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Nitrogen-broadened halfwidths of HF lines in the 1-0 band
JOURNAL
OF MOLECULAR
SPECTROSCOPY
106,
25 l-259 (1984)
Nitrogen-Broadened Halfwidths of HF Lines in the 1-O Band R. EARL THOMPSON Systems and Applied Sciences Corporation, 17 Research Drive, Hampton, Virginia 23664 AND JAE H. PARK, MARY ANN H. SMITH, GALE A. HARVEY, AND JAMES M. RUSSELL III NASA Langley Research Center, Hampton, Virginia 23665
Nitrogen-broadened halfwidths for seven lines in the fundamental infrared band of HF have been determined from laboratory measurements at room temperature. The spectra were recorded using a Fourier transform spectrometer with a nominal resolution of 0.0603 cm-‘. A nonlinear least-squares spectral-fitting technique was used in the data analysis to obtain halfwidth values for the P3 through R3 lines, with an average uncertainty of approximately 15%.
INTRODUCTION
In recent years considerable scientific effort has been devoted to the measurement of HF in the terrestrial stratosphere, since the HF concentration is an indicator of the amounts of chlorofluorocarbons which have been injected and photolytically destroyed in the stratosphere. Most of these measurements, reviewed in a recent World Meteorological Organization report (I), involve the quantitative analysis of spectral lines belonging to the HF 1-O band appearing in atmospheric absorption spectra. This same band will be used by the Halogen Occultation Experiment (HALOE) under development by NASA for flight on the Upper Atmospheric Research Satellite in the 1989 time period. HALOE is a gas-filter correlation instrument which, carries gas cells filled with specific gases, such as HF, which are used as highly selective spectral filters (2). In all of these experiments, a critical step in the interpretation of the data is a proper characterization of the infrared absorption spectrum, including knowledge of the collision broadened halfwidths (3). While line positions, intensities, and self-broadened halfwidths in the HF 1-Oband have been extensively studied (4-10, 19), only three laboratory studies of N2-broadened HF halfwidths have been reported in the literature (10-12); two of these involved measurements in the 2-O band (II) and the pure rotation band (12), while the 1-O band study covered only five lines in the R branch of the 1-O band. In this paper we present the results of laboratory room-temperature measurements of N2-broadened halfwidths for seven lines in the HF 1-O band R branch, including three lines in the P branch that were not measured in the earlier study (to).
251
0022-2852/84 $3.00 Copyright 0
1984 by Academic Press, Inc.
All rights of reproduction in any form reserved.
THOMPSON
252 EXPERIMENTAL
ET AL.
DETAILS AND DATA ANALYSIS
The spectra used in this study were obtained with a Fourier transform infrared spectrometer (Nicolet 7 199) equipped with an InSb detector, a KBr beamsplitter, and a globar source. The gas cell compartment was purged with nitrogen and maintained at 301.5 -e 0.6 K. Thirty-two scans obtained with a path difference of 16.6 cm-’ (nominal 0.0603-cm-’ resolution) were averaged, and the interferogram was transformed with a Happ-Genzel apodization function to obtain each spectrum. The HF gas cell used in this study was a HALOE life-test cell (13) designed to study the containment of HF over an extended time period of several years. The cell is 10.01 f 0.01 cm long with a 2.5cm inside diameter, has Al203 (sapphire) wedged windows with gold walls, and was custom designed and fabricated for long life and gas stability. The cell was filled with a mixture of HF and N2 in June 1981 at room temperature to a total pressure of 0.050 atm and an optical mass of 0.0040 atm-cm, corresponding to a HF volume mixing ratio of 0.0080. An MKS Baratron gauge was used to monitor the fill pressure. One spectrum of the HF absorption for this cell, taken about 6 months after it was filled, is shown in Fig. la. We have noted an initial loss of HF in the cell which is probably due to absorption of HF into the cell walls and possible chemical reactions. Following this initial loss, the cell has shown a long-term stability with only minor changes in the HF mixing ratio, as will be discussed later. However, because of the low HF mixing ratio, the total cell pressure has not been noticeably affected by the HF loss. Also, the low HF mixing ratio means that HF self-broadening can be neglected. Since no polymer spectral features (14) have been observed, the broadening of the monomer lines by the polymers has been ignored. In addition, the analysis of eight scans of the cell has improved the statistical significance of the results given here. The analysis method adopted for retrieval of the HF halfwidths is based on the work of Park (15). This method is similar to the nonlinear least-squares method of Chang and Shaw (16, 17) for analyzing absorption spectra. The method used in this study, like that of Niple and Mankin (I??), employs the fat Fourier transform technique for simulating the spectrum. The instrument line shape is defined by an effective interferogram apodization that includes the Happ-Genzel apodization function, the field of view effect, and instrument noise. The residual phase error is also included in the analysis. Park (15) showed that this technique can separate from the observed
FIG. 1. (a) Laboratory scan of HF 1-O band, December 1981. (b) Example of line used for pressure retrieval (RI).
