Eric Ari6, Nelly Lacome, Philippe Arcas, and Armand Levy
Oxygen-broadened linewidths have been measured at room temperature using a method of laser spectrosco-py. By combining these parameters with previously measured nitrogen-broadening values, air-broadeningparameters have been derived. The averaged experimental data for self-, N2, and 02 broadening have beencompared to theoretical values calculated on the basis of an improved semiclassical model previously used forN 20. Quite satisfactory agreement is observed up to J 50.
1. Introduction
Correct interpretation of infrared spectra recordedwith limb-viewing instruments requires previousknowledge of the vertical temperature profile. Usual-ly, this important information is inferred from sepa-rate measurements (rocketsondes, balloons, etc.) madein several C02 sounding channels. These observationsare thus critical to the success of atmospheric trans-mittance calculations.
Transmittance profiles are usually determined bythe line-by-line integration procedure which consistsin summing the contribution of all individual linesabsorbing in the spectral range under study. So, anyerror in the positions, intensities, and linewidths ofC02 lines will induce, besides inaccuracies related tothe temperature determination, additional uncertain-ties in the retrieved mixing ratios of atmospheric spe-cies.1'2 Similarly, accurate quantification of the ab-sorption and emission of C02 bands (more especially inthe 10-20-,um region) is a crucial problem in the deter-mination of terrestrial cooling rates, thermal equilibri-um in the stratosphere as well as in climate modeling.Considerable effort has therefore been made to im-prove C02 spectroscopy so that carbon dioxide hasprobably been studied more than any other molecule.This is reflected in the periodic updatings of the atmo-spheric data banks3-5 which regularly report new infor-mation concerning C02. However, uncertainties stillexist. These mainly concern the halfwidths of linesand their temperature dependence. Refinement of
The authors are with University of Paris-South, CNRS InfraredLaboratory, Building 350, 91405 Orsay CEDEX, France.
the available data on line shapes is also becoming, inmany cases, a requirement of increasing importance.6
Extensive measurements have been made of self-and N2 broadening of C02 lines for various vibrationalbands.7-28 Some studies also deal with the effectof temperature on the variation of broadening co-efficients.920 -27 As will be seen later, publishedvalues'1 -15, 17-20 2 2-2 7 of C0 2 -N2 widths show rathergood agreement, and it is presently admitted that thebroadening of C02 lines by nitrogen which is essentialin atmospheric calculations is known with reasonableaccuracy. Usually it is assumed that N2-broadeningparameters provide, for atmospheric modeling pur-poses, a sufficient approximation to the air-broaden-ing parameters.29 In many cases, some scaling factoris applied to take into account the effect of oxygenbroadening.30 For only the P(34) line, Bufton et al. 3 1
have directly measured the air-broadened width. Incontrast to the situation for N2, direct measurementsof 0 2-broadening are very scarce.17 23 In view of theincreased level of accuracy required for the sensing oftemperature, it is of interest to perform detailed inves-tigation of these parameters. In addition to their use-fulness in radiative sensing applications, accurate val-ues of C02-02 linewidths are also of importance fortesting theoretical models. We recently reported animproved calculation for linewidths in N20-N 20,N20-N2, and N20-0 2 systems.32 33 The same modelwill be applied here for C02 in order to check itseffectiveness in describing collisions between quadru-polar molecules.
