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Temperature dependence of foreign gas broadening of HCl fundamental lines
JOURNAL
OF MOLECULAR
SPECTROSCOI’Y
Temperature
65, 134-141
(1977)
Dependence of Foreign Gas Broadening of HCI Fundamental Lines ANDRZE J W.
Ckemistry
Department,
MIZIOLEK’
University of Calvornia,
Berkeley,
California
93720
A long-pathlength variable temperature cell has been used to study three hydrogen chloride O-l vibration-rotational lines, P(7), P(8), and P(9) which were broadened by He, Ar, Nz, 02, and CO at room temperature and by Ar at low temperatures down to 190 IL The method employed to extract the linewidths is the equivalent width method. The temperature dependence of the resulting cross sections for the HCl-Ar broadened lines is similar to that recently found for other argon broadened HCl infrared and microwave lines. The results reported here (for high J lines) complement the other results (for low J lines) and together seem to constitute enough new data for further theoretical attempts at describing the process of collisional broadening
in general,
and the broadening
of HCl by argon
in particular.
INTRODUCTION
The case of hydrogen chloride absorption line broadening by foreign gases in both the microwave and infrared regions has been particularly well studied in the past two decades. In the earlier experiments (I-6) the equivalent width method was used to extract spectral line shape information, such as the linewidth parameter, while more recently, high-resolution spectrophotometers and interferometers have been used to obtain lineshape information more directly with apparently only small corrections for “slit” distortions (7-9). Only quite recently has there been experimental information available for the temperature dependence of the HCl-Ar broadened linewidths and shifts in the infrared (9) and the microwave (10) regions. It is the temperature dependence of the linewidths (and their associated cross sections) that gives a solid test to theories (particularly the perturbative (11-16) and semiclassical (17-19)) that have been developed over the years with the purpose of explaining the experimental observables, e.g., magnitude and J dependence of linewidths and shifts. Currently studies of the temperature dependence of linewidths are taking on added importance since these parameters are used (particularly for strong lines broadened by air) in the interpretation from ground base and/or balloon infrared spectra of the mixing ratios of various minor constituents in both the troposphere and stratosphere. Correct determination of these mixing ratios is imperative in order to test our understanding of the atmospheric processes which affect among others, the relationship between these minor constituents and the stratospheric ozone balance. 1Present address:
Chemistry
Department,
University
of California,
Irvine,
California
94720.
134 CoI)yright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN
0022-2852
HCI LINE
BROADENING
I 3.5
With these points in mind, and also with the knowledge that there are gaps in foreign gas broadening information on different HCl lines, we report the temperature dependence of the cross sections for HCl P(7), P(8), and P(9) lines broadened by argon. Jncluded also are room temperature broadening results for the same HCl lines broadened by Ar, He, CO, Nr and 02. The long-pathlength variable temperature cell gave us the opportunity of stud>-ing these relatively weak absorption lines but it also required working with relatively lo\\ resolution. For this reason, the equivalent width method, which has been used SLICXYSSfully for man\-. -vears, was employed in this work for the abstraction of linewidths from spectral rccordings. EXPERIMENTAL
DET:lILS
The long-pathlength variable temperature cell has been described b\- Horn and I’imentel (20). Two light sources have been used in the course of these esperiments, one a 300 W zirconium arc (Sylvania K300) properly housed for infrared operation and two, a carbon furnace following the design of Spanbauer et al. (V) and of Hester and Hand (22). The sprctrophotometer used is a Beckman IR-9 operating single beam. Due to the long pathlengths used (300-620 m) the spectrophotometer slits were kept wide for acceptable signal-to-noise conditions, resulting in an effective spectral slit width of approsimately 2.4 cn-l, not enough to resolve the chlorine isotopic peaks. Typical HCI pressures were in the 2Z7 Torr range while the foreign gases were brbetween 400 and 760 Torr. The cell (3300 liters) was