NITROGEN-BROADENED
HF HALFWIDTHS
253
absorption line the true absorption (i.e., exponential function) and the instrument line shape defined by the effective apodization function (i.e., equivalent to the Fourier series in spectral space). Although the HF halfwidths retrieved in this work are smaller than the halfwidth of the instrument line shape, the two effects for broadening the observed absorption line can be separated easily, provided there is sufficient signal due to true absorption. Therefore, the present technique to retrieve halfwidths is different from the more traditional method that employs the equivalent width analysis of an absorption line for various pressures (19). We have studied the effects that uncertainties in the modeled apodization function have on the two quantities retrieved in the analysis, i.e., optical mass and halIXdth. Errors of 20% in the retrieved effective apodization function produce errors in the optical mass of approximately 2% and errors of less than 4% in the halfividth. In general, the uncertainties in the apodization function are under 10% and, therefore, errors introduced into the analysis are small. This technique has been applied to other HALOE gas cells to monitor cell stability, and the results are consistently good. As an example, an HCl cell filled with a pressure of 0.070 atm and a mixing ratio of 0.02 1 was scanned five times over a period of 1 year. The observed depths and widths of the HCl lines in these scans were approximately the same as those for HF. The average pressure retrieved for the HCl cell was 0.0681 f 0.0028 atm, indicating the reliability of the technique. Because of concerns about HF stability in the cell, the first of two basic steps in the analysis was the determination of the HF optical mass using weak lines which (as will be shown later) are insensitive to errors in gas pressure or line halfwidth. These lines are in the linear region of the curve of growth. This calculation is performed using the relationship T, = exp(-KU),
(1)
where T, and K, are the transmittance and absorption coefficient, respectively, at wave number v, and U is the optical mass. This optical mass is then used in the second step for the analysis of strong lines which are not saturated but are still sufficiently collision-broadened to permit the retrieval of either the gas pressure or line halfwidth. This retrieval is accomplished through the dependence of the Voigt function on the pressure through the Lorentz halfwidth cyLgiven by
(2) where CY:is the halfwidth at standard pressure, PO,and temperature, To, and n is the temperature-dependency exponent. While pressure-induced lineshifts for HF broadened by N2 have been observed by Guelachvili and Smith (20), for the conditions of the present study the shifts are estimated to be less than 0.001 cm-]. Since shifts of this magnitude are smaller than the wavenumber precision of our interferometer, pressure-induced lineshifts were not included in the retrieval algorithm. A set of five lines (P4, P5, P6, R4, and R5) was used for optical mass calculations, and a set of seven lines (P3 through R3) was used for pressure. An example of a pressure line is shown in Fig. I b. A study was made on the effects of errors in halfwidth
254
THOMPSON
ET AL.
on retrieved optical mass or pressure. As expected, the optical mass retrievals from the weak lines are relatively insensitive to halfwidth errors. For halhvidth errors as large as 20% the retrieved optical mass values change less than 2%. However, the halfwidth errors have essentially a one-to-one influence on the retrieved pressure. Because of the relationship of the halfividth to the retrieved pressure as shown in Eq. (2), the percentage error in the retrieved pressure has the opposite sign from the percentage halfwidth change. We also note that the retrieved pressure value depends on the optical mass assumed in the analysis. It is, therefore, important to have accurate knowledge of optical mass and pressure to retrieve halfwidths from the spectra. RESULTS
Preliminary analysis of the first few spectra using the 1980 Air Force Geophysics Laboratory (AFGL) line parameters (5) and the self-broadened halfividth values of Love11 and Herget (6) yielded pressures which were approximately 50% higher than the cell pressure measured at the time of initial gas cell fill. Since the uncertainty in the cell pressure measured at the time of fill is only on the order of a few percent and since the retrieved gas pressure had remained constant but elevated, thus ruling out a cell leak, it was assumed that the AFGL air broadened halfwidth values adopted from Ref. (10) were too low. To achieve results which were more consistent with the cell fill pressure of 0.050 atm, the AFGL halfwidth values were multiplied by 1.5 as a first guess for this analysis. Eight data sets obtained at intervals over a lo-month period were analyzed to obtain optical mass and pressure values. A weighted linear regression was fit to the optical mass results to reduce uncertainties arising from random variations in instrument performance and experimental conditions. The pressures were next recalculated using the optical mass paths taken from the regression. A plot of this analysis is shown in Fig, 2, which displays the optical mass trend and the mean pressure results. The optical mass can be seen to have changed about 14% over the lo-month period of the analysis. The total gas pressure, on the other hand, remained constant over the period, with a mean value of 0.0580 + 0.0035 atm, which is approximately 16% higher than the fill pressure. Assuming this bias in retrieved pressure to be due to line parameter uncertainties, the gas pressure was fixed at 0.050 atm for the halfwidth retrievals. This assumption is valid based on the accuracy of the Baratron gauge used to monitor the cell pressure at fill and on the observed stability of the cell. The optical mass values taken from the linear fit to the data are shown in Fig. 2. The results of the halfwidth analyses for the individual scans are shown in Table I. The mean halfwidths for each HF line and the standard deviations are also shown in the table. These standard deviations represent uncertainties arising from random noise in the spectra. The total uncertainties in the final halfwidth values result from four sources of errors. These include the random noise in the spectra as mentioned above; line strength uncertainties, which can be as high as 10%; the uncertainty in initial cell fill pressure, which is of at most about 5%; and the uncertainty of the retrieved optical mass values due to spectral noise and instrument performance, estimated to be about 4%. These experimental errors were used to arrive at the root sum of squares error (RSS) given in Table II.
NITROGEN-BROADENED
HF HALFWIDTHS
255
FIG. 2. Trends in cell conditions during measurementperiod. Nominal fill conditions(June P = 0.050 atm, U = 0.0040 atm-cm.