I. Experimental
A. Principle of the Method
The present results were obtained by using a well-known method of laser spectroscopy.1014,23 A single-mode single-line frequency-stabilized C02 laser is usedas a source. The emitted radiation is locked on thepeak frequency of a given lasing line and passed
through the absorption cell containing the absorbingCO2-0 2 sample under study. The measured transmis-sion thus immediately gives the peak absorption of theCO2 considered line. The basic assumption of themethod is that the pressure shift of CO2lines is negligi-ble, so that the lasing emitted frequency coincides withthe center of the absorbing line. No systematic mea-surements of line shifts of CO2 have been made so far.In a recent paper, Arcas et al.3 4 reported a measuredvalue of 5 = 0.014 cm- 1 atm- 1 for the self-shifting of theR(6) line in the 3v3 band. The theoretical calculationyielded a value of similar magnitude. It is likely thatthe foreign-gas shifting we are concerned with wouldbe somewhat smaller. For similar molecules, such asN20 and OCS, the self-shifting, as measured in therotational spectrum, was found to be almost negligibleand even unmeasurable for N20.35-37 Since the pres-sure of samples in our experiments never exceeded300-400 Torr, the corresponding shift would yield adetuning of -3-4 X 10-3 cm-1 , thus giving a variationof the measured peak absorption coefficient of, atmost, 1-1.5% (on the assumption of a Lorentzianshape). Therefore, the neglect of shifting effects canbe considered as a reasonably valid approximation.
B. Experimental Details
The -1-m long laser cavity was mounted on Invarrods for heat insulation and the spherical mirror of theresonator was set up on a piezoelectric ceramic. Theprinciple of the stabilization procedure is describedelsewhere.38 The White-type absorption cell wasequipped with KCl windows and careful thermal insu-lation ensured constancy of temperature to better than1 K. The temperature was continuously controlled bya platinum sonde, and pressures were measured with aBaratron gauge. The emerging radiation was directedonto a Hg-Cd-Te detector, and the output signal of thelock-in amplifier was displayed on a chart recorder.
Each run was accomplished as follows: the cell wascarefully evacuated and the base line Io recorded; thedesired pressure of CO2 was then admitted into the celland successive additions of oxygen were made; foreach, the peak transmission at the center of the linewas recorded, when both the temperature and totalpressure were stabilized; the cell was finally evacuatedand the base line recorded again. When only slowvariations of the base line were observed (slight ther-mal drifts mainly due to the cooling of the detector),linear interpolation allowed the determination of theevolution of Io over the duration of the run; otherwise,the run was discarded.
All measurements were made for pressures above100 Torr to ensure that the collisional regime wasestablished, and below 400 Torr to avoid overlappingbetween neighboring lines which would affect the mea-sured peak transmittance.
Only the 10.4-,gm band has been investigated in thiswork.
C. Data Reduction
Each sample is specified by the values of the partialpressures P(CO2) and P(0 2). Assuming that the linestrength does not depend on the foreign gas pressure,the absorption coefficient at the center of the line iswritten as
where T is the temperature, 70(C0 2) is the self-broad-ening parameter, and -yo(CO2-02) is the oxygen-broad-ening parameter. By comparing for a given line thepeak absorption for self- and oxygen broadening, itbecomes
ko (CO2) P(0 2 ) TO (CO 2-0 2 )R = = 1 +
koT (CO2-02) M(C2) 70 (CO2)(2)
The values of both k(CO 2) and yO(C2) have beendetermined in previous work.10 39 The procedure con-sists of measuring the absorption coefficient kT(CO2-02) for a series of values of the ratio P(02 )/P(CO2 )[ensuring in each case that the total pressure P(0 2) +P(CO2) remains within the limits of 100-400 Torr].The corresponding values of R = k'T(CO2)/k T(CO2-0 2)are least-squares fitted to the linear form (2). Theslope of the fitted straight line yields the relativebroadening coefficient
TO(C02-0 2 )
o0(C0 2 )
for the value of the rotational number m under consid-eration, and the oxygen-broadening value -YO(C02-02)is immediately obtained since -yO(CO2) is known. Foreach studied line, 12-18 values of R were used in thefitting, and all quantities involved in Eq. (2) reduced tothe reference temperature 296 K.
D. Results and Discussion
Table I lists the values of the relative broadeningcoefficient a = -yo(CO2 -02)/yo(CO2) at 296 K. Quoteduncertainties are taken as one standard deviation a.For most lines, a lies between 0.002 and 0.005, corre-sponding to an accuracy of 0.3-0.8% on each individuala(m). Only for three lines does a exceed 0.005.