normall\- filled in a sandwich fashion \\-ith 2 aliquots of HCl espanded from 50 liter vacuum line flasks into the center of the chamber sandwiched between three equal additions of the foreign gases. The accuracy of the pressure readings, which \vere done by a mercury manometer, is about O..,:‘;,. The cold runs were conducted on different clays with different HCl:Ar pressurcb ratios. These experiments proceeded by first cooling the cell to the lamest temperature desired, then, introducing the samples, and after sufficient time for thermal equilibration, taking the actual quantitative spectra. After these spectra were taken, the cell was allowed to warm up to the nest temperature of interest after which coolant was again recirculated to ensure no more than a 1” gradient across the cell as monitored h> 11 separate thermocouples. During the spectral recordings, the coolant pump was shut down to eliminate vibrations but the temperature in the cell rose no more than 4” during this time. The gases used for these experiments lJ.ere H(‘l Electronic Grade (99.99:‘; Mathcson), Ar (99.9955, Liquid Carbonic), He (99.999f”; VC Chem Dept.), XL’ Prep (;rade (99.998(‘{, Llatheson), OZ Ultra Pure (99.99’:{, Matheson), and CO Ultra High T’urit>, (99.85 Matheson). These were added directly into the cell without further purification. RESULTS
A detailed discussion of the equivalent width method will not be given here (see, e.g., Refs. (l-6)) ; instead, only the points necessary for our calculations will be mentioned. Briefly, according to the theory, due to our long pathtengths, we are well into the “square root” region where the following equation holds true : TT.?= 4S1_(-fu”pa+ r/y,.),
f.1)
ANDRZEJ
136
W. MIZIOLEK
TABLE I Room TemperatureLine Widths for DifferentHCl P Lines Broadenedby Argon Pressure lx1 (ton)
Pressure .4r(torr)
Pathlength (meters)
pc7ja Y"-1 (cm-latm )
Pwb Yol (cm-latm )
pwc Yol (cm-latm-)
_ 1.49
407
300 460 620
0.0306 0.0259 0.0247
0.0225 0.0271 0.0237
0.0251 0.0216 0.0201
2.60
402
300 460 620
0.0241 0.0227 0.0196
0.0241 0.0275 0.0277
0.0226 0.0221 0.0201
3.12
757
300 460 620
0.0211 0.0202 0.0162
0.0243 0.0201 0.0183
0.0213 0.0226 0.0198
1.99
758
300 460 620
0.0220 0.0202 0.0185
0.0236 0.0198 0.0199
0.0221 0.0209 0.0203
Average
Babrov (6) Rank (1) -1 = S'=3.264cn~-~atm
0.0222t.0011 0.0215
0.0232+.0009
0.0141 0.0150
b s"=1.712cm2arm1 = S0=0.804cm-2atm1
where
s = sop.. W is the experimentally determined equivalent width (in cm-‘), So is the line strength per atmosphere (in crne2 atm-‘), L is the pathlength (in centimeters), 72, rfo are the linewidths per atmosphere for self and foreign broadening (in cm+ atm-l), p,, p, are the pressures of the absorbing and broadening gases (in atmospheres), respectively. Accurate values for So for the P lines considered here are available (23) and are given in Table I. Equation 1 shows that with a large enough pf:p, ratio (which is true in our case), a knowledge of -rao is not necessary for determining the desired quantity, r/O. The pressure ranges (HCl, 2-6 Torr ; Ar, 400-760 Torr) for all of the experiments were such that there was never a problem of absorption in the wings of the reported P lines (overlapping lines of different J values) obscuring a baseline determination. Table I also gives the room temperature results for the P(7), P(8), and P(9) HCl lines broadened by argon, while the room temperature line widths for He, Nz, 02, and CO broadeners are given in Table III. In order to use the equivalent width method for temperatures other than 2% K the line strength So needs to be recalculated. The equation that enables this is:
So(J) =
exp(---E(J)IW,
where ZZO(J), is the dipole moment matrix element (which includes the Herman-Wallis factors), No is the number of molecules per unit volume, and Q is the rotational partition function. Thus, the temperature dependence of So is embodied in the temperature dependence of Y, and in the change of the rotational level populations.
HCl LINE BROADENING
O.Oh5 0.03n 0.0'15 0.03 0.0:: O.O?O O.U.!.: 11.014
Table IV gives the results for the temperature dependence of the HCI linewidths for the P(7), P(8), and Y(9) lines broadened by argon lvhich were based on two cold esperiments. The first spanned the temperature range of 214-257 K with Pncl = 3.00 Torr and PAr = 635 Torr (both measured at 298 K). The second covered the temperature range of 193-270 K with Pnci = 1.98 Torr and p,tr = 734 Torr (both measured
P(7)
0.0?11~.0014
P(R)
O.O?hl..GOlh
P(9)
O.O?i?
P(7)
O.U44'~~.OO,V
P(B)
0.0349~.001h
.00?4
P(9)
O.O3Oi~.OOI?
