■)

"N

Oi CO

Q

.

D D C

APR ' 1972

& B

PHILCO PHILCO-FORD CORPORATION Aeronutronic Division

Newport Baach, California

1 I

M Roprodurod by

NATIONAL TECHNICAL INFORMATION SERVICE

Spnngfiold, Va 23151

Publication No. U-3203

SCIENTIFIC REPORT

THE SHAPES OF COLLISION-BROADENED COp LINES

Prepared for:

Under Contract:

Prepared by:

Approved:

31 August 1968

Advanced Research Projects Agency Washington, D.C.

NOnr 3560(00) ARPA Order No. 237 Amendment No. 26/9-1-67

Darrell E. Burch David A. Gryvnak Richard R. Patty Charlotte E. Bartky

Paul M. Sutton, Manager Physics and Chemistry Laboratories

D D C

APR ? 1972

EinrE B

&

Approved for public reteoae; Diatribation Unlimited

Distribution of this document is unlimited,

PHILCO PHILCO-FORD CORPORATION Aeronutronlc Division Newport Beach, Calif, . 32663

ABSTRACT

The shapes of the extreme wings of self-broadened C09 lines have been

investigated in three spectral regions near 7000, 3800, and 2400 cm"1.

Absorption measurements have been made on the high-wavenumber sides of

band heads where much of the absorption by samples at a few atm is due to

the extreme wings of strong lines whose centers occur below the band heads.

Considerable new information has been obtained about the shapes of self-

broadened C02 lines as well as CO lines broadened by N2, 0 , A, He, and

H2. Beyond a few cm from the line centers all the lines absorb consi-

derably less than Lorentz-shaped lines having the same half-widths. The

deviation from the Lorentz shape decreases with increasing wavenumber in

going from one of the three spectral regions to the next. The absorption

by the wings of H - and He-broadened lines is particularly low, and the

absorption decreases with increasing temperature at a faster rate than

predicted by existing theories.

ii

I

I

TABLE OF CONTENTS

Page

INTRODUCTION AND BACKGROUND 1

EXPERIMENTAL AND ANALYTICAL METHODS 4

SPECTRAL CURVES AND LINE PARAMETERS U

Table 1 - Identification, Positions, and Strengths of Bands . 16

Table 2 - Relative Half-Widths of CO- Lines Broadened by Various Gases 22

NORMALIZED ABSORPTION COEFFICIENTS 27

CURVES OF X VS (v-v ) 36

INFLUENCE OF X ON CALCULATED LINE STRENGTH 57

SUGGESTED FURTHER WORK 63

REFERENCES 66

iii

ILLUSTRATIONS

Page

Figure 1 Representative Spectral Curves in the 7000 cm Region . 12

Figure 2 Representative Spectral Curves in the 3800 cm Region . 14

Figure 3 Representative Spectral Curves in the 2400 cm Region . 19

Figure 4 Normalised Half-Width Q of Self-Broadened C0„ Lines s 2

at 1 atm Plotted Versus J 21

Figure 5 Spectral Curves Showing Comparison of Self-Broadened

and N -Broadened Lines 24

Figure 6 K Versus v for CO Self Broadening Between 6900 s z

and 7100 cm' 28

Figure 7 K for N-, He, and Self Broadening Between 6990

and 7010 cm" 30

Figure 8 K0 for Self and N Broadening Between 37 70 and 4100 cm" 32

o -1 Figure 9 K for Various Gases Between 3770 and 3860 cm 33

iv

«*

i

I

I I I

ILLUSTRATIONS (Continued)

Page

Figure 10 K0 for CO , N , and A in the 2400 cm' Region 35

Figure 11 X for Self-Broadened CO Lines in the 7000 cm' Region 37

Figure 12 X for Lines Broadened by CO , N , and He in the

7000 cm" Region 39

Figure 13 X for Lines Broadened by CO , N , A, 0 , He, and H

in the 3800 cm' Region 40

Figure 14 X(v-v ) for CO , N , and A in the 2400 cm' Region , . 41

Figure 15 Influence of Assumed Line Width on Calculated Curves

of X(v-V ) and K (v) in the 7000 cm Region 43 o s

Figure 16 Curves of X and K Showing Influence of Assumed 2

Line Shape on the Calculated Absorption Coefficient

in the 3800 cm Region 45

Figure 17 Ratio k/k Versus (v-v ) for Self-Broadened Lines max o

in Three Spectral Regions 53

Figure 18 Ratio k/k Versus (v-v ) for N - and A-Broadened max o 2

Lines in Three Spectral Regions 55

Figure 19 k Plotted Versus (v-v ) to Show Influence of X o

on /kdv for a Single Line 58

INTRODUCTION AND BACKGROUND

The shapes of spectral absorption lines has been the subject of

considerable study since Michelson wrote a paper dealing with the

broadening of spectral lines in 1895. The two major factors leading to

the broadening of spectral lines of gases are Doppler broadening and

collision broadening, which is also frequently referred to as pressure

broadening. Doppler broadening arises from the motion of the individual

molecules in a gas and is dominant for gases at high temperatures or at

very low pressures. Collision broadening is related to the pressure, or

to the number of collisions, and is dominant for infrared absorption

lines when the gas is at room temperature and at pressures greater than

a few hundredths of an atm. The mechanism involved in Doppler broadening

is relatively simple so that it is possible to calculate accurately the

true shape of a Doppler-broadened line. However, this is not the case

for collision-broadened lines since present theories do not adequately

explain many of the features which have been observed. I I I

Lack of good experimental data on the shapes of spectral lines is

probably the major cause for the shortcomings of the theory at this point.