1981):
To verify the retrieved halfwidths, three scans were reanalyzed to determine the cell pressure using the new N2-broadened halfwidth values. The mean pressure calculated with the halfwidths obtained in this work is only a few tenths of a percent from the fill pressure. TABLE I Halfwidth Results (cm-’ atm-’ at 301 K) Date
Aug. Sept.
of Scan
12, 1981 2, 1981
P3
0.134
P2
0.143
Pl
0.148
RO
0.152
Rl
0.135
R2
0.100
R3
0.0699
0.129
0.152
0.152
0.156
0.129
0 0958
0.0654
NOV.
3, 1981
0.119
0.132
0.142
0.132
0.123
0.0937
0.0644
Nov.
27, 1981
0.112
0.128
0.134
0.132
0.112
0.0915
0.0568
Dec.
29, 1981
0.125
0.141
0.135
0.133
0.117
0.0973
0.0692
0.144
0.0886
0.0621
Feb.
19, 1982
0.109
0.133
0.134
0.124
Apr.
15, 1982
0.109
0.129
0.136
0.134
0.124
0.0982
0.0724
June
17, 1982
0.0936
0.120
0.128
0.130
0.115
0.0910
0.0611
a
0.116
0.135
0.140
0.138
0.122
0.0945
0.0652
Standard Deviation
0.013
0.010
0.0080
0.010
0.0076
0.0040
0.0052
Percent Deviation
11 b
7.5
5.7
1.3
6.2
4.2
1.9
THOMPSON
256
ET AL.
TABLE II Error Analysis for Nitrogen-Broadened HF Ha&widths Line
T
(Percent Dev. 1 from Table I (random error)
Aa
Aa from 30 uncertainties S (line strength) and P (cell pr essure) mass) U (optic
in
(Peknt)
(PeKent)
(PeKent)
Ba RSS Error
P3
ll.%
10.8
5.%
4.%
16.%
P2
1.5
10.
5.
4.
14.
Pl
5.7
10.
5.
4.
13.
RO
7.3
10.
5.
4.
14.
Rl
6.2
10.
5.
4.
13.
R2
4.2
10.
5.
4.
13.
R3
7.9
10.
5.
4.
14.
DISCUSSION
A comparison of our mean N2-broadened HF halfividth values with those given in previous publications is shown in Table III and is displayed graphically in Fig. 3. Since the earlier 1-O band results (10) were presented in the form of broadening efficiency ratios determined at 298 and 373 K, it was necessary to combine these ratios with self-broadened halfwidth values (6) to obtain Nz-broadened halfwidths. These halfwidth calculations were performed using ~NZ-HF = (~HF-HF)(~),
(3)
where (YN~_HF is the nitrogen-broadened HF halfwidth, (YHF_HF is the self-broadened HF halfwidth, and t is the broadening efficiency ratio. The nitrogen-broadened halfwidths calculated using the broadening efficiency ratios from Smith (10) and the selfbroadened halt+idth values from Love11 and Herget (6) are shown in columns (b), (c), and (d) of Table III. The temperature dependence exponents [see Eq. (2)] of the self-broadened haltidths used to scale from 373 to 298 K were obtained from Smith (21) and are shown in parentheses in column (b). An examination of the N2-broadened haltidths measured in this work indicates that the P-branch halfwidths are systematically 1% to 19% larger than those for corresponding [ml values in the R branch (m = -J in the P branch, J + 1 in the R branch). To first order, the distribution of halfwidths of hydrogen halide molecules broadened by N2 should be symmetric about the band center. However, the measurements of Houdeau et al. (22) indicate that, for HCI 1-O lines with Irnl =G3, N*broadened halfwidths in the P branch are 3-5% higher than those for corresponding R-branch lines. These results, along with our own for the HF 1-O band, suggest that this asymmetry may be real and should be investigated theoretically. Although the temperature dependence of Nz-broadened halfidths for HF has never been measured, the work of Houdeau et al. (22) indicates that N2-broadened halfividths of HCl vary as T-“, where n varies from 0.5 to 0.8. We might expect a
NITROGEN-BROADENED
HF HALFWIDTHS
257
TABLE III Comparison of Measured Nitrogen-Broadened Line
1-O Band this work (a)
T
HF Halfwidths (cm-’ atm-’ at 301 K)
1-O Band Refs. (5, and..(10) Ch1 (0)
(d)
T
2-O Band Ref. (11, (e) 0.026
Pl
0.035
6 5
0.051
4
0.069
3
0.116 5 0.019
0.089
2
0.101
1
0.135 + - 0.019 0.140 + 0.018
RO
0.138 + 0.019
0.109 (1.5)
0.101
0.108 (0.8)
0.104
1
0.122 + 0.016
0.095 (1.4)
0.085
0.090 (0.8)
0.099
2
0.0945+ 0.012
0.082 (0.91)
0.080
0.085 (0.8)
0.090
3
0.0652+ 0.0091
0.056 (0.84)
0.053
0.056 (0.7)
0.070
0.039 (0.70)
0.039
0.040 (0.6)
0.048
0.105
4 5 6
0.030
7
0.023
8
0.024 obtained from
C,a RSS
(a)
Total uncertalntles
(b)
Self broadened halfwidths measured at 373K (6) scaled to 298K by T-" (21) [n given in parentheses], then multTplied by nitrogen broad=ing efficient ratios measured at 298K (la), and the results scaled to 301K by T- t;e5.
error in Table II.
