Measurement of CO2 line broadening in the 10.4-Atm lasertransition at low temperatures
Eric Ari6, Nelly Lacome, and Armand L6vy
The broadening of CO2 rotation-vibration lines has been investigated in the 200-300 K temperature range.From an analysis of four lines (Im = 8, 15, 20, 30), it is found that the temperature exponent is nearlyindependent of the rotational quantum number within the limits of experimental error, for both self- andoxygen broadening. Average values n = 0.86 for C0 2-CO 2 and n 2 = 0.94 for C0 2 -0 2 have been obtained.Comparison is made with the results of the theoretical calculation based on the Robert-Bonamy model.
1. Introduction
We report a preliminary investigation of C02 broad-ening over the 200-300 K temperature range. Carbondioxide is a key molecule in atmospheric transmittancecalculations since it is used as the source of radiancebeing sensed for determining the vertical distributionof temperatures in the earth's atmosphere. Inversionof the so-measured radiances to temperatures requireshigh-accuracy determination of intensities and line-shape parameters in the spectral channels concerned.'In a recent paper,2 a short review of the available dataon self- and nitrogen broadening of C02 at room tem-perature was given. Revised values of the correspond-ing parameters were proposed along with new resultson oxygen broadening. The variation of CO2linewidths with temperature has also engaged the at-tention of many people.3-11 In most cases, self- andnitrogen broadening were reported while oxygenbroadening was analyzed only in Ref. 10. It is one ofour aims to provide new data concerning the tempera-ture dependence of CO2 lines.
It is widely agreed that the variation of linewidthwith temperature may be written in the form
y(7) = (1(To)(TO)T)(
where the reference temperature is, in most cases, theroom temperature. For a given value of J, the expo-
The authors are with University of Paris-Sud, Infrared Laborato-ry (CNRS), Centre d'Orsay, 91405 Orsay CEDEX, France.
nent n is generally assumed to be independent of thevibrational state v. However, the available values of nfor CO2 lines show in some cases wide variations ac-cording to the vibrational transition considered (see,for example, Ref. 4). Also, the compatibility of resultsgiven by different authors raises some difficulties.Thus, investigations by different spectroscopic tech-niques are still necessary to establish reliable data.
As an extension of our previous work,2 we have ana-lyzed the temperature dependence for self- and 02broadening in the laser transition near 10.4 ,gm. As apreliminary step, four lines were studied. The valuesof Iml retained (ImI = 8,15,20,30) were chosen to coverthe range of values currently accessible in laboratoryspectra.
11. Principle of the Method and Experimental Details
The method of laser spectroscopy has been exten-sively described elsewhere'2 and most experimentaldetails are given in a recent paper.2 A single-modesingle-line frequency-stabilized CO2 laser is used as asource, and the emission locked in at the peak frequen-cy of a given line. By measuring the transmission ofthe sample under study, the absorption coefficientk(oo) at the center of the line is immediately derived,provided that the line strength is previously known.The basic assumption is that the pressure shifting oflines remains of negligible magnitude so that the emit-ted frequency and the absorption peak coincide. Thevalidity of such an assumption has been discussedpreviously. 2
In the present experiments, the samples were con-tained in a White-type multipass cell of 1-m baselength, constructed of stainless steel, giving opticalpaths up to 50 m. It was equipped with a jacket
1636 APPLIED OPTICS / Vol. 26, No. 9 / 1 May 1987
cryogenic fluid
M 2 revolvingsonde
LOW TEMPERATUREMULTIPASS CELL
chartrecorder
laser stabilization tis C0 2 N2 +He pump
\ water water
plezo-electricalceramic
I =20mAV 8000v
CO2 LASER
Fig. 1. Schematic view of the experimental device.
permitting the circulation of the coolant fluid (methyl-cyclohexane), and the whole system was wrapped in aninsulating material to minimize thermal exchangeswith ambient air. To prevent condensation of atmo-spheric water vapor on the windows, each was protect-ed by an evacuated cylinder equipped with an externalwindow made of KCl. All the details of the cryogenicdevice were reported before.13 The stability of thetemperature of the samples was "1 K, and it wascontinuously monitored during the experiment by aplatinum sonde.
