sum of Hund’scase-a basis functions used to compute the Hamilto-nian matrices. Thus numerical diagonalization ofthe Hamiltonian for the upper and lower states gives
Table 1. Carbon Plasma Experimental Data and Derived Parameters ofElectron Kinetic Energy Tkin, Electron Number Density Ne,
both the line wave numbers and the Honl–Londonfactors.
Our computations of diatomic line strength followestablished procedures,17–26 except that we do not useVan Vleck transformations. Instead, we use asmany vibrational levels for each perturbing electronicstate as required to fit the measured wave numbersadequately. An advantage of this approach is that asingle FORTRAN subroutine can treat essentially alldiatomic states.
The Honl–London factors for all term value differ-ences are computed: Those transitions for which theHonl–London factor vanishes or is negligibly smallare forbidden. The parity operator and, for homo-nuclear molecules, the operator for the exchange ofidentical nuclei are members of the set of commutingobservables. Thus the unitary transformation thatdiagonalizes the Hamiltonian also diagonalizes thematrix representations of these operators.
In the study reported in this paper, Swan spectrawere recorded at low resolution over most of the vis-ible spectrum. A line-strength file including allknown bands of the Swan system was built from thedata of Phillips and Davis.27 Rydberg-Klein-Reespotentials for the a and d states of 12C2 were com-puted from the vibrational term values that we found
in fitting the Hamiltonian to the measured line posi-tions of Phillips and Davis. The vibrational eigen-functions were computed, and, from them, theFranck–Condon factors and the r centroids. The abinitio electronic transition moment of Chabalowski etal.28 and the r centroids were used to compute Se�n�v�,n�v��. The Re�r� curve was scaled to give a lifetime��d 3�g, v � 0� � 101.8 ns, the value reported byNaulin et al.,29 but for the spectra analyzed here onlythe relative line strength was required. Table 2shows a printed view of a section of the resultantline-strength file for the �0, 0� band.
Equation �1� and the appropriate line-strength fileare the tools that can be used to compute a diatomicspectrum fitting function in which temperature is thefree parameter. With this fitting function and aminimization algorithm, we use the Nelder–Meadmethod30 to find the temperature that makes thesynthetic spectrum best fit an experimental spectrumin the least-squares sense.
In addition, programs that use the same line-strength files have been written for the synthesis ofabsorption and laser-induced fluorescence spectra.All the synthetic spectra shown here, however, wereproduced by a single, simple FORTRAN program for freespontaneous emission. Our method for using di-
Table 2. Section of the Line-Strength File for the d 3�g 7 a 3�u �0, 0� Band
atomic spectra as diagnostic tools was applied for theinterpretation of the currently low-resolution, time-averaged spectra. Yet we note that accurate linepositions and line strengths are required despite thecurrent �low� experimental resolution; moreover, ourmethod can be applied without modification in futureexperiments.
4. Discussion and Conclusions
We have presented and compared measured andcomputed spectra in laser-generated carbon plasmaand applied accurate C2 Swan band line-strengthfiles in the analysis of temporally and spatially aver-aged emission spectra. The advantage of ourmethod of inferring plasma temperature lies in itsgenerality. We also characterized the plasma by useof carbon atomic lines. For future research with la-ser generated carbon plasma, however, application oftime-resolved and spatially resolved laser-inducedbreakdown spectroscopy is recommended.
Numerical diagonalization of the diatomic Hamil-tonian yields accurate term values and much of theinformation required for the computation of all di-atomic matrix elements. Our current C2 Swan line-strength files are made for electric dipole transitions.Programs have been written that use the same line-strengths to compute synthetic absorption spectraand laser-induced fluorescence spectra. However,once one has accurately fitted upper- and lower-levelmodel Hamiltonians to best-fit experimental line po-sition data, one has most of the information requiredfor computing multiphoton and Raman linestrengths. Further, we use the line-strength data tocompute synthetic spectra and in other temperaturemeasurement algorithms such as the Boltzmannplot.
Correlation of measured C2 Swan spectra and for-mation of carbon nanoparticles following laser abla-tion of graphite3 show that higher temperatures areobtained from emission spectra, reflecting excited-state populations, than from laser-induced fluores-cence spectra of C2, reflecting ground-statepopulations. Measurement of time-resolved andspatially resolved C2 molecular spectra should allowus to investigate the temperature difference further.C2 emission spectra were also reported4 subsequentto laser excitation of buckminsterfullerene �C60�.Diatomic molecular spectroscopy, therefore, can beapplied for both monitoring the production and de-tecting the presence of nanoparticles and possiblyalso for evaluating from measured C2 spectra theefficiency with which carbon nanoparticles are gen-erated.
This research is supported in part by the Univer-sity of Tennessee Space Institute’s Center for LaserApplications and by the Hungarian Orszagos Tu-domanyos Kutatasi Alapprogramok Foundation un-der contracts T032549 and T038422. C. G. Pariggerthanks the Optical Society of America for travel sup-port for attendance at the LIBS 2002 conference.
References and Notes1. Abilasha, P. S. R. Prasad, and R. K. Thareja, “Laser-produced
carbon plasma in an ambient gas,” Phys. Rev. E 48, 2929–2933�1993�.
2. S. S. Harilal, C. V. Bindhu, R. C. Issac, V. P. N. Nampoori, andC. G. Vallabhan, “Electron density and temperature measure-ments in a laser produced carbon plasma,” J. Appl. Phys. 82,2140–2146 �1997�.