Cc)
and (d) Self-broadened halfwidths measured at 373K (61 multiplied by nitrogen broadening efficiency ratios measured at 773K (lo), and the results scaled to 301K by T-O-~ [column (c)l or T-" [column (d), n given in parentheses].
(e)
Nitrogen-broadened to 301K by T-Ov5.
halfwidths measured at 373K (11) and scaled
similar temperature dependence for HF. The N2-broadened halfwidth values shown in column (c) of Table III were derived from Refs. (6) and (IO), assuming n = 0.5, while the values in column (d) were derived using values of n from Ref. (22). The differences between the Nz-broadened halfividth values in the HF 1-Oband obtained in this study (column (a)) and those derived from the earlier measurements (columns (b), (c), and (d)) are on the order of the uncertainties in the previous work (23, and depend somewhat on the value of n adopted for the temperature scaling. The halfiKidths of the 2-O band are shown for order of magnitude comparison purposes. In light of the uncertainties of all the measurements shown, no discussion of systematic differences in halfwidths between the 1-Oand 2-O bands will be attempted. SUMMARY
AND CONCLUSIONS
We have determined nitrogen-broadened halfwidths at room temperature for seven lines in the fundamental vibration-rotation band of HF, including three P-branch lines whose N*-broadened ha.lt%vidthshave not been previously measured. These results
258
I
I
I
I
I
I
5
4
3
2
PI
I
RO
I
,
I
I
I
2
3
4
FIG. 3. Comparison of measured halfwidths for HF broadened by N2. Closed circles are the 1-O band from the present work. Open squares are the 1-O band (14) as shown in column (c) of Table III. Open triangles are the 2-O band measured by Meredith and Smith (II) as given in column (e) of Table III.
were obtained through analysis of eight Fourier transform spectra of a sealed absorption cell made at regular intervals over a lo-month period. We note that the original purpose of these measurements was the testing of the integrity of a prototype spacecraft gas cell over an extended time period. Although some loss of HF to the cell walls was detected and measured, the gas pressure remained essentially unchanged, and halfwidths derived from the spectra using a nonlinear least-squares fitting technique are quite consistent from scan to scan. The mean halfwidth values resulting from this study are estimated to have an uncertainty of no more than 15%, and this uncertainty is mainly due to insufficient signal-to-noise to resolve the components contributing to the line shape. A more rigorous experiment designed specifically to measure halfwidths would involve scans at several different broadening gas pressures. Unfortunately, such experiments could not be done within the constraints of the spacecraft program. While the present results should be useful in studies related to the infrared remote sensing of atmospheric HF, we encourage additional high-precision laboratory measurements of halfwidths and intensities in the HF 1-O band. ACKNOWLEDGMENTS This work was accomplished under NASA Contracts NAS I - 15890 and NAS 1-17265. The authors wish to acknowledge the work of Dr. J. T. Twitty (NASA Contract NASl-15493) and Mr. D. J. Richardson (NASA Contract NASl-15890) for their past help in developing algorithms used in this work. We would also like to thank Dr. D. F. Smith, Dr. R. H. Tipping, and Dr. C. P. Rinsland for helpful discussions relating to this work. RECEIVED:
November
17, 1983 REFERENCES
1. R. D. HUDSON,E. I. REED, AND R. D. BOJKOV,unpublished results, 198 I. 2. J. M. RUSSELL,J. H. PARK, AND S. R. DRAYSON,Appl. Opt. 16,607-612 (1977).
3. C. P. RINSLAND,M. A. H. SMITH,J. H. PARK, G. A. HARVEY,J. M. RUSSELL,ANDD. J. RICHARDSON, unpublished results, 1982. 4. J. F. OGILVIE,W. R. RODWELL,AND R. H. TIPPING,J. Chem. Phys. 73, 5221-5229 (1980).
NITROGEN-BROADENED
HF HALFWIDTHS
259
5. L. S. ROTHMAN,A. GOLDMAN,J. R. GILLS, R. H. TIPPING,L. R. BROWN,J. S. MARGOLIS,A. G.
6. 7. 8. 9. IO. 11. 12. 13.
MAKI, AND L. D. G. YOUNG, Appl. Opt. 20, 1323-1328 (1981). R. J. L~VELLAND W. F. HERGET,J. Opt. Sot. Amer. 52, 1374-l 376 (1962). C. BOULET,D. ROBERT,AND L. GALATRY,J. Chem. Phys. 65, 5302-5314 (1976). J. J. HINCHENAND R. H. HOBBS,J. Opt. Sac. Amer. 69, 1546-1549 (1979). R. BEIGANG,G. LITFIN,AND R. SCHNEIDER, Whys.Rev. A 20. 229-232 (1979). D. F. SMITH,Spectrochim. Acta 12, 224-232 (1958). R. E. MEREDITHAND F. G. SMITH,J. Chem. Phys. 60, 3388-339 1 (1974).