P(7)
0.02L5
P(8) P(9)
0.0?39'.0015 O.O234~.OOlh
P(7) I'(H) l'(9)
0.0452'.00?1 0,
.OOlh
O.O553..OO?J
“AI.i 00,<
ANDRZEJ
138
W. MIZIOLEK TABLE I"
TemperatureDependenceof Line Widths and Cross Sectionsfor IlClBroadened by Argon Temperature Experiment Absorption Number Line OK
So -1 (cF2atm )
P(7) P(8) P(9)
1.627 0.547 0.156
0.0492~.0031
0.0455+.0056 0.0443t.0138
52.6k3.3 48.6i5.9 47.4i14.8
210
P(7) p(8) P(9)
1.969 0.734 0.234
0.0406-'.0040 0.0389'.0029 0.0402?-.0037
45.314.5 43.4t3.2 44.at4.1
214
P(7) P(8) P(9)
2.048 0.778 0.255
0.0308i.0010 0.0323'.0013 0.0348i.0027
34.7kl.l 36.5t1.5 39.2i3.1
235
P(7) P(8) P(9)
2.428 1.023 0.375
0.0246'.0005 0.0273k.0002 0.0265*.0015
29.1iO.6 32.2f0.3 31.3Q.8
241
P(7) P(8) P(9)
2.528 1.093 0.413
0.0305'.0019 0.0301F.0017 0.0304'.0033
36.4t2.2 35.9i2.0 36.3t3.9
257
P(7) P(8) P(9)
2.775 1.278 0.518
0.0210i.0005 0.0247+.0008 0.0246?.0002
25.9to.9 30.5f0.9 30.310.2
259
P(7) p(8) P(9)
2.803 1.300 0.532
0.0271t.0003 0.0274+.0009
33.6k0.4 33.9t1.1 34.7Q.l
270
P(7) P(B) P(9)
2.950 1.423 0.607
0.0239~.0013 0.0242*.0014 0.0227+.0014
30.2t1.6 30.6t1.7 28.721.8
P(7) P(8) P(9)
3.264 1.712 0.804
0.0222~.0011 0.0232*.0009 0.0216f.0004
29.5t1.5 30.Bt1.2 28.6tO.5
193
298
see
Table I
at 298 K). Each of the low-temperature linewidths is based on two or three different measurements, i.e., pathlengths (for primary data see Ref. (24)). DISCUSSION
Tables I, II, and III show that whenever a comparison can be made, most of our results agree within 1.5% with those from other laboratories. A comparison in Table II of the Babrov et al. (6) linewidth results for the P(1) through P(6) lines with the interferometric results of Levy et al. (8) and Houdeau et al. (9) shows general agreement to within 1079, whereas the results of Rank et al. (7) for the same lines are somewhat higher (~2.5ojc) than those of the other three. A comparison such as this seems to illustrate two important points. One, that our results fall reasonably within the scatter (albeit high) of data from all the laboratories (or probably would if more room temperature values for these lines would be available). Two, the measurement of the linewidth parameters is clearly not an easy undertaking since results using the same method, i.e., equivalent width or interferometric, by different laboratories are not as much in agreement as would be desired. Because of this apparent lack of good agreement, a closer look at the uncertainties inherent in our measurements is in order. The uncertainties associated with our results should in actuality be somewhat larger than the nominal 10% (one standard deviation). There are also contributions due to the equivalent width method-specifically, the assumption of a Lorentzian line. Deviations (usually small) have been observed at the wings of the lines, which in our case
HCI LINE
BROADENING
13!,
would be additive with contributions from the Cl 35 and 37 lines. Furthermore, xc would espect that the -yao (Eq. (1)) would show greater temperature dependence than yy and thus affect our calculations to some small extent. For these reasons, it is felt that a more realistic uncertainty for the data reported here should be +lSf;,. In order to compare our temperature dependent linewidth results with those from other laboratories, as well as theoretical calculations, the linewidths, y”, are converted into cross sections, (T. This is done via the “Heisenberg uncertainty principle” formula: yo = (.YoCJ)/(27rC),
(4)
where No is again equal to the number of perturber molecules per unit volume, fi is the average relative velocity in a collision, u is the optical cross section, and c is the velocity of light. Table IV gives the temperature dependence of the cross sections as calculated from the linenidths. Although there are no experimental or theoretical results for the P(7), P(S), or P(9) lines, it is instructive to compare our results with those obtained for other absorption lines and this is done in Fig. 1. Figures la and lb are for the P(1) and P(4) lines, respectively, and show the difference between the theoretical (N&en and Gordon (19), solid line), the microwave (Van Aalst et al. (IO), dotted line), and infrared (Houdeau et al. (9), dashed line) results. Figure lc gives our results for P(X). According to the semiclassical theory of Neilsen and Gordon, the low J states (where both strong and weak collisions are important) are particularly affected by the attractive part of the potential, especially the Pl(cos8) term. On the other hand, the high J states (where mostly strong collisions are important) have been found to be affected
!
90
FE. 1. (a, b) Temperature dependence of the cross sections for the HCI P(l) and P(4) lines (solid line, Ref. (19), is theoretical; dashed line, Ref. (Y), is infrared; dotted line, Ref. (IO), is microwave). (c) shows our results for P(8).
