analysis of combined spectra of nh and n_2

Analysis of combined spectra of NH and N2

David H. Plemmons, Christian Parigger, James W. L. Lewis, and James O. Hornkohl

Gas phase diagnostics with multispecies diatomic spectra is discussed. Analyses of spectra from the A3Pi

7 X3S2 system of NH and the C3Pu 7 B3Pg second-positive system of N2 are presented. Multispeciesspectroscopy is applied to experimental spectra obtained from laser-induced breakdown plasmas inanhydrous ammonia gas and a low-pressure discharge lamp. © 1998 Optical Society of America

OCIS codes: 140.3460, 300.0300, 350.5400.

1. Introduction

Laser-induced breakdown ~LIB! plasmas character-istically exhibit rich emission spectra. Microsec-onds following the breakdown event of moleculargases, the plasma spectra are usually dominated bydiatomic spectra that typically result from atomicrecombination and subsequent energy transfer pro-cesses. These spontaneous emission spectra oftenserve as diagnostics of the plasma and can yield tem-peratures and relative species concentrations of theplasma. Here we are concerned with LIB of atmo-spheric pressure NH3 vapor and the study of theresulting overlapped recombination spectra of thewell-known NH A3Pi 3 X3S2 and the N2 second-positive, C3Pu 3 B3Pg, electronic transitions.

The investigation presented here has applications,for example, in the study of laser ignition of combus-tible gases. The NH radical is known to occur in aregion near the flame front, and measurement of NHemission spectra is potentially of use in the mappingof dynamic effects. Measurements of NH are eval-uated for the determination of temperature. Spec-tra from low-pressure ammonia gas are evaluatedfirst, subsequently plasma temperature is inferred toinvestigate the post-breakdown and post-shockwavekernel.

Overlapped NH–N2 systems were partially re-solved to determine as a function of the absorbed

When this research was undertaken the authors were with theCenter for Laser Applications, University of Tennessee Space In-stitute, Tullahoma, Tennessee 37388-8897. D. H. Plemmons isnow with Teledyne Brown Engineering, 300 Sparkman Drive, NW,Huntsville, Alabama 35805.

Received 14 March 1997; revised manuscript received 25 August1997.

0003-6935y98y122493-06$15.00y0© 1998 Optical Society of America

energy the relative contributions of the NH and N2emission signals. Using these results, we found thedependence of the plasma temperature on the ab-sorbed energy of the LIB event. Estimates of the ex-tent of the plasma, as manifested by the spatialvariation of the plasma temperature, were obtainedapproximately 5 ms following the breakdown event.

To accomplish these objectives, we made use of twocomputer codes.1–3 The first provided molecular linestrengths4 and synthetic spectra of the radiatingspecies for specified vibrational and rotational tem-peratures, Tv and Tr, respectively. The second com-putational technique, a Nelder–Mead algorithm,5determines the best values6–8 of Tv and Tr and rela-tive species densities for either experimental or syn-thetic spectra.

2. Computation of Synthetic Spectra

We performed a refit of the original data by Brazier etal.9 to obtain a suitable set of molecular constants forour model Hamiltonian. Subsequently, these molec-ular parameters are used to compute the linestrengths. It is noteworthy that our method repro-duces the NH experimental line positions of Brazieret al. with a standard deviation of 0.003 cm21.

The many differences, large and small, betweenvarious model Hamiltonians that have been dis-cussed in the literature make the use of reportedmolecular parameters difficult. For example, Rens-berger et al.10 mentioned large differences, of the or-der of 1–2 Å, between their calculated NH linepositions and experimentally measured line posi-tions.

Figures 1 and 2~a! are examples of synthetic spec-tra that one can easily compute using a line strengthfile. Figure 1 is a low-resolution synthetic spectrum,which shows the content of our line strength file forthe N2 second-positive system. Figure 2~a! gives amuch higher resolution synthetic spectrum, com-

20 April 1998 y Vol. 37, No. 12 y APPLIED OPTICS 2493

puted with the same program and line strength fileused to compute the spectrum of Fig. 1, and should becompared with the experimental spectrum of Roux etal.11,12 reproduced in Fig. 2~b!.

3. Glow Discharge Spectrum

The emission of a commercially available low-pressure discharge tube of high-purity nitrogen wasused to demonstrate the combined application ofthese two computer codes. The spectrum of Fig. 3shows a low-resolution Dn 5 0 sequence of the N2second-positive spectrum corrupted by the 0–0 bandof NH. The spectrum was dispersed and recordedwith the same Jobin–Yvon spectrometer and CCD

Fig. 1. Low-resolution theoretical spectrum that shows the con-tent of our N2 second-positive system line strength file. The cal-culation was performed for a rotational temperature of 450 K anda vibrational temperature of 4500 K to enhance the vibrationalband structure. The Gaussian linewidth of this spectrum is 10cm21 FWHM.