G. BACHET,C. R. Acad. Sci. Paris, Ser. B 274, 1319-1321 (1972). E. M. SULLIVAN,R. E. THOMPSON,G. HARVEY, J. H. PARK, AND D. RICHARDSON,unpublished
results, 1983. 14. D. F. SMITH,J. Chem. Phys. 28, 1040-1056 (1958). 15. J. H. PARK,Appl. Opt 22, 835-849 (1983). 16. Y. S. CHANGAND J. H. SHAW, Appl. Spectrosc. 31, 213-220 (1977). 17. Y. S. CHANGAND J. H. SHAW, J. Quant. Spectrosc. Radiat. Transfer 18, 491-499 (1977). 18. E. NIPLE,W. G. MANIUN,A. GOLDMAN,D. G. MURCRAY,AND F. J. MURCRAY,Geophys. Res. Lett.
19. 20. 21. 22. 23.
7, 489-492 (1980). C. CRANE-ROBINSON AND H. W. THOMPSON,Proc. R. Sot. A 272,441-452 (1962). G. GUELACHVILI AND M. A. H. SMITH,J. Quant. Spectrosc. Radiat. Transfer 20, 35-47 (1978). D. F. SMITH,J. Mol. Spectrosc. 3, 473-485 (1959). J. P. HOUDEAU,M. LARVOR,AND C. HAEUSLER,Canad. J. Phys. 58, 3 18-324 (1980). D. F. SMITH,personalcommunication, 1983.
OF MOLECULAR
SPECTROSCOPY
106,
25 l-259 (1984)
Nitrogen-Broadened Halfwidths of HF Lines in the 1-O Band R. EARL THOMPSON Systems and Applied Sciences Corporation, 17 Research Drive, Hampton, Virginia 23664 AND JAE H. PARK, MARY ANN H. SMITH, GALE A. HARVEY, AND JAMES M. RUSSELL III NASA Langley Research Center, Hampton, Virginia 23665
Nitrogen-broadened halfwidths for seven lines in the fundamental infrared band of HF have been determined from laboratory measurements at room temperature. The spectra were recorded using a Fourier transform spectrometer with a nominal resolution of 0.0603 cm-‘. A nonlinear least-squares spectral-fitting technique was used in the data analysis to obtain halfwidth values for the P3 through R3 lines, with an average uncertainty of approximately 15%.
INTRODUCTION
In recent years considerable scientific effort has been devoted to the measurement of HF in the terrestrial stratosphere, since the HF concentration is an indicator of the amounts of chlorofluorocarbons which have been injected and photolytically destroyed in the stratosphere. Most of these measurements, reviewed in a recent World Meteorological Organization report (I), involve the quantitative analysis of spectral lines belonging to the HF 1-O band appearing in atmospheric absorption spectra. This same band will be used by the Halogen Occultation Experiment (HALOE) under development by NASA for flight on the Upper Atmospheric Research Satellite in the 1989 time period. HALOE is a gas-filter correlation instrument which, carries gas cells filled with specific gases, such as HF, which are used as highly selective spectral filters (2). In all of these experiments, a critical step in the interpretation of the data is a proper characterization of the infrared absorption spectrum, including knowledge of the collision broadened halfwidths (3). While line positions, intensities, and self-broadened halfwidths in the HF 1-Oband have been extensively studied (4-10, 19), only three laboratory studies of N2-broadened HF halfwidths have been reported in the literature (10-12); two of these involved measurements in the 2-O band (II) and the pure rotation band (12), while the 1-O band study covered only five lines in the R branch of the 1-O band. In this paper we present the results of laboratory room-temperature measurements of N2-broadened halfwidths for seven lines in the HF 1-O band R branch, including three lines in the P branch that were not measured in the earlier study (to).
251
0022-2852/84 $3.00 Copyright 0
1984 by Academic Press, Inc.
All rights of reproduction in any form reserved.
THOMPSON
252 EXPERIMENTAL
ET AL.
DETAILS AND DATA ANALYSIS
The spectra used in this study were obtained with a Fourier transform infrared spectrometer (Nicolet 7 199) equipped with an InSb detector, a KBr beamsplitter, and a globar source. The gas cell compartment was purged with nitrogen and maintained at 301.5 -e 0.6 K. Thirty-two scans obtained with a path difference of 16.6 cm-’ (nominal 0.0603-cm-’ resolution) were averaged, and the interferogram was transformed with a Happ-Genzel apodization function to obtain each spectrum. The HF gas cell used in this study was a HALOE life-test cell (13) designed to study the containment of HF over an extended time period of several years. The cell is 10.01 f 0.01 cm long with a 2.5cm inside diameter, has Al203 (sapphire) wedged windows with gold walls, and was custom designed and fabricated for long life and gas stability. The cell was filled with a mixture of HF and N2 in June 1981 at room temperature to a total pressure of 0.050 atm and an optical mass of 0.0040 atm-cm, corresponding to a HF volume mixing ratio of 0.0080. An MKS Baratron gauge was used to monitor the fill pressure. One spectrum of the HF absorption for this cell, taken about 6 months after it was filled, is shown in Fig. la. We have noted an initial loss of HF in the cell which is probably due to absorption of HF into the cell walls and possible chemical reactions. Following this initial loss, the cell has shown a long-term stability with only minor changes in the HF mixing ratio, as will be discussed later. However, because of the low HF mixing ratio, the total cell pressure has not been noticeably affected by the HF loss. Also, the low HF mixing ratio means that HF self-broadening can be neglected. Since no polymer spectral features (14) have been observed, the broadening of the monomer lines by the polymers has been ignored. In addition, the analysis of eight scans of the cell has improved the statistical significance of the results given here. The analysis method adopted for retrieval of the HF halfwidths is based on the work of Park (15). This method is similar to the nonlinear least-squares method of Chang and Shaw (16, 17) for analyzing absorption spectra. The method used in this study, like that of Niple and Mankin (I??), employs the fat Fourier transform technique for simulating the spectrum. The instrument line shape is defined by an effective interferogram apodization that includes the Happ-Genzel apodization function, the field of view effect, and instrument noise. The residual phase error is also included in the analysis. Park (15) showed that this technique can separate from the observed
FIG. 1. (a) Laboratory scan of HF 1-O band, December 1981. (b) Example of line used for pressure retrieval (RI).
