JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Total Absorptance of Ammonia in the Infrared*

WILBUR L. FRANCECapitol University, Columbus, Oh1io 43209

AND

DUDLEY XVILLIASs

Kansas Stale University, an11ahattan, Kansas 66504(Received 14 June 1965)

The total or integrated absorptance fA (z)dv has been measured at 26'C for the ammonia bands near950, 1628, and 3300 cm-' in samples of pure ammonia and of ammonia mixed with nitrogen. The results aredisplayed graphically with fA (v)dv shown as a function of absorber concentration w and an equivalentpressure P., which depends upon the partial pressures of the two gases. The equivalent pressure of a givensample is expressed in terms of the total pressure of the sample, the partial pressure of ammonia, and a self-broadening coefficient B, which is related by simple kinetic theory to the ratio of the optical collision diam-eters of ammonia and nitrogen. The graphs can be used to predict the total absorptance of ammonia in anysample at laboratory temperature for which the values of w and P, are known, provided these values liewithin the range covered in the present study. Values have been obtained for the band strengths S==fkG()dvfor the absorption bands studied. The self-broadening coefficient B for ammonia is greater than the corre-sponding values for telluric gases obtained in earlier studies.INDEX HEADING: Absorption; Infrared; Spectra.

CURRENT interest in the study of planets by the.methods of conventional earth-based astronomy

and by modern space-exploration probes has stimulatedlaboratory investigations of "synthetic atmospheres" inan effort to obtain a better understanding of the trans-mission of infrared radiation through planetary atmos-pheres. The absorption of infrared radiation by thetelluric gases C02, H20, CH4 , N20, and CO has beeninvestigated in earlier studies.'-5 The present investiga-tion has been concerned with the infrared absorptionby synthetic atmospheres containing ammonia NH3 ,large quantities of which have been detected spectro-scopically in the atmospheres of Jupiter and Saturn.6

Although the temperature of the Jovian atmosphere isreported to be - 1400 C and that of Saturn may be evenlower, it is hoped that the results obtained in the presentstudy, which was conducted at 270C, may serve as apreliminary step in the quantitative interpretationof the infrared spectra of these and possibly otherplanets.

Because the spectral absorptance A (v) for the vibra-tion-rotation bands of a gas is a rapidly varying func-tion of frequency, measured values of A (v) are stronglydependent on the slit function of the spectrograph em-ployed. However, it has been shown theoretically and

*Supported in part by the U. S. Air Force Cambridge ResearchLaboratories under a contract with the Ohio State UniversityResearch Foundation.

1 J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc. Am.46, 186, 237, 242, 334, 452 (1956).

2 D. E. Burch and D. Williams, Appl. Opt. 1, 473, 587 (1962).3 D. E. Burch, D. A. Gryvnak, and D. Williams, Appl. Opt. 1,

759 (1962).' D. E. Burch, W. L. France, and D. Williams, Appl. Opt. 2,

585 (1963).5 D. E. Burch and D. Williams, Appl. Opt. 3, 55 (1964).6 G. P. Kuiper, Ed., The Atmiospheres of th1e Earth and Planets

(University of Chicago Press, Chicago, 1951), 2nd ed., p. 364.7J. R. Nielsen, V. Thornton, and E. B. Dale, Rev. Mod. Phys.

16, 307 (1944); D. E. Burch, J. N. Howard, and D. Williams, Phys.

experimentally7 that the measured value of the totalabsorptance fA (v)dv associated with a band in a givensample is independent of the spectral slit width em-ployed, provided the limits of the integral are chosen toinclude all spectral absorptance associated with the ab-sorption band. Earlier studies of telluric gases at am-bient laboratory temperatures have shown that thevalue of fA (v)dv for a given band depends upon theabsorber concentration (or optical density) w and thepartial pressures pa and pb of the absorbing and non-absorbing gases in the sample; the contribution of thenonabsorbing molecules to fA (v)dv is through theircollision broadening effects on the spectral lines of theabsorbing molecules. In earlier studies,8 the "line-broad-ening abilities" of various gases have been measuredrelative to nitrogen, which has been selected as a "stand-ard" for atmospheric studies. Self-broadening is also animportant factor in the spectrum of an atmosphericgas and it is convenient to introduce a self-broadeningcoefficient B that gives a measure of the line-broadeningability of the absorbing gas relative to nitrogen.8