The optical system inside the cell was mounted onInvar rods; furthermore, thermal contractions in themounting of the mirrors could be compensated byexternal screws allowing, when necessary, adjustmentof the optical setting; this was checked by an auxiliaryHe-Ne laser. Figure 1 gives a schematic view of theexperimental setup. The revolving mirror Ml allowedthe C02 laser to be directed onto a grating spectrome-ter to identify the emitted line. The stability of theemitted power was monitored throughout a given run:for this purpose, the optical cell was bypassed by rock-ing down the mirror M2 so that the laser beam wasdirectly focused onto the detector for measuring at anytime the emitted energy.
Pressures were measured with a Baratron gaugeworking in the 0-1000-Torr range and the stated puri-ty of gases (CO2 and 02) was better than 99.998%.
Ill. Data Reduction
A. Self-Broadening Measurements
For each temperature T, the absorption coefficientat the center of the line is given by
kT = (1/L) ln[I0(aO)/It (a)]. (2)
In the Lorentz approximation (which strictly holdshere, since all pressures range in the 100-400-Torrinterval),
kT= SO(T)hr-yo(T), (3)
So(T) is the line strength and -yo(T) is the self-broaden-ing coefficient at temperature T, for the standard pres-sure of 1 atm. Here So(T) is easily derived from thecorresponding value at room temperature So(To), bymeans of the usual relation So(T) = So(To)f(T), with
f(T) = ToQint(T0) exp E"(J) ( -- T)I ' (4)
where Qint is the internal partition function and E"(J)
1 May 1987 / Vol. 26, No. 9 / APPLIED OPTICS 1637
Hg Cd Teo
grating -
is the rotational energy of the lower level. Taking intoaccount the Lorentzian relation
So(TO) = rkTyo(To), (5)
kT becomeskT = S(T)f(T)ryo(T) = k T-f(T)yo(T 0 )/yo(T). (6)
Since yo(Tf is expressed as yo(T) = yo(To)(T/T)n, themeasured quantity kT is given by
kT = kTy(7)(TOT)-n (7)
The values of the absorption coefficients kTo for all thelines in the 10.4-pm laser transition were previouslymeasured.12 Optimized values have been derived byleast-squares fitting these results.' 4 The f(T) is easilycalculated for a given line of quantum number J.Equation (8) may then be written in the linear form:
ln[kT/f(T)I = lnkTo - n ln(T 0/T), (8)
Table . Temperature-Dependent Exponent for the Self-Broadening ofC02 (To = 296 K)
(a) Room-temperature value of the peak absorption coefficient kT-taken as
a free parameter.
(b) kT constrained to the smoothed value of Ref 2.
(c) values derived from the linewidth values given in Table I of Ref 10.
All values of kToare expressed in 10-3 cn7I. Quoted uncertainties are one
standard deviation.
So that n is derived by least-squares fitting the ob-served quantities ln[kT/f(T)] as a function of ln(To/7f.In this fit, nkTo can be either constrained to the valuepreviously determined at room temperature or kept asa free parameter. In the present case, both procedureswere used to check the consistency of the measure-ments. An alternative derivation of n would consist ofexpressing first the linewidth yo(T) from the measuredabsorption coefficient kT. Obviously, both deriva-tions are equivalent, provided that the choice of room-temperature values So(To) is consistent with the corre-sponding values of kTo adopted in Eq. (8).
B. Oxygen Broadening Measurements
For a given mixture P(CO2) + P(02 ), the linewidth attemperature T may be written as
which shows that kT(CO2-O2) depends only on theratio of the partial pressures of C02 and O2. If n andn2 are the temperature exponents for the self- andoxygen broadening, respectively, kT(CO2-O 2 ) becomes
In practice, the data processing is as follows: kT(CO2-02) is determined experimentally; then, from theknowledge of the line intensity SO(To) and of f(T), theL(T) is obtained immediately. Then, the quantityM(7) = y'oT (C 2-0 2)(TO/y)n2 P(0 2)/P(CO2 ) may beextracted from
M(T) = L(T) - yT(CO -CO2)(T0 /T)nl. (15)
The room temperature broadening coefficientsg'Y(CO2-CO2) and -yo(CO2-O2) are given in our previ-
ous work,2,'2 and n1 was determined above. Thus, byleast-squares fitting the values of lnM(T) as a functionof ln(To/T), the n2 is easily derived. Here again, it ispossible either to constrain -yjTO(C2-0 2) to thesmoothed value obtained in Ref. 14 or to leave it as afree parameter.