NITROGEN-BROADENED
HF HALFWIDTHS
253
absorption line the true absorption (i.e., exponential function) and the instrument line shape defined by the effective apodization function (i.e., equivalent to the Fourier series in spectral space). Although the HF halfwidths retrieved in this work are smaller than the halfwidth of the instrument line shape, the two effects for broadening the observed absorption line can be separated easily, provided there is sufficient signal due to true absorption. Therefore, the present technique to retrieve halfwidths is different from the more traditional method that employs the equivalent width analysis of an absorption line for various pressures (19). We have studied the effects that uncertainties in the modeled apodization function have on the two quantities retrieved in the analysis, i.e., optical mass and halIXdth. Errors of 20% in the retrieved effective apodization function produce errors in the optical mass of approximately 2% and errors of less than 4% in the halfividth. In general, the uncertainties in the apodization function are under 10% and, therefore, errors introduced into the analysis are small. This technique has been applied to other HALOE gas cells to monitor cell stability, and the results are consistently good. As an example, an HCl cell filled with a pressure of 0.070 atm and a mixing ratio of 0.02 1 was scanned five times over a period of 1 year. The observed depths and widths of the HCl lines in these scans were approximately the same as those for HF. The average pressure retrieved for the HCl cell was 0.0681 f 0.0028 atm, indicating the reliability of the technique. Because of concerns about HF stability in the cell, the first of two basic steps in the analysis was the determination of the HF optical mass using weak lines which (as will be shown later) are insensitive to errors in gas pressure or line halfwidth. These lines are in the linear region of the curve of growth. This calculation is performed using the relationship T, = exp(-KU),
(1)
where T, and K, are the transmittance and absorption coefficient, respectively, at wave number v, and U is the optical mass. This optical mass is then used in the second step for the analysis of strong lines which are not saturated but are still sufficiently collision-broadened to permit the retrieval of either the gas pressure or line halfwidth. This retrieval is accomplished through the dependence of the Voigt function on the pressure through the Lorentz halfwidth cyLgiven by
(2) where CY:is the halfwidth at standard pressure, PO,and temperature, To, and n is the temperature-dependency exponent. While pressure-induced lineshifts for HF broadened by N2 have been observed by Guelachvili and Smith (20), for the conditions of the present study the shifts are estimated to be less than 0.001 cm-]. Since shifts of this magnitude are smaller than the wavenumber precision of our interferometer, pressure-induced lineshifts were not included in the retrieval algorithm. A set of five lines (P4, P5, P6, R4, and R5) was used for optical mass calculations, and a set of seven lines (P3 through R3) was used for pressure. An example of a pressure line is shown in Fig. I b. A study was made on the effects of errors in halfwidth
254
THOMPSON
ET AL.
on retrieved optical mass or pressure. As expected, the optical mass retrievals from the weak lines are relatively insensitive to halfwidth errors. For halhvidth errors as large as 20% the retrieved optical mass values change less than 2%. However, the halfwidth errors have essentially a one-to-one influence on the retrieved pressure. Because of the relationship of the halfividth to the retrieved pressure as shown in Eq. (2), the percentage error in the retrieved pressure has the opposite sign from the percentage halfwidth change. We also note that the retrieved pressure value depends on the optical mass assumed in the analysis. It is, therefore, important to have accurate knowledge of optical mass and pressure to retrieve halfwidths from the spectra. RESULTS
Preliminary analysis of the first few spectra using the 1980 Air Force Geophysics Laboratory (AFGL) line parameters (5) and the self-broadened halfividth values of Love11 and Herget (6) yielded pressures which were approximately 50% higher than the cell pressure measured at the time of initial gas cell fill. Since the uncertainty in the cell pressure measured at the time of fill is only on the order of a few percent and since the retrieved gas pressure had remained constant but elevated, thus ruling out a cell leak, it was assumed that the AFGL air broadened halfwidth values adopted from Ref. (10) were too low. To achieve results which were more consistent with the cell fill pressure of 0.050 atm, the AFGL halfwidth values were multiplied by 1.5 as a first guess for this analysis. Eight data sets obtained at intervals over a lo-month period were analyzed to obtain optical mass and pressure values. A weighted linear regression was fit to the optical mass results to reduce uncertainties arising from random variations in instrument performance and experimental conditions. The pressures were next recalculated using the optical mass paths taken from the regression. A plot of this analysis is shown in Fig, 2, which displays the optical mass trend and the mean pressure results. The optical mass can be seen to have changed about 14% over the lo-month period of the analysis. The total gas pressure, on the other hand, remained constant over the period, with a mean value of 0.0580 + 0.0035 atm, which is approximately 16% higher than the fill pressure. Assuming this bias in retrieved pressure to be due to line parameter uncertainties, the gas pressure was fixed at 0.050 atm for the halfwidth retrievals. This assumption is valid based on the accuracy of the Baratron gauge used to monitor the cell pressure at fill and on the observed stability of the cell. The optical mass values taken from the linear fit to the data are shown in Fig. 2. The results of the halfwidth analyses for the individual scans are shown in Table I. The mean halfwidths for each HF line and the standard deviations are also shown in the table. These standard deviations represent uncertainties arising from random noise in the spectra. The total uncertainties in the final halfwidth values result from four sources of errors. These include the random noise in the spectra as mentioned above; line strength uncertainties, which can be as high as 10%; the uncertainty in initial cell fill pressure, which is of at most about 5%; and the uncertainty of the retrieved optical mass values due to spectral noise and instrument performance, estimated to be about 4%. These experimental errors were used to arrive at the root sum of squares error (RSS) given in Table II.
