Integrated Intensity of NO Fundamental

U. P. Oppenheim, Yair Aviv, and Aharon Goldman

The statistical band model was applied to the NO fundamental vibration band and a criterion was estab-

lished for the validity of the linear region. Transmittance measurements of NO mixed with helium werecarried out in this region and the integrated intensity was found to be 125 i 8 cm ' atm 1 at 2730K.

Introduction

The intensity of the fundamental vibration rotationband of NO which is centered at 5.3 u has been measuredby at least eleven independent laboratories.'-" How-ever, it is a disturbing fact that the results of all thesemeasurements do not converge to a single value.Rather, the results are spread out between 70 cm-2

atm-' at 273 0K (Penner and Weber3) and 145 cm-2

atm-' at 273 0K (Dinsmore and Crawford2). The mostaccurate work seems to be the study of Abels and Shaw'0

who gave a value of 122 cm-2 atm-' at 273 0K, based ona detailed line by line study of the band. Nevertheless,it seems useful to make another independent determina-tion of the band intensity by the application of recentlydeveloped theories.

The present study applies spectral band modeltheory to the NO fundamental. Instead of applyingthe theory to the band as a whole, it is applied to smallspectral intervals within the band. Each transmit-tance measurement T at a given frequency is consideredto be an average value of the true transmittance be-cause of the averaging effect of the finite spectral slitwidth. Band model theory states that if the slit isfairly wide (of the order of 10 cm-') it includes enoughlines to justify certain averaging procedures. Thisapproach has recently been applied successfullyto a number of problems in quantitative molecularspectroscopy.' 2 -'5 In many cases it was found that allpoints within a band could be represented by the sta-tistical model at all temperatures. The band modelparameters in the case of the statistical model are

U. P. Oppenheim is with the Department of Physics, Technion-Israel Institute of Technology, Haifa, Israel; Y. Aviv is pres-ently with Israel Aircraft Industries, Lod Airport; A. Goldmanis presently with the Department of Physics, University of Den-ver, Denver, Colorado.

Received 3 February 1967.This work was sponsored by a grant from the Air Force Office

of Scientific Research through the European Office of Aerospace

Research (OAR), U. S. Air Force.

27ry/d and x/L, where y (cm-' atm-') is the meanhalf-width of the lines at unit pressure, d (cm-') is themean distance between adjacent lines, L (cm) is theoptical path, length, and x is the dimensionless para-meter of Ladenburg-Reiche given by x = S0 L/27ry0 ,where SI (cm- 2 atm-') is the mean line intensity atunit pressure.

Once x/L is determined for every frequency in theband, it is a simple matter to determine the path lengthfor which the band is in the linear region at all fre-quencies. Usually the criterion for the linear region istaken to be x < 0.2, requiring a cell length L whichsatisfies L < 0.2 (x/L) -1.

In a preliminary study in our laboratory, it was foundthat the statistical model applied to all frequencieswithin the NO fundamental. This was deduced fromthe fact that everywhere in the band the relation(lnT)/p = constant, held over a large range of pressurep when the spectral slit width was - 10 cm-' or more.A band model analysis was carried out, and it was foundthat the highest value of x/L, corresponding to themaximum in the R-branch at a frequency of 1905 cm-',was 3 cm-'. According to the criterion mentionedbefore, it therefore followed that a cell shorter than 0.07cm was required for the linear region to be valid. Sincesuch short cells were not available it was decided toreduce x by mixing the gas with an infrared inactivegas, such as helium. Using the notation of Ref. 15 wefind that for a mixture, x is given by xmixture = (Bpa/pe)x,where B is the self-broadening coefficient,'6 Pa is thepartial pressure of the absorbing gas (NO in our case)and Pe is the equivalent pressure of the gas mixture.By setting B = 1 (see Ref. 7) and thus taking Pe equalto the total pressure p, it is seen that in a mixture ofNO in a foreign gas the parameter x is reduced approxi-mately in the ratio pa/pt. By preparing suitable mix-tures it is therefore fairly easy to reach the linear region,even with relatively long cells.