A plot of the measured values of a against the rota-tional number Iml (Fig. 1) shows immediately that nosignificant variation of a as a function of Iml can bedetected. The data points are randomly distributedabout a mean value except Iml = 8 which noticeablydeparts from all other points. Thus, a can be consid-ered as constant all over the vibrational transitionunder study. A weighted average (with normalizedweights proportional, for each Iml, to 1/a2) gives themean value a = 0.652 + 0.013.
Similar measurements were made previously byBulanin et al.2 3 Their results are in good agreementwith ours up to Iml 30, but a noticeable discrepancyappears for higher values of ml. Their results for Iml= 36 and Iml = 42 are somewhat higher than ours,
a Values given in parentheses are one standard deviation in thelast digit.
suggesting an increase of a vs Iml which is not corrobo-rated by the present work.
Reichle and Young40 have investigated the foreigngas broadening in the 15-ym bands of CO2 with amedium resolution. These authors define a band-averaged broadening factor F by reference to nitrogenbroadening. For oxygen, they give a value of F = 0.85corresponding to a = 0.65. It is easily shown that thisresult agrees fairly well with our value of a, as also doesthe determination by Burch et al.41 : F = 0.81 yieldinga = 0.62.
Table I also displays the values of the oxygen-broad-ened linewidths YO(CO2-0 2). These are derived fromour previously measured1039 self-broadening coeffi-cients yo(CO2). In practice a fit was performed on theexperimental data of Ref. 10 and the smoothed valuesretained.
Regarding now the accuracy of these calculated pa-rameters for oxygen broadening, it is quite clear thatthe main source of error lies in the uncertainty on theself-broadening values. The relative broadening abil-
0.74
0.7
0.66
0.62
0.58
0.54
ity a has been shown to be determined with fairly goodprecision. Even by taking two standard deviations tobe the experimental error on a, this amounts to arelative precision of -3%. This is much less than theuncertainty on yo(C02) values. The great amount ofpublished data 7 -2 4 on self-broadening of CO2 shows-at first sight-an important scatter and the questionmay be raised of defining reference values of TOW(C2)that could be used for further applications. Carefulinspection of all these data leads to the following obser-vations:
(a) No clear dependence on the involved vibrationalstates is apparent within limits of experimental error.This situation is very similar to that encountered forthe self-broadening of N20, the twin molecule ofCO2.3242 It was found that, except for Iml values in the10-25 interval for which some discussion was possible,all curves of y vs Iml for different authors and severaldifferent transitions were almost undiscernible.
(b) When comparing, for a given value of Iml, all theavailable values of self-broadened widths, it appearsthat they lie within an interval of 10-12 X 10-3 cm1atm- 1. This is consistent with the currently quotedlimits of experimental uncertainty (0.005 cm-1atm-1) in such measurements. However for low Imlvalues, the scatter of data is much greater and thediscrepancy between reaches in a few cases 20-25 X10-3 cm-' atm-1.
These observations are evident from the plot givenin Fig. 2. All the available experimental data aredisplayed, including recent results2443 which give valu-able indications on the behavior of the self-broadeningcoefficients for high Iml values (60 m 80).
It appears reasonable to perform a global fittingyielding for each Iml an averaged value of greater reli-ability. Among all the available material, only twosets of data have been discarded:
Those of Meyer et al.17
: these authors have studiedonly four lines and the corresponding results are verycontradictory: for example, yo = 0.108 cm-1 atm- 1 forR(20) and y = 0.135 for P(20).
Those of Boldyrev et al.'2 and Vasilevski et al.' 3 :the first lie far below those of most authors. Thedeparture from the final fit increases continuously and
a
, Iml
0 20 30 40Fig. 1. Relative broadening coefficient of 02 as a function of Iml;a(m) = yO(m)co,-o2/'yo(m)cO2: o, Bulanin et al.23; this work, experi-
Fig. 2. Self-broadening coefficients of CO2 as a function of Iml at296 K: +, Refs. 7-24; o, Tubbs and Williams,9 A, Ari6 et al. ,10 -least-squares fitting of all experimental data (encircled data have
been discarded in the least-squares fitting).