Fig. 2. ~a! High-resolution ~0.1 cm21 FWHM! theoretical spec-trum of a portion of the N2 second-positive system with Tr 5 Tv 5450 K. ~b! Experimental spectrum of Roux et al.11 The alternationof intensities produced by nuclear spin statistics can be observedfor a L-doubled spectrum only when the L doublets are resolved.A factor of 2 intensity alternation ~i.e., a nuclear spin of 1! can beseen in both Roux et al.’s experimental spectrum and the syntheticspectrum.

2494 APPLIED OPTICS y Vol. 37, No. 12 y 20 April 1998

detector described below. Also shown in the figure isa nonequilibrium synthetic spectrum fitted to thedata, again with the NH and N2 line strength files.This time the rotational temperature Tr, the vibra-tional temperature Tv, and the ratio of excited-statepopulation densities were allowed to vary. How-ever, the vibrational and rotational temperatureswere assumed to be the same for the two species.From the resulting fit ~Tr 5 570 K, Tv 5 4200 K!, onecan conclude that the N2 molecules are clearly not invibrational–rotational equilibrium, as the fitted vi-brational temperature is an order of magnitudelarger than the rotational temperature.

We note that the accuracy of NH temperatures islow as a result of the overlapped NH spectra and thecomparatively low concentration of NH in the dis-charge. As a result, there is no suggestion that thevibrational and rotational temperatures of NH andN2 are actually equal.

4. Laser-Induced Breakdown Spectra

A. Experiment

A pulsed Nd:YAG ~Continuum YG680S! laser wasused to generate optical breakdown in research-gradeanhydrous ammonia. The Nd:YAG laser is Qswitched and emits 1.064-mm pulses with a pulsewidth of 6 ns FWHM. The laser operates in manylongitudinal modes, which gives mode beating andhence temporal substructure to the 6-ns pulse. Theoutput pulses were beam expanded with a 43antireflection-coated beam expander. The ex-panded pulses were focused with an antireflection,plano-convex, 100-mm focal length lens into a vac-uum cell that contained the ammonia gas at 100 Torr.The beam diameter of the expanded laser pulses wasapproximately 20 mm. The gas cell is equipped with37.5-mm uncoated fused-silica windows on four sides,and the cell was positioned so that these windowswere in the horizontal plane. The plasma emissionwas imaged, perpendicular to the laser-pulse propa-gation, with one-to-one magnification onto an 800-mm-diameter fiber-optic cable, which was opticallycoupled to a spectrometer. The spectrometer usedto disperse the spectrum was a Jobin–Yvon crossedCzerny–Turner 0.64-m spectrometer equipped with a

Fig. 3. Nonequilibrium NH–N2 experimental and theoreticalspectra with Tr 5 570 K, Tv 5 4200 K, and ~N2!y~NH! 5 4.7.


1200-gymm grating. The spectrum was recordedwith an intensified CCD detector ~EG&G PARCOMA4, Model 1530-CUV equipped with a lens-coupled intensifier!. We accomplished wavelengthcalibration by comparing the experimental spectrumto a theoretical spectrum.

The experimental spectra were recorded 0.5 ms af-ter the laser pulse with a gate width of 10 ms andconsist of an average of 1000 events. The averageenergy per pulse was 60 mJ.

B. Description of Combined NH and N2 Spectra

Figure 4 shows an experimental NH A3Pi 3 X3S2

spectrum and poorly fitted synthetic spectrum ob-tained with only the NH line strength file and as-sumed vibrational–rotational equilibrium. Thelargest disparities between experiment and theoryare in the region of the strongest bands of the Dn 5 0sequence of the N2 C3Pu3 B3Pg second-positive sys-tem. An appropriately scaled N2 second-positivetheoretical spectrum is also shown in Fig. 4. Thetheoretical NH spectrum shown in Fig. 4 was fittedonly to the spectral region outside the influence of theN2 second-positive system ~l $ 338 nm!. The shorterwavelength portion of the NH spectrum was calcu-lated from the resulting best-fit temperature ~4670K!. The N2 spectrum was calculated for a tempera-ture of 5000 K.

Attempts to fit the entire experimental spectrumwith only NH resulted in significant increases in tem-perature ~DT . 700 K!. In fitting the spectrum, theprogram attempts to duplicate the intensity ratio be-tween the strong 0–0 and 1–1 Q branches and at thesame time reproduce the R- and P-branch rotationalstructure. The superposition of the N2 0–0 bandand the NH 1–1 band at 337 nm is the primary causeof the increase in fitted temperature. A typical fit isshown in Fig. 5. The largest disparities are in theregion of the N2 system and the NH 2–2 vibrationalband.