IV. Results and Discussion
Table I gives the values obtained for the tempera-ture exponent nj in C02 self-broadening. It is seenthat the values of kTo(CO2) retrieved in the fit are veryclose to those directly determined at room tempera-ture: in the most unfavorable case, for the P(20) line,the agreement is better than 2%. This is a good cor-roboration of the consistency of the measurements.However, the results are more disappointing when onecompares the values of nj yielded by the two differentfits (according to whether kT is fixed or a free parame-ter). For the two lines P(8) and P(30), the agreementis quite satisfactory; it remains acceptable for R(15)but for P(20) the difference in the values of n1 reaches20% which is very large. This is obviously due to theexponential form of the temperature dependence rela-tionship. Strong variations in the exponent n result invery small differences in the corresponding values ofkT. This means that the peak-absorption coefficientis not an effective intermediate for sensing the influ-ence of temperature on linewidths since it is almostinsensitive to the temperature variation. Anothercause of uncertainty is the presence of hot bands which
1638 APPLIED OPTICS / Vol. 26, No. 9 / 1 May 1987
can significantly contribute, even at room tempera-ture, to the observed absorption. This is typicallyexemplified byP(20) which is in close coincidence withR(23) of the (0111)-(1110), transition (the two linecenters differ by <10-3 cm-). Munjee and Christian-sen'5 have shown that the magnitude of the contribu-tion of R(23) can be estimated to -6% of the measuredabsorption at room temperature, which is far fromnegligible. But for lower temperatures this contribu-tion decreases very rapidly. Thus, in processingP(20), we have discarded the measurement made atambient temperature; we then observed a substantialimprovement in the standard deviation of the fit, andthe initial departure of the two values of nj was consid-erably reduced.
It is of interest to compare these results with thoseprovided by other authors. There are very few investi-gations of the self-broadening of C02 at reduced tem-peratures. Valero et a. 6 -9 have studied both the in-tensities and linewidths in several different vibrationaltransitions for three temperatures: 197, 233, and 294K. They report only the measured widths but do notattempt to extract the corresponding values of n.From their results, we have derived, for the sake ofcomparison, the values of n for P(8) and R(15). In thecase of P(8), the three bands studied yield n = 0.59, n =0.48, and n = 0.65 while for R(15), values of 0.55,0.40,0.67, and 0.36 are obtained for four different bands.These values are not consistent with ours, but thecomparison is incomplete since the uncertainties oftheir measurements are not specified. Furthermore,values of n 0.5 are probably too small since theywould correspond to hard-sphere collisions. On theother hand the results of Tubbs and Williams 6 yield n>> 1 for almost all lines.
Measurements are also available for elevated tem-peratures. Comparison can be made assuming thatEq. (1) still holds for T > To with a constant value of nfor both low and high temperatures. Ely and McCub-bin'7 give an estimate of n 1 for the P(20) line of thelaser transition. Eng and Mantz'8 have studied P(20)and P(18) at 300 and 384 K. The corresponding valuesof n are found to be 0.882 and 0.764, respectively,which is in very good agreement with the present work.
Bulanin et al.'0 have considered, in their derivationof coefficient n, averaged values of the linewidth foreach pair of lines (P and R) starting from the sameinitial level. Thus, to make a comparison with ourresults, we have recalculated n for each P and R linetaken separately, from their own results, at both roomtemperature To and 523 K. The corresponding valuesof n are also given in Table I. Within the limits ofuncertainty, they show good agreement with ours, ex-cept for the higher Iml values for which their resultsseem to decrease systematically (n 0.75 for Iml = 35and n 0.65 for Iml 45).