Iml increases, reaching, for example, 0.024 cm-' atm-1for Iml = 41. As for Vasilevski et al., the magnitude oftheir results is in some cases twice the currently admit-ted values, which raises an unexplained problem.
Regarding the results of Tubbs and Williams,9 Fig. 2shows clearly that some of their measured values areexceedingly distant from most other data. This is thecase for several data points in the range 5 <Iml < 25.These have been eliminated from the final fit. In allother cases, all the sets of experimental data have beenretained without making any arbitrary selection.
Table II gives the proposed fitted values for the self-broadened widths of CO2. It appears that our mea-surements are close to the fitted curve, in the 10 < m K50 range the deviation never exceeds 5 X 10-3 cm-1
atm-1 and it is very often smaller.The fitting for low Iml values however raises some
doubts: the discrepancies between authors are solarge that the true shape of the curve yo(m) in thisinterval cannot be established with sufficient uncer-tainty.
Finally, the fitted values for 0 2-broadening are list-ed in Table II, and their experimental uncertainty isestimaged to 4-5%.
E. Nitrogen-Broadened and Air-Broadened Linewidths
These results can be combined with the correspond-ing ones for N2 broadening to compute the air-broad-ened widths. In contrast to the situation for self-broad-ening, intercomparison of all the published data forC02-N211 15,17-20,22-28,31 reveals that all of them agreeto within limits of experimental error (except for Oo-date and Fujioka' 8). As was done for C02-CO2, aglobal fit was then given averaged values (Fig. 3). Theresults are listed in Table II. Finally, the air-broaden-ing parameters are derived by making use of the rela-tion
and the values obtained are also given in the last col-umn of Table II. For the P(34) line our value is in closeagreement with that directly measured by Bufton etal. 31
111. Theoretical Calculation of the Broadening of CO 2Lines
A. Generalities
The method for calculating collision-broadenedlinewidths for molecular systems where quadrupolarinteractions dominate was described extensively in arecent paper.32 Here we briefly recall only the outlinesof the formalism as developed by Robert and Bon-amy. 44
For an isolated Lorentzian line i f, the halfwidthat half-intensity is written as
N' b Re [ vf()dv 27rbdbS(b),L '2J2 J
with
S(b) = 1-(1 - Siddle)
X exp[- (S2 outerf + S2outeri + S2middle)],
where Nb is the number density of perturbing mole-cules,
PV2J2 is the density of the state v2J2) of the per-turber,
v is the relative velocity, andb is the impact parameter.
The S2 quantities have their usual significance of theAnderson-Tsao-Curnutte theory,45 46 the superscriptsD and ND referring to the diagonal and nondiagonalparts of S2 middle.
The main features of the calculation are as follows:(a) The differential cross section S(b) is expressed
by means of the linked-cluster theorem, so that a par-tial summation of all V-orders leads to an exponentialform of S2 (b). As a result, a cutoff procedure is nolonger needed and the arbitrariness of the convention-al ATC calculation is removed.
(b) The collision geometry is described by an equiv-alent straight trajectory which is more realistic, forclose collisions, than the usual ATC straight path.
(c) The interaction potential consists of the usualelectrostatic part (quadrupole-quadrupole) supple-
0.1
0.es
0.08
0.07
0.06
0.05s
0.04
0.03
0.02
0.01
.4
.4+ 4.44 +44
I I I I I . , I I I I I I . , , Im l0 20 30 40 50 60 70 80
Fig.3. N-broadening coefficients of CO 2 as a function of Iml at 296K: +, Refs.8,11,13,18,20,22-25,31,43;-, least-squares fitting of
all experimental data.
mented by an atom-atom model47 which accounts forboth the long- and short-range anisotropic interac-tions.