To decrease the disparities between theory and ex-periment, we repeated the fitting of the synthetic

Fig. 4. Experimental spectrum and a theoretical spectrum calcu-lated from the parameters resulting from a spectral fit to l $ 338nm. The theoretical spectrum underpredicts the experiment inthe region of the N2 second-positive system. The expected N2

contribution is shown along the bottom of the figure. The Gauss-ian linewidth of the theoretical spectra is 15.5 cm21.

spectrum using line strengths for both NH and N2.In the fitting procedure, the rotational and vibra-tional temperatures are again assumed to be thesame. This common temperature and the intensitycontribution of each species were allowed to vary un-til the sum of the squared residuals between the ex-perimental and synthetic spectra was minimized.The addition of N2 into the model gives the fit shownin Fig. 6, in which the standard deviation in the sumof the squared residuals is reduced by a factor of 2compared with that of Fig. 5. The best-fit tempera-ture of 4950 K is 280 K ~or 6%! larger than the rota-tional fit of Fig. 4. In a previous paper,7 a confidenceinterval of 65% for the fitted temperature was in-ferred from parameter studies. The results aboveare consistent with this evaluation.

The NH–N2 spectrum is consistent with the as-sumption of thermal equilibrium between the rota-tional and vibrational states. We previouslyreported temperatures inferred from CN violet6 andC2 Swan7 spectra emitted from laser-produced plas-mas in which equilibrium between the rotational andvibrational states was also observed.

Further analysis on the degree of equilibrium thatexists in the optical plasma can be accomplished

Fig. 5. Fitting only NH to the experimental spectrum causes thetheory to underpredict the intensity in the middle of the spectrum,which contains the N2 contribution, and overpredict the intensityin the spectral region, which contains no N2 contribution. TheGaussian linewidth of the theoretical spectra is 15.5 cm21.

Fig. 6. Experimental spectrum and a theoretical NH–N2 fit.The theory slightly overpredicts the intensity in the region of theNH 2–2 band ~l . 339.3 nm!. The Gaussian linewidth of thetheoretical spectra is 15.5 cm21.

through the relative emission intensities of theNH–N2 spectra. The following analysis shows thatthe observed spectra are either not in chemical or notin thermodynamic equilibrium, or both.

The emission intensities calculated from the linestrength files are in the form of absolute intensity perexcited-state molecule. The total intensity for twoexcited-state molecules is

Itotal 5 I1 1 RI2, (1)

where R is a scaling factor for relative intensitiesbetween two molecular species and can be equated tothe relative excited-state number density. If themolecules are in complete thermodynamic equilib-rium, then the excited-state number density ratio canbe related to the ground-state number density ratioby the relation

N20

N10 5 R

Q2

Q1, (2)

where Ni0 is the ground-state number density of spe-

cies i and Qi is its partition function.For the fitted spectrum in Fig. 6, R 5 1.6 3 105.

The ratio of partition functions QN2yQNH at 5000 K

was estimated to be 1.5. Therefore the ratio ofexcited-state to ground-state number densityamounts to NN2

0yNNH0 . 2 3 105.

The Gordon–McBride chemical equilibrium code13

at 100 Torr and 5000 K predicts that NN2

0yNNH0 .

2 3 103. Electronic partition functions tell us that at5000 K the ground electronic state of N2 will be al-most 100% occupied whereas that of NH will be 98%occupied. These results imply that ~a! the moleculesare not in chemical equilibrium andyor ~b! the as-sumption of electronic equilibrium cannot be justi-fied.

Spectra recorded at earlier times in the plasmacontain lines of atomic hydrogen, atomic nitrogen,and its ions. The NH–N2 spectra observed in theplasma decay are the result of recombination fluores-cence, and therefore chemical and electronic equilib-rium should not necessarily be expected at early timedelays in the plasma decay. However, for longenough time delays after the laser-induced plasmainitiation ~of the order of tens of microseconds de-pending on the laser-pulse energy!, diatomic spectrahave been observed in electronic and chemical equi-librium.14,15 Thus one can only infer from theNH–N2 spectra that the intensity contribution ofeach excited-state molecule inferred from the best fitabove is the population density ratio of excited-statemolecules that radiatively decay to the lower elec-tronic state.

5. Laser-Pulse Energy Variation Study

A. Experiment

In this experiment, the laser-pulse energies were var-ied to investigate the effects of absorbed energy onthe NH–N2 signal level and the vibrational–rotational temperature. Pulse energies were varied


from subthreshold values, in which breakdown didnot occur and a signal was not observed, as high as 60mJ.