3. S. Arepalli, P. Nikolaev, W. Holmes, and C. D. Scott, “Diag-nostics of laser-produced plume under carbon nanotube growthconditions,” Appl. Phys. A 69, 1–9 �1999�.
4. S. Arepalli, C. D. Scott, P. Nikolaev, and R. E. Smalley, “Elec-tronically excited C2 from laser photodissociated C60,” Chem.Phys. Lett. 320, 26–34 �2000�.
5. A. A. Puretzky, D. B. Geohegan, X. Fan, and S. J. Pennycook,“In situ imaging and spectroscopy of single-wall carbon nano-tube synthesis by laser vaporization,” Appl. Phys. Lett. 76,182–184 �2000�.
6. S. S. Harilal, “Expansion dynamics of laser ablated carbonplasma plume in helium ambient,” Appl. Surf. Sci. 172, 103–109 �2001�.
7. C. G. Parigger, G. Guan, and J. O. Hornkohl, “Measurementand analysis of OH emission spectra following laser-inducedbreakdown,” Appl. Opt. 42, 5986–5991 �2003�, and referencestherein.
8. J. O. Hornkohl and C. G. Parigger, “Boltzmann EquilibriumSpectrum Program �BESP�,” http.��view.utsi.edu�besp.
9. C. G. Parigger, J. O. Hornkohl, A. M. Keszler, and L. Nemes,“Laser-induced breakdown spectroscopy: molecular spectrawith BESP and NEQAIR,” in Laser Induced Plasma Spectros-copy and Applications, Vol. 81 of OSA Trends in Optics andPhotonics Series �Optical Society of America, Washington,D.C., 2002�, pp. 104–105.
10. C. Parigger, D. H. Plemmons, J. O. Hornkohl, and J. W. L.Lewis, “Spectroscopic temperature measurements in a decay-ing laser-induced plasma using the C2 Swan system,” J.Quant. Spectrosc. Radiat. Transfer 52, 707–711 �1994�.
11. A. E. Siegman, Lasers �University Science, Mill Valley, Calif.,1986�, Chap. 17, pp. 676–677.
12. S. L. Chin, “Laser beam transport,” in Laser Applications inPhysical Chemistry, D. K. Evans, ed. �Marcel Dekker, NewYork, 1989�, Chap. 2, pp. 39–62.
13. R. N. Compton and J. C. Miller, “Multiphoton ionization pho-toelectron spectroscopy: MPI-PES,” in Laser Applications inPhysical Chemistry, D. K. Evans, ed. �Marcel Dekker, NewYork, 1989�, Chap. 6, pp. 221–306.
14. N. W. Ashcroft and N. D. Mermin, Solid State Physics �Holt,Rinehart & Winston, New York, 1976�, p. 304.
15. G. M. Weyl, “Physics of laser-induced breakdown: an up-date,” in Laser-Induced Plasmas and Applications, L. J. Radzi-emski and D. A. Cremers, eds. �Marcel Dekker, New York,1989�, Chap. 1, pp. 1–67.
16. H. R. Griem, Plasma Spectroscopy �McGraw-Hill, New York,1964�, Tables 4 and 5.
17. J. H. Van Vleck, “The coupling of angular momentum vectorsin molecules,” Rev. Mod. Phys. 23, 213–227 �1951�.
18. I. Kovacs, Rotational Structure in The Spectra of DiatomicMolecules �American Elsevier, New York, 1969�, p. 14.
19. R. N. Zare, A. L. Schmeltekopf, W. J. Harrop, and D. L. Al-britton, “A direct approach for the reduction of diatomic spec-tra to molecular constants for construction of RKR potentials,”J. Mol. Spectrosc. 46, 37–66 �1973�.
20. B. R. Judd, Angular Momentum Theory for Diatomic Molecules�Academic, New York, 1975�, pp. 4–5.
21. M. Mizushima, The Theory of Rotating Diatomic Molecules�Wiley, New York, 1975�.
22. J. D. Graybeal, Molecular Spectroscopy �McGraw-Hill, NewYork, 1988�, pp. 54–61.
23. H. Lefebvre-Brion and R. W. Field, Perturbations in the Spectraof Diatomic Molecules �Academic, Orlando, Fla., 1986�, p. 98.
24. R. N. Zare, Angular Momentum �Wiley, New York, 1988�.25. H. W. Kroto, Molecular Rotation Spectra �Dover, New York,
1992�, pp. 15–17.26. P. R. Bunker and P. Jensen, Molecular Symmetry and Spec-
troscopy, 2nd ed. �NRC Research Press, Ottawa, Canada,1998�.
27. J. G. Phillips, and S. P. Davis, The Swan System of the C2
Molecule �U. California Press, Berkeley, Calif., 1968�.
28. C. F. Chabalowski, R. J. Buenker, and S. D. Peyerimhoff,“Theoretical study of the electronic transition moments for thed 3�g7 a 3�u �Swan� and e 3�7 a 3�u �Fox–Herzberg� bandin C2,” Chem. Phys. Lett. 83, 441–448 �1981�.
29. C. Naulin, M. Costes, and G. Dorthe, “C2 radicals in a super-sonic molecular beam. Radiative lifetime of the d 3�g statemeasured by laser-induced fluorescence,” Chem. Phys. Lett.143, 496–500 �1988�.
30. J. A. Nelder, and R. Mead, “A simplex method for functionminimization,” Comput. J. 7, 308–313 �1965�.