It is experimentally difficult to observe the true shape of infrared lines

because of the finite spectral slitwidth of spectrometers used to make

the measurements. At low pressure, the transmittance near the center of

a typical line changes so rapidly with wavenumber that the true contour

cannot be observed. At high pressures, the lines are usually so wide

that overlapping by neighboring lines is important, and the contribution

by an individual line cannot be determined. Although the true shape very

close to the line center cannot be measured directly with spectrometers,

considerable information about the shapes of the lines can be obtained by

measuring their equivalent widths for samples covering large ranges of

pressure and absorber thickness. The equivalent width of a line is equal

to /A(v)dv, where A(v) is the observed absorptance. The results of

measurements of this sort for several different gases indicate that the

shape of a collision-broadened line near its center is at least similar

to he well-known Lorentz line shape (Eq. (6)).

2 3 Benedict, Herman, Moore, and Silverman"' have found that the wings

of HCl and CO lines deviate significantly from the Lorent?. line shape a

few cm from their centers. These gases were studied because the

relatively wide spacing of their absorption linos make it possible to

observe the contribution of a single line at a point a lew cm'1 from its

center. However, absorption by the extreme wings of lines of other gases

of astrophysical interest is difficult to measure since the absorption at

any wavenumber is usually complicated by nearby lines. Exceptions to this

occur near some of the CO,, bands which arise from changes in the vibra-

tional quantum number v3 and have band heads in the R-branches. On the

high-wavenumber side of such a band head the absorption is due to the

extreme wings of the lines whose centers occur below the band head.

Winters, Silverman, and Benedict (WSB)4 have made use of this feature

of the V3 band of CO,, to investigate the shapes of the extreme wings of

the lines. These workers have found that the wings of the CO lines are

quite sub-Lorentzian, i.e., they absorb considerably less than lines having

the same half-width and the Lorentz shape. They have also found that the

shapes of the wings of lines broadened by argon or N,, are quite different

from self-broadened lines.

The present investigation extends the WSB work to two other spectral

regions near 3800 cm'1 and near 7000 cm"1; it also includes an investiga-

tion of broadening by other foreign gases and some data on the influence

of temperature on line shape. We have found the extreme wings of the

lines to be sub-Lorentzian in all three spectral regions for several dif-

ferent broadening gases. The shapes of the lines also depend on the

wavenumber and on temperature in a manner not explained by any theory known

to the authors. Some very interesting results have also been obtained

for broadening by two light gases, He and H. .

EXPERIMENTAL AND ANALYTICAL METHODS

Spectral curves were obtained by using two different spectrometers

in the three spectral regions. A Perkin-Elmer spectrometer, Model 112,

with a LiF prism and thermocouple detector, was employed near 2400 cm"1.

The two spectral regions near 3800 cm'1 and 7000 cm"1 were investigated

with a small grating spectrometer employing a PbS detector cooled with

liquid nitrogen.

The samples used in the 2400 cm" region varied in pressure up to

1 atlti and were contained in a multiple-pass absorption cell with a base

length of approximately 29 meters. This cell as well as a shorter one

with a 1-meter base length contained samples investigated in the other

two spectral regions. The shorter one was used at pressures as high as

15 atm and at temperatures up to approximately 431 K. The 2400 cm"1

data were obtained before the shorter absorption cell was constructed;

therefore, the daUi in this spectral region do not contain any samples at

high pressures or elevated temperatures. The apparatus and experimental

techniques have been discussed in detail previously.

Samples consisted of either pure CO or mixtures of CO with one of

the following broadening gases: N2, 02, A, He, and H . The partial

pressure of C02 is denoted by p and the total pressure by P. Partial

pressures of the other gases are denoted by PN ^ Pn , • . ., etc. All 2 02

pressures are given in atm with standard pressure of 1 atm denoted by a

superscript, such as p .

The geometrical path length of the radiation through the sample is

given by L, and the absorber thickness u is given by

u(atm cmSTp) = p(atm) [l+0.005p] L(cm) 273/e(0K). (1)

The factor fl+0.005p] accounts for the non-linearity in the relati on

between the pressure and density of C02, and (273/8) reduces the absorber

thickness to standard temperature, 273,K.

T(v) represents observed transmittance of a sample at wavenumber v, and

T'Cv) is the true transmittance that would be observed with infinite resolv-

ing power. The absorption coefficient K(v) is related Lo '] ' (v) by

T'Cv) exp [-uK(v)|, or K(v) --JLT(->). u

In a region of overlapping lines, K(v) is the sum (; . k (v)) of ihv

absorption coefficients due to the individual lines.