140
ANDRZEJ
W. MIZIOLEK
primarily by the repulsive part of the potential, again especially that part with Pl(cos.0) symmetry. Even though there are no theoretical results for the P(7), P(8), and P(9) lines to compare with, an extrapolation of the available low J theoretical values indicates that our cross section results are probably not only somewhat greater in magnitude, but also have a considerably larger temperature dependence. Thus, in accordance to theory, the repulsive part of the anisotropic potential may have been underestimated. Van Aalst et al. have concluded that the large discrepancy found between their low J lines and the calculations of Neilsen and Gordon was due to the underestimation of the PlA coefficient of the first Legendre polynomial in the attractive part of the anisotropic potential. Houndeau et al. also found that calculations of cross sections using a modified version of the Anderson (perturbative) theory resulted in the worsening of agreement with experiment; i.e., the calculated values were smaller than the experimental ones, as the temperature was lowered. CONCLUSION
The linewidths of the HCl P(7), P(8), and P(9) lines have been reported for various foreign gas broadeners at room temperature and for Ar at a number of low temperatures. The resulting cross sections have been found to be quite strongly temperature dependent. This resultris similar to the behavior found for lower P lines by other experimenters working on the HCl-Ar collisional broadening case in the infrared and microwave regions. It should be mentioned that preliminary results for HBr lines broadened by argon (25) also indicate a considerable temperature dependence of the cross section, possibly even greater than that for the HCl-Ar case. A comparison with theoretical calculations for the HCl-Ar broadened case indicates that the Pl(cosB) term may have been previously underestimated by theory. It is hoped, therefore, that the information provided here for high J lines augmented with the recent values for low J lines will be useful for further studies, especially theoretical, of the phenomenon of collisional broadening and in the elucidation of the details of the interaction potential between HCl and Ar. The results given above also raise two important points. One, that clearly definitive work needs to be done to eliminate the uncertainties in the linewidths that exist now. Hopefully with the use of tunable infrared lasers (e.g., diode) line shapes will be measured directly. The second important point is that the temperature dependence of the HCl linewidths is probably not a unique characteristic of argon broadening, but it undoubtedly also occurs with air, N 1, 02, etc., broadeners (the magnitude for each case will have to be determined experimentally). This factor is important (as mentioned in the introduction) in quantifying (27) the mixing ratios of this and most likely other minor constituents in the atmosphere. The use of room temperature linewidth data (28) will have to be replaced by experimental results determined at the appropriate temperatures (210-280 R) when it becomes available. ACKNOWLEDGMENTS The author would like to thank Professor George C. Pimentel for numerous fruitful discussions. Also, research support from the National Aeronautics and Space Administration is gratefully acknowledged (NASA Grant NGL-0.5-003-286).
RECEIVED : November
1, 1976
141
HCl LISIS BROADENING REFERENCES f.- W. S. BE;XIXXCT,K. HI~XMAN,G. E. Iiloo~ls, mu S. S~r.vx~vn.u, C’an. J. Phys. 34, 830 (1056). Z.-W. S. BENEDICT,R. HERMAN, G. E. MOORF:,AXD S. SII.V~R~~~.~N, Can. J. Pkys. 34, 850 (1056). 3. J. 5. 6. 7. R.
D. R. EATON AND H. W. THOMPSON,Proc. Roy. Sot. (London) Sect. A 251, 458 (lY5Y). D. R. EATON ANUH. W. TNOMPSON,Proc. Roy. Sot. (London) Sect. A 251, 475 (1959). H. BABROV, G. AMEER, AND W. BENESCH,J. Mol. Speclrosc. 3. 185 (1959). H. BABROV, G. AMEER, ANDW. BFXESCH,.r. C/wt. P/I_vs.33, 145 (1960). I>. H. RANK, D. P. EASTMAN,B. S. RAO, ANDT. A. WIGGINS, J. Mol. Spectrosc. 10, 34 (1963). A. LEVY, E. PIOLLET-MARIEL,AND C. BOULET,J. Quant. Spectrosc. Rad. Trans. 13, 673 (1973).
9. J. P. HOUDEAU,M. LARVOR, AND C. HAEZ.SLER,J. @ant. S’pectrosc. Rad. Trans. 16, 457 (1976), 10. R. M. v.1~ A.ZLST,J. A. SCHULJRMAN, ANDJ. V.ZKDER ELSKFN, Clrenl. Phys. Lett. 35, 558 (1075). II. P. W. AXDERSON,Phys. Rev. 76, 647 (1949). 12. R. M. HERMAN, Plzys. Rev. 132, 262 (1963). 13. R. M. HERMAN,J. C/rem.Phys. 44, 1346 (1966). 1-I. R. H. TIPPING AND R. M. HERDIAN,J. Quunt. Spectrosc. Rad. Tram. 10, 881 (1970). .I_?. RI. GIRAUD,D. ROBERT, ANDL. G,ZLATRY,.I. Clreirz.Phys. 53, 352 (1970). 16. C. BOUIXT, P. ISN~RD, ANDA. LEVY, J. Quant. Spectrosc. Rad. Trans. 13, 897 (1973). 17. 18. IO. 20. ,?I.