As was previously done for N20,3233 particular at-tention was paid to the choice of molecular parametersintroduced in the calculation: quadrupolar momentsof the colliding species and atom-atom parameters.The basic requirement is that the same set of values beused for the three systems under study: C02-CO2,C02-N2, and C0 2-0 2. The approach is similar to thatpreviously adopted for N20. In the case of C0 2-CO2,the electrostatic contribution dominates due to themagnitude of the quadrupole of C02, and the atom-atom part is of small influence. The value of Qco2 canthen be properly adjusted. For C0 2-0 2, the oppositeoccurs: the smallness of the quadrupole of 02 makesthe electrostatic contribution of almost negligiblemagnitude, the atom-atom part prevails, and the ef-fect of varying the corresponding parameters can betested. Finally, for C02-N 2 the calculation is sensitiveto both parts of the potential, thus allowing a globaltest to be performed.
B. Details of the Calculation and Results
The final values of the quadrupoles adopted aregiven in Table III, along with the atom-atom parame-ters and the rotational constants. For Qco2, we retainthe value 3.6 X 10-26 esu. When using the recom-mended value of Stogryn and Stogryn,45 Qco2 = 4.3 X10-26, far too large linewidths are calculated.
A similar observation was previously reported bySrivastava and Zaidi49 who calculated self-broadenedCO2widths in both Raman and IR spectra; also, severalrecent papers suggest using a smaller value of Qco2:Amos et al.50 in their theoretical study of the collision-induced Raman spectrum of C02; Murthy et al.,5'Pandey et al.
5 2 (NMR data), Morrison and Hay5 3 (abinitio calculations). For N2 and 02, the adopted val-ues are 1.3 and 0.39, respectively. The latter is therecommended value48; whereas Harries54 in his surveyof the reported values of QN2 also proposes QN2 = 1.3 ±0.2, consistent with Stogryn's recommended 1.52.
Fig.4. 02-broadening coefficients of CO2 as a function of ml at 296K. Experimental: +, this work; X, Cousin et al.43 Theoretical,Qco2 = -3.6 and Qo2 = -0.39: . . .. ., mean atom-atom potential;----- minimum atom-atom potential; , extrapolated
atom-atom potential.
Table IV
The adjustment of the atom-atom energy coeffi-cients raises more serious problems. We consider firstthe C02-02 system which allows the fitting of thevalues for C-C and 0-0 interactions (C-O is calculat-ed by the usual combination rules). When using themidpoint values given by Oobatake and 0oi47 calculat-ed widths are systematically too large by an amount of-8 X 10-3 cm-' atm-1. The deviation is reduced byonly a factor of 2 when taking the lower limit (definedby Oobatake on the basis of a 10% accuracy in fittingsecond virial data). So one is led to adopt for theatom-atom parameters final values smaller than themidpoint ones by an amount twice the range of varia-tion defined in Ref. 47. This is shown in Fig. 4 whichdisplays the smoothed experimental values of O(C02-02) and the calculated ones.
The extrapolated atom-atom parameters for C andO are then introduced in the calculation of C02 -N2linewidths to test the quadrupole of N2 and to simulta-neously adjust the atom-atom parameters for nitro-gen. The calculation is found to be less sensitive to thevariation of the quadrupole than it is to the atom-atomvalues. So that finally, QN2 = 1.3 (as was adopted forN20-N2
33) and atom-atom coefficients for N extrapo-lated in the same way as for C and 0 provide the bestcompromise.
As an example, Fig. 4 displays the experimentalresults for Yo(C02-02) and the values calculated withthree different combinations of atom-atom parame-ters and quadrupoles. Curve 3 calculated with Qco2 =3.6, Qo2 = 0.39, and the above defined extrapolatedatom-atom potential yields the best fit to our experi-mental data up to Iml = 50. However a slight discrep-ancy appears in the 65 m 80 range between therecently measured values of Cousin et al.43 and thecalculated ones. The departure is 0.008-0.010 cm-'atm-' which is to some extent acceptable, since very
close collisions are involved for such Iml values. Forlarge Iml values, even the atom-atom model obviouslyfails to account for short-range interactions.