Thus, for a given temperature, it has been possibleto express total absorptance fA (v)dv as a function ofw and an equivalent pressure P0 defined by

P,= P+ (B- l)pa,

where P is the total pressure of a gas sample consistingof a binary mixture of an absorbing gas and nitrogen,and pa is the partial pressure of the absorbing gas. Ifseveral nonabsorbing gases are present, their effects canbe included by the use of the measured relative line-broadening abilities mentioned above.

Rev. 94, 1424 (1954); H. J. Babrov, J. Opt. Soc. Am. 51, 171(1961).

81D. E. Burch, E. B. Singleton, and D. Williams, Appl. Opt.1, 359 (1962).

70

VOLUME 56, NUMBER I JANUARY 1966

January 1966 TOTAL ABSORPTANCE OF AMMONIA IN THE INFRARED

EXPERIMENTAL METHODS

The general experimental methods employed in meas-suring fA (v)dv and of determining self-broadening co-efficients have been described in earlier papers.?'8 In thepresent study a double-beam, single-pass Perkin-ElmerModel 21 spectrometer was employed. This spectrographwas equipped with dual multiple-traversal absorptioncells, which provided path lengths that are multiplesof 4 m up to a maximum of 40 m. When shorter absorp-tion path lengths were desired, these cells could be by-passed and shorter cells could be inserted. In normaloperations, gas samples were introduced to the "samplecell," while the "reference cell" was evacuated. Thetechniques employed in gas handling, pressure measure-ment, etc. have been described previously.2

Pressures are given in mm Hg, absolute. The valuesof absorber concentration w are measured by the pro-duct of path length in cm and the partial pressure cor-rected to standard temperature and expressed in atmos-pheres; the resulting unit, the atm-cm, is convenientfor atmospheric work.

It is believed that pressure measurements are accurateto -1%0 for pressures greater than 10 mm Hg. The un-certainties in total absorptance JA (v)dv are estimatedas 4t 20% for JA (v)dv< 10 cm-l and zE45% for fA (v)dv>25 cm-'.

RESULTS

The near infrared spectrum of ammonia9 consists ofthree major regions of absorption: (1) the 950-cm-lregion, associated with the band V2; (2) the 1628-cm-'region, associated with the bands V4 and 2

v2; and (3) the3300-cm-1 region, associated with bands vi, V3, and2 P4.

A. The 950-cm-' Region

Typical spectra obtained for the 950-cm-l band areshown in Fig. 1. The curves shown in the top panelgive results for a small value of w; the inversion doublingof the V2 fundamental is clearly demonstrated by thesecurves. The increase of absorptance with increasing P6is also quite evident. The curves in the lower panelsrepresent results obtained with much larger values ofw. These curves indicate that at low frequencies theV2 fundamental overlaps the "hot band" (

2v2-V2),

which is centered at 629.3 cm-'. Band limits of 1300cm-' and 660 cm-l were used in obtaining JA (v)dv forthe 950-cm-1 region.

More than 100 spectra were obtained for the 950-cm-lregion, with absorption cell lengths 1.55, 6.35, and 400cm. Different mixtures of ammonia and nitrogen wereused to provide absorber concentrations in the range0.009 to 47 atoms-cm and total pressures in the range2 to 3000 mm Hg. Equivalent pressures were obtainedfrom the measured pressures and the value B = 6.2 h 1.0obtained experimentally for this band.