Finally, if P(20) is excepted according to the abovediscussion, no significant variation in n with the rota-tional quantum number J is apparent in our measure-ments; to within the experimental uncertainty, n canbe considered constant over the range of values Iml <
Table II. Temperature-Dependent Exponent for the Oxygen-BroadeningOf C02
(c) averaged values for the P and R line of same J.
All values of linewidths are expressed in cm Iatm-1.Quoted uncertainties
are one standard deviation on the last digit.
30. Therefore, an average value can be derived, whichis n1 = 0.86 + 0.06 (the quoted uncertainty being onestandard deviation).
Table II gives the values obtained for the tempera-ture exponent n2 in oxygen broadening. In the least-squares fitting, the values of yTo(CO2-CO2), Y-yo(CO2-02) and nj were constrained to fixed values; the roomtemperature self-broadening coefficients are those giv-en in Ref. 12, the smoothed values of yyT(CO2-0 2) wereobtained previously,2 while nj was determined in thepresent work. For the first three lines, n2 is found tobe constant and the magnitude of the standard devi-ation does not exceed 10%. The results for P(30) areless satisfactory: a value n2 1.1 is obtained whichseems overestimated.
No measurements of oxygen broadening of C02 linesat reduced temperatures have been made so far. Com-parison can be made only with the values of Bulanin etal.' 0 at 523 K. These values are also reported in TableII. It is immediately seen that their results are sys-tematically lower than ours by 10-15%. It was notpossible to separately recalculate the individuallinewidths for the P and R lines as was done above forself-broadening. Bulanin et al. give only the values ofn2; the broadening coefficients 0(CO2-02) are notreported in their paper.
However, we must note that our values of n2 are ofthe same magnitude as those obtained for the twin-system N20-0 2 by a quite different experimental tech-nique (high resolution FTS). For N 0-02, it isfound 3"19 that n2 varies from 0.85 (for Iml = 2) to 1.02(for Iml = 40). The same is observed when comparingC02-0O2 (present work) and N20-N 20. Finally, ifone discards P(30), which can raise doubts as to thepossibility of undetected systematic errors, n2 appearsto be constant for any Iml; we can thus adopt an averagevalue, n2 = 0.94 0.10. It is then possible, from theaverage values of nj and n2 along with the smoothedlinewidths for self- and oxygen broadening, to deter-mine a set of optimized parameters at 220 K. These
1 May 1987 / Vol. 26, No. 9 / APPLIED OPTICS 1639
Table Ill. Self- and Oxygen-Broadened Llnewldths of CO2 at 220 K
Yj(Co2 - C02) cm 1atm1 y,(0 2 - 02) cm |atm 1
Iml exp. theor. exp. theor.
(a) (b)
8 0.1461 0.1372 0.1047 0.0988
15 0.1428 0.1297 0.0991 0.0934
20 0.1376 0.1282 0.0933 0.0872
30 0.1242 0.1171 0.0826 0.0796
(a) derived from the room-tomperature optimized values of Ref 2.
with n = 0.86
(b) derived from Ref 2 with n2 = 0.94
can be compared with the theoretical values calculatedwithin the framework of the model of Robert andBonamy.20 All the details about cross-sectional calcu-lations, trajectories, and expression of the potentialshave been given elsewhere.2 We only emphasize herethat the basic requirement we prescribe in performingthe calculation is that the same set of molecular pa-rameters (quadrupole moments and atom-atom coef-ficients) be used for any temperature considered.Therefore we keep here all the values already given inTable III of Ref. 2 without any further adjustment.
Table III summarizes the results obtained for thefour lines under study. The calculated self-broaden-ing parameters are in acceptable agreement with theoptimized experimental results. For three of the lines,the departures are -7-9 X 10-3 cm-' atm-'; only forR(15) does the difference reach 12 X 10-3 cm-' atm-1which is nearly the experimental error. For C02-02,the calculation closely reproduces the experimentaldata. On the whole, the theory correctly accounts forthe observed results. The problem is now to makeavailable more systematic data, over a wider range ofIm values, with improved experimental accuracy.This will be done in a forthcoming study by Fouriertransform spectroscopy.
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