NITROGEN-BROADENED
HF HALFWIDTHS
255
FIG. 2. Trends in cell conditions during measurementperiod. Nominal fill conditions(June P = 0.050 atm, U = 0.0040 atm-cm.
1981):
To verify the retrieved halfwidths, three scans were reanalyzed to determine the cell pressure using the new N2-broadened halfwidth values. The mean pressure calculated with the halfwidths obtained in this work is only a few tenths of a percent from the fill pressure. TABLE I Halfwidth Results (cm-’ atm-’ at 301 K) Date
Aug. Sept.
of Scan
12, 1981 2, 1981
P3
0.134
P2
0.143
Pl
0.148
RO
0.152
Rl
0.135
R2
0.100
R3
0.0699
0.129
0.152
0.152
0.156
0.129
0 0958
0.0654
NOV.
3, 1981
0.119
0.132
0.142
0.132
0.123
0.0937
0.0644
Nov.
27, 1981
0.112
0.128
0.134
0.132
0.112
0.0915
0.0568
Dec.
29, 1981
0.125
0.141
0.135
0.133
0.117
0.0973
0.0692
0.144
0.0886
0.0621
Feb.
19, 1982
0.109
0.133
0.134
0.124
Apr.
15, 1982
0.109
0.129
0.136
0.134
0.124
0.0982
0.0724
June
17, 1982
0.0936
0.120
0.128
0.130
0.115
0.0910
0.0611
a
0.116
0.135
0.140
0.138
0.122
0.0945
0.0652
Standard Deviation
0.013
0.010
0.0080
0.010
0.0076
0.0040
0.0052
Percent Deviation
11 b
7.5
5.7
1.3
6.2
4.2
1.9
THOMPSON
256
ET AL.
TABLE II Error Analysis for Nitrogen-Broadened HF Ha&widths Line
T
(Percent Dev. 1 from Table I (random error)
Aa
Aa from 30 uncertainties S (line strength) and P (cell pr essure) mass) U (optic
in
(Peknt)
(PeKent)
(PeKent)
Ba RSS Error
P3
ll.%
10.8
5.%
4.%
16.%
P2
1.5
10.
5.
4.
14.
Pl
5.7
10.
5.
4.
13.
RO
7.3
10.
5.
4.
14.
Rl
6.2
10.
5.
4.
13.
R2
4.2
10.
5.
4.
13.
R3
7.9
10.
5.
4.
14.
DISCUSSION
A comparison of our mean N2-broadened HF halfividth values with those given in previous publications is shown in Table III and is displayed graphically in Fig. 3. Since the earlier 1-O band results (10) were presented in the form of broadening efficiency ratios determined at 298 and 373 K, it was necessary to combine these ratios with self-broadened halfwidth values (6) to obtain Nz-broadened halfwidths. These halfwidth calculations were performed using ~NZ-HF = (~HF-HF)(~),
(3)
where (YN~_HF is the nitrogen-broadened HF halfwidth, (YHF_HF is the self-broadened HF halfwidth, and t is the broadening efficiency ratio. The nitrogen-broadened halfwidths calculated using the broadening efficiency ratios from Smith (10) and the selfbroadened halt+idth values from Love11 and Herget (6) are shown in columns (b), (c), and (d) of Table III. The temperature dependence exponents [see Eq. (2)] of the self-broadened haltidths used to scale from 373 to 298 K were obtained from Smith (21) and are shown in parentheses in column (b). An examination of the N2-broadened haltidths measured in this work indicates that the P-branch halfwidths are systematically 1% to 19% larger than those for corresponding [ml values in the R branch (m = -J in the P branch, J + 1 in the R branch). To first order, the distribution of halfwidths of hydrogen halide molecules broadened by N2 should be symmetric about the band center. However, the measurements of Houdeau et al. (22) indicate that, for HCI 1-O lines with Irnl =G3, N*broadened halfwidths in the P branch are 3-5% higher than those for corresponding R-branch lines. These results, along with our own for the HF 1-O band, suggest that this asymmetry may be real and should be investigated theoretically. Although the temperature dependence of Nz-broadened halfidths for HF has never been measured, the work of Houdeau et al. (22) indicates that N2-broadened halfividths of HCl vary as T-“, where n varies from 0.5 to 0.8. We might expect a
NITROGEN-BROADENED
HF HALFWIDTHS
257
TABLE III Comparison of Measured Nitrogen-Broadened Line
1-O Band this work (a)
T
HF Halfwidths (cm-’ atm-’ at 301 K)
1-O Band Refs. (5, and..(10) Ch1 (0)
(d)
T
2-O Band Ref. (11, (e) 0.026
Pl
0.035
6 5
0.051
4
0.069
3
0.116 5 0.019
0.089
2
0.101
1
0.135 + - 0.019 0.140 + 0.018
RO
0.138 + 0.019
0.109 (1.5)
0.101
0.108 (0.8)
0.104
1
0.122 + 0.016
0.095 (1.4)
0.085
0.090 (0.8)
0.099
2
0.0945+ 0.012
0.082 (0.91)
0.080
0.085 (0.8)
0.090
3
0.0652+ 0.0091
0.056 (0.84)
0.053
0.056 (0.7)
0.070
0.039 (0.70)
0.039
0.040 (0.6)
0.048
0.105
4 5 6
0.030
7
0.023
8
0.024 obtained from
C,a RSS
(a)
Total uncertalntles
(b)
Self broadened halfwidths measured at 373K (6) scaled to 298K by T-" (21) [n given in parentheses], then multTplied by nitrogen broad=ing efficient ratios measured at 298K (la), and the results scaled to 301K by T- t;e5.