Our experiment was carried out by introducing a mix-ture of approximately one part NO in nine parts He intoa cell 0.446 cm in length. In this way the maximum

August 1967 / Vol. 6, No. 8 / APPLIED OPTICS 1305

1.0

0.8

wC.)Z 0.6 t

U)

as 0.4-

0.2

0-1 750 1800 1850 1900

WAVENUMBER (cm-')1950 2000

Fig. 1. Transmittance of several NO-He mixtures in the regionof NO fundamental. Partial pressure of NO (pa in atm) is indi-cated on each curve. Ratio of pa to pt was 1:9.99.5 for all mix-

tures.

value of Xmixture was estimated to be (for x/L = 3 cm-')Xmixture = (L)L(Bpa/Pe) = 0.134, at the peak of theR-branch. Since this value was below 0.2 and most ofthe band had still lower values of x it was assumed thatthe linear region had been reached. We also experi-mented with N2 as a broadening gas and found that ithad the same broadening ability as He. This justifiedour present use of the value B = 1, which had previouslybeen found for N2 broadening.7

It should be noted that the present method does notrequire a total gas pressure which is high enough forthe rotational fine structure of the band to be smearedout. Rather, our study showed that the measuredvalue of - (p0L) - f nT d over the band was inde-pendent of the total pressure when the latter variedfrom 1 atm to 28 atm. This was in agreement withprevious observations' 4 which showed that the linearregion was determined by x, rather than by the totalpressure, as was assumed in the Wilson-Wells-Penner-Weber method for finding the integrated band in-tensity. Of course, the spectral absorption coefficientcould be derived directly by multiplying the parametersof the band model 27r-y/d and x/L to obtain (27ryO/d)X (x/L) = /d. Here 80/d stands for the averageabsorption coefficient (over the spectral slit width) fromwhich the band intensity may be derived by calculatingthe integral

Sband = fband dp.

In the present study this calculation was not attempted,since not enough accurate data were available on theband parameters.

Experimental

Absorption spectra were obtained by the use of aPerkin-Elmer model 12G grating spectrometer. A de-tailed description of the optical system has been pub-lished elsewhere.' 4 A single absorption cell was used,which was made of inconel and was of conventional

design. It had two sapphire windows (2 5-mm diam X3 mm thick), which were sealed to the cell by neoprene0-rings. The distance between the windows was 0.446cm. NO was obtained from the Matheson Co. and hada minimum nominal purity of 99.0%. It was purifiedby first condensing it in a liquid nitrogen trap and pump-ing out volatile impurities. By gradually removing theliquid nitrogen from the trap the NO was vaporizedslowly, and only the first vapor fraction was used forspectral measurements. The infrared spectra of thisfraction showed no trace of impurities, even under highresolution. Since the trap and the gas handling systemwere made of thick-walled stainless steel it was possibleto build up NO pressures between 0 atm and 50 atm byrepeated distillation. Pressures up to 5 atm were readto an accuracy of 0.1% on a set of manometersmade by the Heise Bourdon Tube Co. Higher pressurereadings were made with Bourdon type manometers,manufactured by United States Gauge (1400T testgauge), to an accuracy of 0.25%.

A stainless steel mixing cylinder, filled with a largenumber of glass beads, was used to prepare the gasmixtures. In a typical experiment the cylinder wasfilled with NO to a pressure of 5 atm and closed off.The rest of the system was subsequently evacuated andHe admitted until a pressure of 60 atm was reached.This pressurized helium was then admitted to the

Table I. Measurements of the Integrated Band Intensity ofNO Fundamental

Sband (cm-2 ati')pa (atm) Pt (atm) at 2730 K

0.779 7.788 124.51.460 14.950 124.62.140 21.393 126.52.842 28.399 125.6

Table II. Summary of Band Intensity Measurements of NOFundamental in cm-2 atm-' at 2730K

Band Ref-Author intensity -Method erence

Havens 121 Dispersion, low 1resolution

Dinsmore and 145 29 Intensity ' 2Crawford T 1.

Penner and Weber 70 7 Intensify 3Vincent-Geisse 82 High resolution A4Schurin and Clough 111 7 Intensity, self- 5

broadeningJames 138 i 6 High resolution 6Ford and Shaw 115 4 9 Curves of growth 7Alamichel 132 3 Dispersion, high 8

resolutionBreeze and Ferriso 76 - 7 Shock tube, emis- 9

sionAbels and Shaw 122 i 6 High resolution 10Feinberg and Camac 124 i 22 Shock tube, I I

emissionPresent results 125 i 8 Band modelsi

1306 APPLIED OPTICS / Vol. 6, No. 8 / August 1967

mixing cylinder until a total pressure of 50 atm wasestablished in the whole system. Care was taken thathelium was streaming into the mixing cylinder until thelatter was closed off, in order to avoid a back flow ofNO during mixing. The mixing cylinder was thenvigorously shaken for about 5 min, while the rest of thesystem was again evacuated. Finally, the gas mix-ture was admitted to the absorption cell. During theexpansion of the gas into the cell the total pressure fellto about 30 atm.