K. W. W. I). K.
G. GORDON,J. Clrem Phys. 44, 3083 (1966). B. NKILSRNAND R. G. GORDON,J. Chew. Phys. 58, 4131 (1973). B. NKILSENANDR. G. GORDON,J. C/lerrr.Phys. 58, 414Y (1973). HORS >YND G. C. PIVENTEL, dppk Opt. 10, 1892 (19il). SP.ANIIAUER, P. E. FRALEY, AND K. SAR,\I<~RIRAO, .4ppl. Opt. 2, 1340 (1963).
22. W. LJ. 25. 26. 27. 2X.
R. M. HEXTER .~NDC. W. HAKD, .4pp2. Opt. 7, 2161 (1968). R. A. TOTH, R. H. HUNT, AND E. K. PLYLER, J. Afol. Specfrrisc. 35, 110 (1970). A. W. Pl’rIZIOLEK, Ph.D. Dissertation, Univrrsity of California, Berkeley, 1976. A. W. MIZIoLq Unpublished results. R. A. ToTIf AXI) L. A. DARNTON,J. Mol. Spectrosc. 49, 100 (1974). C. B. I~ARME:R, Can. J. Chew 52, 1.544 (1974). hf. ACKI.:KM.\N, D. FRIMOVT,A. GIR.&RD,M. (~OTTICNIES, .wm C. MULLER, Geophys. (19761.
Res. Let!. 3, 81
OF MOLECULAR
SPECTROSCOI’Y
Temperature
65, 134-141
(1977)
Dependence of Foreign Gas Broadening of HCI Fundamental Lines ANDRZE J W.
Ckemistry
Department,
MIZIOLEK’
University of Calvornia,
Berkeley,
California
93720
A long-pathlength variable temperature cell has been used to study three hydrogen chloride O-l vibration-rotational lines, P(7), P(8), and P(9) which were broadened by He, Ar, Nz, 02, and CO at room temperature and by Ar at low temperatures down to 190 IL The method employed to extract the linewidths is the equivalent width method. The temperature dependence of the resulting cross sections for the HCl-Ar broadened lines is similar to that recently found for other argon broadened HCl infrared and microwave lines. The results reported here (for high J lines) complement the other results (for low J lines) and together seem to constitute enough new data for further theoretical attempts at describing the process of collisional broadening
in general,
and the broadening
of HCl by argon
in particular.
INTRODUCTION
The case of hydrogen chloride absorption line broadening by foreign gases in both the microwave and infrared regions has been particularly well studied in the past two decades. In the earlier experiments (I-6) the equivalent width method was used to extract spectral line shape information, such as the linewidth parameter, while more recently, high-resolution spectrophotometers and interferometers have been used to obtain lineshape information more directly with apparently only small corrections for “slit” distortions (7-9). Only quite recently has there been experimental information available for the temperature dependence of the HCl-Ar broadened linewidths and shifts in the infrared (9) and the microwave (10) regions. It is the temperature dependence of the linewidths (and their associated cross sections) that gives a solid test to theories (particularly the perturbative (11-16) and semiclassical (17-19)) that have been developed over the years with the purpose of explaining the experimental observables, e.g., magnitude and J dependence of linewidths and shifts. Currently studies of the temperature dependence of linewidths are taking on added importance since these parameters are used (particularly for strong lines broadened by air) in the interpretation from ground base and/or balloon infrared spectra of the mixing ratios of various minor constituents in both the troposphere and stratosphere. Correct determination of these mixing ratios is imperative in order to test our understanding of the atmospheric processes which affect among others, the relationship between these minor constituents and the stratospheric ozone balance. 1Present address:
Chemistry
Department,
University
of California,
Irvine,
California
94720.