error in Table II.
Cc)
and (d) Self-broadened halfwidths measured at 373K (61 multiplied by nitrogen broadening efficiency ratios measured at 773K (lo), and the results scaled to 301K by T-O-~ [column (c)l or T-" [column (d), n given in parentheses].
(e)
Nitrogen-broadened to 301K by T-Ov5.
halfwidths measured at 373K (11) and scaled
similar temperature dependence for HF. The N2-broadened halfwidth values shown in column (c) of Table III were derived from Refs. (6) and (IO), assuming n = 0.5, while the values in column (d) were derived using values of n from Ref. (22). The differences between the Nz-broadened halfividth values in the HF 1-Oband obtained in this study (column (a)) and those derived from the earlier measurements (columns (b), (c), and (d)) are on the order of the uncertainties in the previous work (23, and depend somewhat on the value of n adopted for the temperature scaling. The halfiKidths of the 2-O band are shown for order of magnitude comparison purposes. In light of the uncertainties of all the measurements shown, no discussion of systematic differences in halfwidths between the 1-Oand 2-O bands will be attempted. SUMMARY
AND CONCLUSIONS
We have determined nitrogen-broadened halfwidths at room temperature for seven lines in the fundamental vibration-rotation band of HF, including three P-branch lines whose N*-broadened ha.lt%vidthshave not been previously measured. These results
258
I
I
I
I
I
I
5
4
3
2
PI
I
RO
I
,
I
I
I
2
3
4
FIG. 3. Comparison of measured halfwidths for HF broadened by N2. Closed circles are the 1-O band from the present work. Open squares are the 1-O band (14) as shown in column (c) of Table III. Open triangles are the 2-O band measured by Meredith and Smith (II) as given in column (e) of Table III.
were obtained through analysis of eight Fourier transform spectra of a sealed absorption cell made at regular intervals over a lo-month period. We note that the original purpose of these measurements was the testing of the integrity of a prototype spacecraft gas cell over an extended time period. Although some loss of HF to the cell walls was detected and measured, the gas pressure remained essentially unchanged, and halfwidths derived from the spectra using a nonlinear least-squares fitting technique are quite consistent from scan to scan. The mean halfwidth values resulting from this study are estimated to have an uncertainty of no more than 15%, and this uncertainty is mainly due to insufficient signal-to-noise to resolve the components contributing to the line shape. A more rigorous experiment designed specifically to measure halfwidths would involve scans at several different broadening gas pressures. Unfortunately, such experiments could not be done within the constraints of the spacecraft program. While the present results should be useful in studies related to the infrared remote sensing of atmospheric HF, we encourage additional high-precision laboratory measurements of halfwidths and intensities in the HF 1-O band. ACKNOWLEDGMENTS This work was accomplished under NASA Contracts NAS I - 15890 and NAS 1-17265. The authors wish to acknowledge the work of Dr. J. T. Twitty (NASA Contract NASl-15493) and Mr. D. J. Richardson (NASA Contract NASl-15890) for their past help in developing algorithms used in this work. We would also like to thank Dr. D. F. Smith, Dr. R. H. Tipping, and Dr. C. P. Rinsland for helpful discussions relating to this work. RECEIVED:
November
17, 1983 REFERENCES
1. R. D. HUDSON,E. I. REED, AND R. D. BOJKOV,unpublished results, 198 I. 2. J. M. RUSSELL,J. H. PARK, AND S. R. DRAYSON,Appl. Opt. 16,607-612 (1977).
3. C. P. RINSLAND,M. A. H. SMITH,J. H. PARK, G. A. HARVEY,J. M. RUSSELL,ANDD. J. RICHARDSON, unpublished results, 1982. 4. J. F. OGILVIE,W. R. RODWELL,AND R. H. TIPPING,J. Chem. Phys. 73, 5221-5229 (1980).
NITROGEN-BROADENED
HF HALFWIDTHS
259
5. L. S. ROTHMAN,A. GOLDMAN,J. R. GILLS, R. H. TIPPING,L. R. BROWN,J. S. MARGOLIS,A. G.
6. 7. 8. 9. IO. 11. 12. 13.
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