I G. Herzberg, Molecular Spectra and Molecular Structure. ISInfrared and Rainan Spectra of Polyatomnic Molecules (D. VanNostrand Co., Inc., New York, 1945), pp. 295-296.

Ed0z

cc0U,a3

C-)

WAVENUMBER in cm-'

0z

a-4v)0

(I,-

zULS

Lu0l-

Li0z

0-

0CoU)

0a:Lu

0:

1200 1000 B00

WAVENUMBER in cm1

-a 1200 (000 0oo

WAVENUMBER in cm-1

FiG. 1. Typical spectra of ammonia samples in the 950-cm-1 region.

Figure 2 shows a logarithmic plot of some of the dataobtained in the 950-cm-l region; each curve givesfA (v)dv for a given absorber concentration w as a func-tion of equivalent pressure P0 and thus shows the effectof addition of nitrogen. The longer curves at the top ofthe figure were obtained with a path length of 400 cm,while the lower curves were obtained with shorter cells.The onset of saturation is evident in the topmost curves.

In Fig. 3 the total absorptance of samples of pureammonia is shown as a function of equivalent pressure;for these curves, each of which corresponds to a differentpath length, the absorber concentration w is not con-

71

72 W. L. FRANCE

400

IS 10000c.(-

4C

40-0,

4

10 40 l0o 400 1000 4000

AND D.

0w in atmcm

= 9.86

NH3 n0o,

950 cm-' -gw OO~o n7

0.7r22 0,306

,o 0 o a- 0.0772

0f.0372

0.0192

- - 0.00935

5

lo0

15

Pe in mm Hg

FIG. 2. Total absorptance in the 950-cm-' region as a functionof equivalent pressure for various samples having constant ab-sorber concentration.

100 400

Pe in mm Hg

FIG. 3. Total absorptance of the 950-cm-1 region as a functionof equivalent pressure for samples in which absorber concentrationis proportional to equivalent pressure.

10

W I L L I A M S

1800 1600WAVENUMBER in cm'

300 16 00WAVENUMBER in cm'

FIG. 5. Typical spectra of ammonia samplesin the 1 628-cm-' region.

6E 0mmP 4 Hg3000

.E 15C040 - 7 60300

75

4

001 0.04 0.1 04 1 4 0 40w in olm cm

FIG. 4. Total absorptance in the 950-cm-1 region for various valuesof equivalent pressure as a function of absorber concentration.

stant but is proportional to P,. Saturation effects areobserved for smaller pressures for the longer pathlengths since the corresponding values of w are greater.

Figure 4 gives the most useful summary of the resultsobtained for the 950-cm-1 region. The curves givefA (v)dv as a function of absorber concentration w;each curve represents a different value of equivalentpressure P0 and is based on data such as those shownin Figs. 2 and 3. From Fig. 4 the value of total absorp-tance for any sample can be determined provided thevalues of w and P, are known and fall within the rangecovered in the experimental work. Interpolation willyield values of total absorptance for values of P, lying

Vol. 56

zI-

0

zw0)Ura.

w inP ein mm Hg atM cm

115.5 0.153314.0 0.153

1 630.0 0.153

I I I I I I _ _

14 00MU 1

January1966 TOTAL ABSORPTANCE OF AMMONIA IN THE INFRARED

between the values corresponding to the curves. Theplotted points have been omitted in order to facilitateinterpolation; each curve is drawn over the range of wcovered by the data without any extrapolations.

B. The 1628-cm'1 Region

Typical spectral absorptance curves for the 1628-cm-lregion are shown in Fig. 5, with data for samples withsmall w in the top panel and for samples with larger win the lower panels. For large values of w, the V4 funda-mental is overlapped slightly at the low-frequency endby the V2 fundamental and at the high-frequency endby the much less intense 2 V2 band centered by 1922 cm-1.In the present study, the total absorptance was meas-ured in the range from 2000 to 1300 cm-'; most of theabsorption can be attributed to the V4 fundamental.