The experimental setup was the same as that inSection 4 with the following additions. To achievethe desired degree of energy attenuation withoutchanging the temporal or spatial characteristics ofthe laser pulses, optical flats were placed in the beampath. The optical flats were inserted as matchedpairs to prevent beam walk. An energy meter ~Sci-entech, Model P50, calibrated for 1.06 mm! wasplaced after the vacuum cell to monitor the averagepulse energy of the optical breakdown pulses.

Spectra were recorded with a detector gate width of1 ms and time delays of 0.5 and 1 ms. Emissionsignals were averaged over 1000 laser shots for eachpulse energy studied.

B. Results

Temperatures were inferred from spectral fits to thecombined NH–N2 profiles as discussed in Section 4.The experimental and theoretical profiles are essen-tially the same as those shown in Fig. 6. NH–N2signal levels were determined from the difference inintensities at 336.01 nm ~the peak of the 0–0 band!and 327.82 nm ~which served as the background!.

We determined average incident energies for eachdata point by evacuating the cell so that opticalbreakdown would not occur. Reflective losses of therear window of the cell were measured and correctedfor in all energy measurements. During the acqui-sition of the spectra, average transmitted energieswere measured so that the average energy per pulseabsorbed by the optical breakdown plasma could bedetermined.

Figure 7 shows the resulting temperature as afunction of the absorbed energy. The temperatureappears to very quickly approach an asymptoticvalue relative to the considered abscissa values. It islikely that a saturation occurs in the optical plasma.Yalcin et al.16 found that as more energy is added tothe optical breakdown pulse, both the electron num-ber density and temperature quickly saturate. Thatis, as the pulse energy increases above some critical

Fig. 7. Inferred temperatures versus laser-pulse energy absorbedby the optical breakdown plasma: filled circles, 0.5–1.0-ms delay;open squares, 1.0–2.0-ms delay.

value, the plasma becomes larger rather than hotterand more dense.

Figure 8 shows the NH–N2 emission signal level~detector counts! versus absorbed energy. The sig-nal level was measured at the peak of the NH 0–0band ~336 nm!. The emission signal shown in Fig. 8also appears to approach an asymptotic value as theabsorbed energy increases. This behavior impliesthat there is a maximum number density of NH mol-ecules that are created by the optical breakdown.This behavior is consistent with the saturation dis-cussed above.

6. Spatially Resolved Spectra

In this experiment we generated optical breakdownin pure ammonia gas at atmospheric pressure byflowing the gas through a flat flame burner. Theburner was positioned in front of the entrance slit ofthe spectrometer, and the breakdown was imagedonto the entrance slit. The orientation of the slitwas perpendicular to the optical axis of the focusedlaser beam. A CCD detector was used to record thespectra. The horizontal dimension of the CCD arrayrecords the spectral signature of the dispersed radi-ation, and the vertical dimension of the CCD arrayresolves variations along the spectrometer entranceslit and hence at right angles to the optical axis of the

Fig. 9. Spatially resolved NH–N2 spectra.

Fig. 8. NH–N2 signal versus laser-pulse energy absorbed by theoptical plasma: filled circles, 0.5–1.0-ms delay; open squares, 1.0–2.0-ms delay.

laser beam. The laser used in this experiment was aCoherent Infinity 40-100 Nd:YAG laser system.The average incident energy was 47 mJ and the av-erage absorbed energy was 42 mJ. The laser pulsewidth was 3.5 ns FWHM.

Figure 9 shows an image of the spatially resolvedNH–N2 spectra. The ordinate represents the spatialdimension of the spectrometer slit, and the abscissarepresents the spectral dispersion of the spectrome-ter. This image was acquired at a time delay of 4.8ms after the breakdown pulse with a 1-ms gate width,and it represents an average of 1000 laser shots. Ashock expansion has occurred at such time delays;however, NH spectroscopy is of interest in the studyof post-shockwave kernel behavior at or near atmo-spheric pressure.

The same fitting procedure as described in Sections1 and 4 was applied to these spectra. The resultingtemperatures across the plasma are shown in Fig. 10.The uncertainties shown in Fig. 10 represent 65%.Figures 9 and 10 show that the spatial extent of theNH emission from the plasma is approximately 2mm. Although there appears to be some structurein the temperature profile, especially near the peak,the variation is fairly smooth over the NH emissionregion. The experimental uncertainties of the dataand the optical depth estimates of the plasma contra-indicated the Abel inversion of the data.

This material is based on research that is in partsupported by the National Science Foundation undergrant CTS-9512489.

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Fig. 10. Inferred temperatures across the optical breakdownplasma.


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1

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analysis of combined spectra of nh and n_2

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