Before a mixture was admitted to the cell, the spec-tral region around 5.3 u was recorded in order to obtaina blank curve. Immediately after the cell was filled,the same region was scanned again and the transmissionof the sample was recorded. In this way a series oftransmission spectra were recorded under the sameblank curve for a series of samples with diminishing total(and partial) pressures but with constant x. This seriesof mixtures was obtained simply by pumping off someof the gas in the cell between runs. With the help ofsuch a set of spectra we could test our assumption that- (PaL) -1 f lnT dv over the band was independent oftotal pressure once the linear region was reached (xsmall enough).

The results of the transmittance for a series of fourpressures are shown in Fig. 1. The spectra were takenwith a mechanical slit width of 800 /u, corresponding toabout 15 cm-'. It is seen that the rotational fine struc-ture is not resolved, although high resolution studies ofthe same samples showed that the fine structure wasnot smeared out. Each spectrum allowed an indepen-dent estimate of the band intensity by the calculationof

Sband = -(PaL)Y 'f lnT dv.

The results obtained from the spectra in Fig. 1 aresummarized in Table I.

The spectra were taken at a temperature of 22°C andSband was reduced to C by assuming an inversedependence of the band intensity on the absolute tem-perature. Several mixtures were prepared and theirspectra were measured in this way. After averagingover all results our best value for S-,. was 125 8cm-2 atm-' at 2730K.

A comparison with results of other workers is shownin Table II. It is seen from Table II that the presentresult lies within the limits of experimental error of themajority of the results, except those of Penner andWeber3 , Vincent-Geisse 4 , and Breeze and Ferriso9 ,whose values for Sband cluster around 75 cm-2 atm-'. Itis difficult to explain the latter low value for Sband, whichlies well outside the limits of experimental error reportedby the rest of the authors.

The authors are indebted to S. Ariov, whose technicalhelp is greatly appreciated.

Note added in proof: In a recent paper by P. Varanasi andS. S. Penner [J. Quant. Spectry. Radiative Transfer 7, 279(1967)], the NO fundamental was redetermined by the use ofPenner's method of self-broadening. The result obtained was128 ± 10 cm-2 atm-' at 273aK, in good agreement with thepresent results.

References

1. R. J. Havens, Ph.D. dissertation, University of Wisconsin,Madison (1938).

2. H. L. Dinsmore and B. L. Crawford, Jr., Rept. NR-019-104, University of Minnesota (1949).

3. S. S. Penner and D. Weber, J. Chem. Phys. 21, 649 (1953).4. J. Vincent-Geisse, Compt. Rend. 239, 251 (1954).5. B. Schurin and S. A. Clough, J. Chem. Phys. 38, 1855

(1963).6. T. C. James, J. Chem. Phys. 40, 762 (1964).7. D. L. Ford and J. H. Shaw, Appl. Opt. 4, 1113 (1965).8. C. Alamichel, Ph.D. thesis, Universit6 de Paris (1965).9. J. C. Breeze and C. C. Ferriso, J. Chem. Phys. 41, 3420

(1964).10. L. L. Abels and J. H. Shaw, J. Mol. Spectry. 20, 11 (1966).11. R. M. Feinberg and M. Camac, Symposium on Molecular

Structure and Spectroscopy, Paper Z5, Columbus, Ohio(1966).

12. U. P. Oppenheim and Y. Ben-Aryeh, J. Opt. Soc. Am. 53,344 (1963).

13. U. P. Oppenheim and Y. Ben-Aryeh, J. Quant. Spectry.Radiative Transfer 4, 559 (1964).

14. A. Goldman and U. P. Oppenheim, J. Opt. Soc. Am. 55, 794(1965).

15. U. P. Oppenheim and A. Goldman, J. Opt. Soc. Am. 56,675 (1966).

16. D. E. Burch, E. B. Singleton, and D. Williams, Appl. Opt.1, 359 (1 962).

reported by STANLEY S. BALLARD, Department of Physics and Astronomy,University of Florida, Gainesville, Florida. Professor Ballard hopes to receive newsand comments for this column, which should be sent to him at the above address

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August 1967 / Vol. 6, No. 8 / APPLIED OPTICS 1307