Considerable difficulty was encountered in obtaininga value of B for the V4 band because of marked differ-ences in self-broadening and nitrogen-broadening invarious parts of the band. However, a value of 5.77±0.35 was used in calculating Pe for use with the datafor the 1628-cm-' region.

Summary graphs showing JA (P)dv as a function ofw are shown in Fig. 6. These plots are based on data ob-tained with 138 different samples and are analogous tothe plots shown in Fig. 4 for the 950-cm-' region andare based on intermediate plots corresponding to thoseshown in Figs. 2 and 3. It should be remarked that theV4 ammonia band overlaps the V2 band of water vaporat 1595 cm-l and that considerable care was taken toeliminate spurious effects due to water vapor in thelaboratory.

C. The 3300-cnm- Region

Typical spectral absorptance curves for the 3300-cm-' region are shown in Fig. 7; the absorptance in theregion is due to the overlapping bands Pi, V3, and 2

V4 ofammonia. Care was taken to eliminate spurious effectsdue to the adjacent bands of atmospheric carbon dioxideand water vapor. The over-all intensities of the bandsin this region were not sufficiently great to permit theaccurate determination of a B-value for the region; in

400'

tooE

40. 50

4

0.01 0.04 0.1 0.4 1 4 10 40

w in atm cm

FIG. 6. Total absorptance in the 162 8-cm-1 region for variousvalues of equivalent pressure as a function of absorber concen-tration.

W 200z

0 400inmC 60

zL)O 80Wa.

73

WAVENUMBER in cm-

0W4z

a-

n0'

L.UzUJa-

24

4'

6

8

10

Lid0

a-I-0In

z

0W

a:Lta.

D -

0 - P in mm Hg wintmcm

2485 3.045 160 3.045090 6.237355 6.23

0

) I I I I I I

3600 3400 3200WAVENUMBER in cm-'

3000

3400 32(WAVENUMBER in cm-1

FIG. 7. Typical spectra of ammonia samplesin the 3300-cm-1 region.

computing Pe, the value B= 6.1 was assumed; this isthe value obtained for the 950-cm-1 region.

The summary plots of JA (v)dv as a function of wfor various values of Pe is given in Fig. 8; these plotsare based on 100 spectral records of the region. Sincethe bands in this region are not as intense as those inthe other spectral regions, the onset of saturation is notobserved in the summary plots.

DISCUSSION OF RESULTS

It would be possible to obtain empirical equationsgiving fA (v)dv in terms of w and Pe for the variousabsorption bands for limited ranges of these variables.However, it is believed that the graphical representa-tions given in Figs. 4, 6, and 8 provide a more useful

v

W. L. FRANCE AND D. WILLIAMS

400

E

C

c

100

40

10

0.1 0.4 1 4 lo 40w in atm cm

FIG. 8. Total absorptance in the 3300-cm-1 region for variousvalues of equivalent pressure as a function of absorber concen-tration.

method of presenting the results and provide a sounderbasis for possible extrapolation of the data, since clearerestimates of the "dangers" can be obtained. No seriousattempts were made to fit the observed results to anyof the current band models,'0 but it would appear thatPlass's random Elsasser model could be employed.

It can be seen from the graphs of fA (v)dv as a func-tion of w and P, that f A (v)dv is more strongly depend-ent upon w than upon P,,. Under conditions where the"strong-line approximation" predicts" that fA (v)dvshould be proportional to (wP,)4, it is found that theslopes of the curves indicate an approximizate propor-tionality to wi1 but not to P, 1t. By consideration of thelinear portions of plots of fA (v)dv versus w and P0 , itis possible to express the total absorptance as a functionof WmPn.

The values of in and it obtained for ammonia arelisted in Table I along with corresponding values ob-tained for telluric gases reported in earlier studies. It

TABLE I. Comparison of band parameters of variousabsorbing gases.