134 CoI)yright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN
0022-2852
HCI LINE
BROADENING
I 3.5
With these points in mind, and also with the knowledge that there are gaps in foreign gas broadening information on different HCl lines, we report the temperature dependence of the cross sections for HCl P(7), P(8), and P(9) lines broadened by argon. Jncluded also are room temperature broadening results for the same HCl lines broadened by Ar, He, CO, Nr and 02. The long-pathlength variable temperature cell gave us the opportunity of stud>-ing these relatively weak absorption lines but it also required working with relatively lo\\ resolution. For this reason, the equivalent width method, which has been used SLICXYSSfully for man\-. -vears, was employed in this work for the abstraction of linewidths from spectral rccordings. EXPERIMENTAL
DET:lILS
The long-pathlength variable temperature cell has been described b\- Horn and I’imentel (20). Two light sources have been used in the course of these esperiments, one a 300 W zirconium arc (Sylvania K300) properly housed for infrared operation and two, a carbon furnace following the design of Spanbauer et al. (V) and of Hester and Hand (22). The sprctrophotometer used is a Beckman IR-9 operating single beam. Due to the long pathlengths used (300-620 m) the spectrophotometer slits were kept wide for acceptable signal-to-noise conditions, resulting in an effective spectral slit width of approsimately 2.4 cn-l, not enough to resolve the chlorine isotopic peaks. Typical HCI pressures were in the 2Z7 Torr range while the foreign gases were brbetween 400 and 760 Torr. The cell (3300 liters) was normall\- filled in a sandwich fashion \\-ith 2 aliquots of HCl espanded from 50 liter vacuum line flasks into the center of the chamber sandwiched between three equal additions of the foreign gases. The accuracy of the pressure readings, which \vere done by a mercury manometer, is about O..,:‘;,. The cold runs were conducted on different clays with different HCl:Ar pressurcb ratios. These experiments proceeded by first cooling the cell to the lamest temperature desired, then, introducing the samples, and after sufficient time for thermal equilibration, taking the actual quantitative spectra. After these spectra were taken, the cell was allowed to warm up to the nest temperature of interest after which coolant was again recirculated to ensure no more than a 1” gradient across the cell as monitored h> 11 separate thermocouples. During the spectral recordings, the coolant pump was shut down to eliminate vibrations but the temperature in the cell rose no more than 4” during this time. The gases used for these experiments lJ.ere H(‘l Electronic Grade (99.99:‘; Mathcson), Ar (99.9955, Liquid Carbonic), He (99.999f”; VC Chem Dept.), XL’ Prep (;rade (99.998(‘{, Llatheson), OZ Ultra Pure (99.99’:{, Matheson), and CO Ultra High T’urit>, (99.85 Matheson). These were added directly into the cell without further purification. RESULTS
A detailed discussion of the equivalent width method will not be given here (see, e.g., Refs. (l-6)) ; instead, only the points necessary for our calculations will be mentioned. Briefly, according to the theory, due to our long pathtengths, we are well into the “square root” region where the following equation holds true : TT.?= 4S1_(-fu”pa+ r/y,.),
f.1)
ANDRZEJ
136
W. MIZIOLEK
TABLE I Room TemperatureLine Widths for DifferentHCl P Lines Broadenedby Argon Pressure lx1 (ton)
Pressure .4r(torr)
Pathlength (meters)
pc7ja Y"-1 (cm-latm )
Pwb Yol (cm-latm )
pwc Yol (cm-latm-)
_ 1.49
407
300 460 620
0.0306 0.0259 0.0247
0.0225 0.0271 0.0237
0.0251 0.0216 0.0201
2.60
402
300 460 620
0.0241 0.0227 0.0196
0.0241 0.0275 0.0277
0.0226 0.0221 0.0201
3.12
757
300 460 620
0.0211 0.0202 0.0162
0.0243 0.0201 0.0183
0.0213 0.0226 0.0198
1.99
758
300 460 620
0.0220 0.0202 0.0185
0.0236 0.0198 0.0199
0.0221 0.0209 0.0203
Average
Babrov (6) Rank (1) -1 = S'=3.264cn~-~atm
0.0222t.0011 0.0215
0.0232+.0009
0.0141 0.0150
b s"=1.712cm2arm1 = S0=0.804cm-2atm1
where
s = sop.. W is the experimentally determined equivalent width (in cm-‘), So is the line strength per atmosphere (in crne2 atm-‘), L is the pathlength (in centimeters), 72, rfo are the linewidths per atmosphere for self and foreign broadening (in cm+ atm-l), p,, p, are the pressures of the absorbing and broadening gases (in atmospheres), respectively. Accurate values for So for the P lines considered here are available (23) and are given in Table I. Equation 1 shows that with a large enough pf:p, ratio (which is true in our case), a knowledge of -rao is not necessary for determining the desired quantity, r/O. The pressure ranges (HCl, 2-6 Torr ; Ar, 400-760 Torr) for all of the experiments were such that there was never a problem of absorption in the wings of the reported P lines (overlapping lines of different J values) obscuring a baseline determination. Table I also gives the room temperature results for the P(7), P(8), and P(9) HCl lines broadened by argon, while the room temperature line widths for He, Nz, 02, and CO broadeners are given in Table III. In order to use the equivalent width method for temperatures other than 2% K the line strength So needs to be recalculated. The equation that enables this is:
So(J) =
exp(---E(J)IW,
where ZZO(J), is the dipole moment matrix element (which includes the Herman-Wallis factors), No is the number of molecules per unit volume, and Q is the rotational partition function. Thus, the temperature dependence of So is embodied in the temperature dependence of Y, and in the change of the rotational level populations.