Similar observations can be made for the two othersystems considered here. For both C02-CO2 and
C0 2-N 2, the agreement is quite satisfactory up to ml =40. The departure from measured values remainswithin the limits of experimental error, i.e., 0.003-0.005 cm'1 atm-1. For high l, larger deviations, asimportant as 0.006-0.010 cm-' atm-', are observedand the degradation increases with increasing Iml. Allthe calculated values are presented in Table IV. Fi-nally, it must be emphasized that the model used re-mains semiclassical, and one should not expect it toprovide good results out of its own limits of validity.An additional test of the ability of the model in correct-ly describing the broadening mechanisms of quadru-polar molecules would be to investigate the tempera-ture dependence of the linewidth parameters. Thiswill be done in a forthcoming paper.
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41. D. E. Burch, E. B. Singleton, and D. Williams, "Absorption LineBroadening in the IR," Appl. Opt. 1, 359 (1962).
42. N. Lacome and A. Levy, "A Parametric Deconvolution Method:Application to Two Bands of N2 0 in the 1.9 am Region," J. Mol.Spectrosc. 71, 175 (1978); "Line Strengths and Self-BroadenedLinewidths of N2 0 in the 2 m Region," 85, 205 (1981) andreferences quoted therein.
43. C. Cousin, R. LeDoucen, J. P. Houdeau, C. Boulet, and A. Henry,"Air Broadened Linewidths, Intensities and Spectral Line-shapes for CO2 at 4.3 m in the Region of the AMTS Instru-ment," Appl. Opt. 25, 2434 (1986).
44. D. Robert and J. Bonamy, "Short Range Force Effects in Semi-classical Molecular Line Broadening Calculations," J. Phys. 40,923 (1979).
45. P. W. Anderson, "Pressure Broadening in the Microwave andInfrared Regions," Phys. Rev. 76, 647 (1949).
46. C. J. Tsao and B. Curnutte, "Line-Widths of Pressure-Broad-ened Spectral Lines," J. Quant. Spectrosc. Radiat. Transfer 2,41(1962).
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54. J. E. Harries, "Temperature Dependence of Collison-InducedAbsorption in Gaseous N2," J. Opt. Soc. Am. 69, 386 (1979).
0
Meetings continued from page 2570
1987January
5-9 Optical Info. Processing & Holography Gordon Res.Conf., Santa Barbara S. Case, Elec. Eng. Dept., U. ofMN, Minneapolis, MN 55455
7-9 Infrared Detectors & Systems course, Lake Buena VistaV. Amico. U. of Central FL, Orlando, FL 32816
11-17 Optoelectronics & Laser Applications in Science & Engi-neering, Los Angeles SPIE,P.O. Box 10,Bellingham,WA 98227
14-16 Picosecond & Optoelectronics Top. Mtg., Lake Ta-hoe OSA Mtgs. Dept., 1816 Jefferson P., N.W.,Wash., DC 20036
19-22 Conf. on Optical Fiber Communication/Int. Conf.on Integrated Optics & Optical Fiber Communi-cation, Reno OSA Mtgs. Dept., 1816 Jefferson Pl.,N.W., Wash., DC 20036
26-28 Laser Analytical Spectroscopy Top. Mtg., Lake Ta-hoe OSA Mtgs. Dept., 1816 Jefferson P., N.W.,Wash., DC 20036
26-28 Noninvasive Assessment of the Visual System Top.Mtg., Lake Tahoe OSA Mtgs. Dept.,1816 JeffersonPl., N.W., Wash., DC 20036
26-29 Laser Applications to Chemical Analysis Top. Mtg.,Lake Tahoe OSA Mtgs. Dept., 1816 Jefferson P.,N.W., Wash., DC 20036
28-30 34th Ann. Conf. Western Spectroscopy Assoc., PacificGrove D. Saperstein, IBM, E42/13, 5600 Cottle Rd.,San Jose, CA 95193
February
8-11
9-10
ISCC Williamsburg Conf. on Appearance, WilliamsburgD. Alman, E.I. Du Pont Co., 945 Stephenson Hgwy.,P.O. Box 2802, Troy, MI 48007
Southwest Conf. on Optics, Albuquerque OSAMtgs. Dept., 1816 Jefferson P., N.W., Wash., DC20036