Self-broadeningGas Band int i coefficient B

CH4 3020 cm-' 0.55 0.22 1.30±40.081306 cm-' 0.48 0.30 1.38±t0.08

NH, 950 cm-' 0.56 0.34 6.2 ±1.01628 cm-' 0.54 0.40 5.77±0.343300 cmn' 0.59 0.34 ...

H20 5332 cm-' 0.53 ... 5.0 ±1.53700 cm-' 0.49 ... ...

N20 2224 cm-' 0.53 0.37 1.12±40.07C02 3716 cm-' 0.58 0.38 1.30±0.08

3609 cm-'2350 cm-' 0.54 0.40 ...1064 cm-' 0.75 0.23 ...961 cm-' 0.78 0.20 ...

CO 2143 cm-' 0.55 0.44 1.02±0.06

10 V. M. Elsasser, Harvard Meleorological Stedies No. 6 (Har-vard University, Cambridge, Mass., 1942); R. M. Goody, Quart.J. Roy. Meteorol. Soc. 78, 165 (1952); G. N. Plass, J. Opt. Soc.Am. 48, 690 (1958).

" G. N. Plass, J. Opt. Soc. Am. 50, 868 (1960).

-"".I , I , I'""I ''' ... I- NH3

3300 cm-'

P, in mm Hg30001500760300150

l l l s l l l will be noted that, if we neglect the "hot bands" ofCO2, the departure from strict square-root dependenceon PA is greatest for CH4 with NH3 coming next in thetable. The closest approach to square-root dependencewas obtained in the case of CO.

Also listed in Table I are the values of self-broadeningcoefficients B. It will be noted that the largest values ofB were obtained with the strongly polar molecules NH3and H20. The tempting conclusion that electric dipolemoment has the most important influence on B is prob-ably correct. Although it might appear that the "physi-cal size" is most important in determining departuresfrom the square-root relationship, it should be pointedout that numerous weak lines in the spectrum areprobably responsible for the departure from the square-root dependence on w and PA. Many more such linesmay occur in the spectrum of the spherical-top CH4 ,the symmetric top NH3, and the asymmetric top H20than in the spectra of the linear molecules N20, CO2,and CO.

The self-broadening coefficient B can be related tothe optical collision diameters by simple kinetic-theoryconsiderations. The ratio of collision diameters forNH3-NH3 collisions to those for NH3-N2 are: 2.3640.20 from B values for the 950-cm-' band and 2.284-0.07 from B-values for the 1628-cm-' band.

In studies of molecular spectroscopy an importantquantity is the band strength S= Jfk (v)dv, where k (v)is the exponential absorption coefficient and the limitsof integration include the entire vibration-rotation band.At a given temperature, the band strength is in firstapproximation directly proportional to the transitionprobabilities. The band strength can be evaluated if thevalue of the product k(v)w<<l throughout the entireband, a situation that can be realized for small w andlarge P0 . Under these circumstances

S= fk(v)dv= (l/w)f A (v)dv,

where w and fA (v)dv are both directly measurable.Based on present measurements in the 950-cm-1 region,the band strength of the V2 fundamental has the value7904±30 atm-' cm-2. Measurements in the 1628-cmr4

region give S= 150±5 atm-n cm-2 for the V4 band. Thecombined band strengths of Pi, V3, and 2V4 in the vicinityof 3300 cmnl amount to only 474±3 atm'l cnm2. Thelimitations on the precision of band-strength determina-tions lie in the precision with which small values of wcan be measured and on the validity of the assumptionthat le(v)w<<1 at all frequencies within the band.

We hope that this work will provide an initial steptoward a quantitative understanding of some aspects ofthe infrared spectra of the outer planets. A succeedingstep will involve a study of the effects of temperature onthe total absorptance of ammonia.

We wish to express our appreciation to David McCaa,L. Abels, and others for assistance with various partsof the work.

74r Vol. 5 6