HCl LINE BROADENING
O.Oh5 0.03n 0.0'15 0.03 0.0:: O.O?O O.U.!.: 11.014
Table IV gives the results for the temperature dependence of the HCI linewidths for the P(7), P(8), and Y(9) lines broadened by argon lvhich were based on two cold esperiments. The first spanned the temperature range of 214-257 K with Pncl = 3.00 Torr and PAr = 635 Torr (both measured at 298 K). The second covered the temperature range of 193-270 K with Pnci = 1.98 Torr and p,tr = 734 Torr (both measured
P(7)
0.0?11~.0014
P(R)
O.O?hl..GOlh
P(9)
O.O?i?
P(7)
O.U44'~~.OO,V
P(B)
0.0349~.001h
.00?4
P(9)
O.O3Oi~.OOI?
P(7)
0.02L5
P(8) P(9)
0.0?39'.0015 O.O234~.OOlh
P(7) I'(H) l'(9)
0.0452'.00?1 0,
.OOlh
O.O553..OO?J
“AI.i 00,<
ANDRZEJ
138
W. MIZIOLEK TABLE I"
TemperatureDependenceof Line Widths and Cross Sectionsfor IlClBroadened by Argon Temperature Experiment Absorption Number Line OK
So -1 (cF2atm )
P(7) P(8) P(9)
1.627 0.547 0.156
0.0492~.0031
0.0455+.0056 0.0443t.0138
52.6k3.3 48.6i5.9 47.4i14.8
210
P(7) p(8) P(9)
1.969 0.734 0.234
0.0406-'.0040 0.0389'.0029 0.0402?-.0037
45.314.5 43.4t3.2 44.at4.1
214
P(7) P(8) P(9)
2.048 0.778 0.255
0.0308i.0010 0.0323'.0013 0.0348i.0027
34.7kl.l 36.5t1.5 39.2i3.1
235
P(7) P(8) P(9)
2.428 1.023 0.375
0.0246'.0005 0.0273k.0002 0.0265*.0015
29.1iO.6 32.2f0.3 31.3Q.8
241
P(7) P(8) P(9)
2.528 1.093 0.413
0.0305'.0019 0.0301F.0017 0.0304'.0033
36.4t2.2 35.9i2.0 36.3t3.9
257
P(7) P(8) P(9)
2.775 1.278 0.518
0.0210i.0005 0.0247+.0008 0.0246?.0002
25.9to.9 30.5f0.9 30.310.2
259
P(7) p(8) P(9)
2.803 1.300 0.532
0.0271t.0003 0.0274+.0009
33.6k0.4 33.9t1.1 34.7Q.l
270
P(7) P(B) P(9)
2.950 1.423 0.607
0.0239~.0013 0.0242*.0014 0.0227+.0014
30.2t1.6 30.6t1.7 28.721.8
P(7) P(8) P(9)
3.264 1.712 0.804
0.0222~.0011 0.0232*.0009 0.0216f.0004
29.5t1.5 30.Bt1.2 28.6tO.5
193
298
see
Table I
at 298 K). Each of the low-temperature linewidths is based on two or three different measurements, i.e., pathlengths (for primary data see Ref. (24)). DISCUSSION
Tables I, II, and III show that whenever a comparison can be made, most of our results agree within 1.5% with those from other laboratories. A comparison in Table II of the Babrov et al. (6) linewidth results for the P(1) through P(6) lines with the interferometric results of Levy et al. (8) and Houdeau et al. (9) shows general agreement to within 1079, whereas the results of Rank et al. (7) for the same lines are somewhat higher (~2.5ojc) than those of the other three. A comparison such as this seems to illustrate two important points. One, that our results fall reasonably within the scatter (albeit high) of data from all the laboratories (or probably would if more room temperature values for these lines would be available). Two, the measurement of the linewidth parameters is clearly not an easy undertaking since results using the same method, i.e., equivalent width or interferometric, by different laboratories are not as much in agreement as would be desired. Because of this apparent lack of good agreement, a closer look at the uncertainties inherent in our measurements is in order. The uncertainties associated with our results should in actuality be somewhat larger than the nominal 10% (one standard deviation). There are also contributions due to the equivalent width method-specifically, the assumption of a Lorentzian line. Deviations (usually small) have been observed at the wings of the lines, which in our case
HCI LINE
BROADENING
13!,
would be additive with contributions from the Cl 35 and 37 lines. Furthermore, xc would espect that the -yao (Eq. (1)) would show greater temperature dependence than yy and thus affect our calculations to some small extent. For these reasons, it is felt that a more realistic uncertainty for the data reported here should be +lSf;,. In order to compare our temperature dependent linewidth results with those from other laboratories, as well as theoretical calculations, the linewidths, y”, are converted into cross sections, (T. This is done via the “Heisenberg uncertainty principle” formula: yo = (.YoCJ)/(27rC),
(4)
where No is again equal to the number of perturber molecules per unit volume, fi is the average relative velocity in a collision, u is the optical cross section, and c is the velocity of light. Table IV gives the temperature dependence of the cross sections as calculated from the linenidths. Although there are no experimental or theoretical results for the P(7), P(S), or P(9) lines, it is instructive to compare our results with those obtained for other absorption lines and this is done in Fig. 1. Figures la and lb are for the P(1) and P(4) lines, respectively, and show the difference between the theoretical (N&en and Gordon (19), solid line), the microwave (Van Aalst et al. (IO), dotted line), and infrared (Houdeau et al. (9), dashed line) results. Figure lc gives our results for P(X). According to the semiclassical theory of Neilsen and Gordon, the low J states (where both strong and weak collisions are important) are particularly affected by the attractive part of the potential, especially the Pl(cos8) term. On the other hand, the high J states (where mostly strong collisions are important) have been found to be affected
!
90
FE. 1. (a, b) Temperature dependence of the cross sections for the HCI P(l) and P(4) lines (solid line, Ref. (19), is theoretical; dashed line, Ref. (Y), is infrared; dotted line, Ref. (IO), is microwave). (c) shows our results for P(8).
140
ANDRZEJ
W. MIZIOLEK
primarily by the repulsive part of the potential, again especially that part with Pl(cos.0) symmetry. Even though there are no theoretical results for the P(7), P(8), and P(9) lines to compare with, an extrapolation of the available low J theoretical values indicates that our cross section results are probably not only somewhat greater in magnitude, but also have a considerably larger temperature dependence. Thus, in accordance to theory, the repulsive part of the anisotropic potential may have been underestimated. Van Aalst et al. have concluded that the large discrepancy found between their low J lines and the calculations of Neilsen and Gordon was due to the underestimation of the PlA coefficient of the first Legendre polynomial in the attractive part of the anisotropic potential. Houndeau et al. also found that calculations of cross sections using a modified version of the Anderson (perturbative) theory resulted in the worsening of agreement with experiment; i.e., the calculated values were smaller than the experimental ones, as the temperature was lowered. CONCLUSION
The linewidths of the HCl P(7), P(8), and P(9) lines have been reported for various foreign gas broadeners at room temperature and for Ar at a number of low temperatures. The resulting cross sections have been found to be quite strongly temperature dependent. This resultris similar to the behavior found for lower P lines by other experimenters working on the HCl-Ar collisional broadening case in the infrared and microwave regions. It should be mentioned that preliminary results for HBr lines broadened by argon (25) also indicate a considerable temperature dependence of the cross section, possibly even greater than that for the HCl-Ar case. A comparison with theoretical calculations for the HCl-Ar broadened case indicates that the Pl(cosB) term may have been previously underestimated by theory. It is hoped, therefore, that the information provided here for high J lines augmented with the recent values for low J lines will be useful for further studies, especially theoretical, of the phenomenon of collisional broadening and in the elucidation of the details of the interaction potential between HCl and Ar. The results given above also raise two important points. One, that clearly definitive work needs to be done to eliminate the uncertainties in the linewidths that exist now. Hopefully with the use of tunable infrared lasers (e.g., diode) line shapes will be measured directly. The second important point is that the temperature dependence of the HCl linewidths is probably not a unique characteristic of argon broadening, but it undoubtedly also occurs with air, N 1, 02, etc., broadeners (the magnitude for each case will have to be determined experimentally). This factor is important (as mentioned in the introduction) in quantifying (27) the mixing ratios of this and most likely other minor constituents in the atmosphere. The use of room temperature linewidth data (28) will have to be replaced by experimental results determined at the appropriate temperatures (210-280 R) when it becomes available. ACKNOWLEDGMENTS The author would like to thank Professor George C. Pimentel for numerous fruitful discussions. Also, research support from the National Aeronautics and Space Administration is gratefully acknowledged (NASA Grant NGL-0.5-003-286).
RECEIVED : November
1, 1976
141
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Res. Let!. 3, 81