(2)

The strength, S, of an individual line is related to k(v) and a

shape factor f(a, v-v ) by o

l<(v) = S f((>, v-v ), where (3)

00

/ f(ü, v-Vo) = 1, and (4)

-00

00

S = / k(v)dv. (5) -00

For a Lorentz line, which is generally agreed to be approximately correct

for collision-broadened lines when vv is small

V"' V_Vo) i 2' (Lorentz) (v-Vo) I Q

WhenCv-v^ "> ., Eq. (6) reduces to

f(o, v-v ) f ( ,, v-v )X(v-v ) X(v-vo)

(v-vo) •

(6)

V"' V"Vo) . ' .2' (for (v-v ) »a) O) IT (V-V ) O '

O

We have found that when (v-V0) » t, the Lorentz shape is not

appropriate; however, the shapes can be expressed by the following

equation:

(8)

■ ■

I I

The correction factor X(v-V ) is probably very near unity within a few

tenths of a cm of the line center where the Lorentz shape is generally

agreed to be valid. The next-to-last section of this paper deals with

the shapes of lines broadened by several atm of gas at points where

(v-v ) may be a few cm yet not large in comparison to a. Under this

condition, Eq. (8) is not appropriate unless X is expressed as a function

of a as well as (v-v ). However, Y. can be expressed satisfactorily as a

function of (v-v ) when (v-v )» a. which is the case for most of the o o '

results presented in this paper. The primary objective of the present

investigation has been to determine the functional relationship between

X(v-v ) and (v-v ) for large (v-v ). o o o

It is understood that k, K, T1, T, f, and X are functions of v,

(V"V ), or Q as indicated previously. However, in order to simplify the

equations and figures, we have omitted the appropriate indication of the

variables upon which these functions depend.

Representative spectral curves in the 7000 cm region are shown in

Fig. 1. The location of the very sharp band head near h988.6 cm is

apparent in Curve A, which represents a sample of relatively large

absorber thickness and low pressure. Many of the stronger lines in the

R-branch of this band are crowded together within a narrow interval a

few cm below the band head. No lines of any significance occur between

the band head nnd 7100 cm ; therefore, the absorption indicated by

Curves B and C in this region is due to the extreme winj^s ol lines

occurring below the band head.

At a distance a few times greater than a above the band head, the

contribution to the absorption coefficient by a single line for a sample

of pure C0„ is given by

Sri*.

IT(V-V )' o

Sa p(l+0.005p)X

Jtp (v-v ) (9)

where the subscript s denotes self broadening, and ,0 is the half-width s

at 1 atm. Since Q is proportional to the number density of the molecules,

rather ihan to pressure, the factor (i'Ü.OObp) is included to account lor

the non-linearity in the relationship between these two quantities. The

total abcorption coefficient is given by thu sum of the contributions of

all of the individual lines,

E k I S>'L

S > . p(lfü.005p)

o- np (v-v )'

(10)

For a mixture of p atm ot CO., and p. atm ol broadening K.is. tin total

absorption coefficient is given by

K --J~-ri-,) K p(l+0,005p) < %

i P (v-v ) L

o ± o ■.

b.^b] (11)

I I i

The subscript b denotes broadening by a non-absorbing broadening gas; a

specific broadening gas such 0 or N,. will be denoted by the appropriate

subscript. The normalized absorption coefficients K and K^ correspond

to 1 atm pressure. The half-width of a C0„ line broadened by 1 atir, of a

foreign gas b in a mixture with C0o when p '■ p, is denoted by ,°. The Z D h

ratio of the normalized half-widths ((x/o ) is assumed to bo the same for D S

all lines for a given broadening gas. The non-linearity in the relation-

ship between number density and pressure for the ton-ign broadening gases

was negligible.

Since Ihere are no absorption lines between the band head and

7100 cm , the absorption coefiicient K does not change rapidly, except

very near the band head. Therefore, the true transmitlance 1 ' (. ) in this

region closely approximates the transmittance T('. ) observed with our

spectrometer. Values ol K at several ditterenl wavenumbers w.re deter-

mined from spectral curves ot pure CO samples b ,• substituting T(-. ) for

T'Cv) in Eq. (II) with p. 0. These values ol K0 were then used In

Eq. (II) with values of T I rom spectral curves for mixtures of CO., and a

broadening gas in order to determine K. .

Values of the line strengths, S, were calculated by use ot thi

ft 7 appropriate theoretical expressions ' from exptr imtntal 1 v «I« termined

strengths, Sv, of the vibr.it ion-rotat Ion bands. Values ot lor all ot

the lines were determined trom inlormation discusRed below. The absorption

coetlicient K for a particular wavenumbtr was calculattd by substituting

into Fq. (II) the appropriate values of and St, along with assumed

>

I I I I I

values of X. For a particular broadening gas, we assumed that X was a

slowly-changing function of (v-v ) only, and that this function was the

same for every line in any one of the- three spectral regions. However,

we found that each broadening gas required a different X function in each

of the three spectral regions. Each X function was represented by a

table of X vs (v--.o) which served as input lor a computer that was used

to perform the calculations. Each table was modifu-d on a trial-and-error

basis until all thi' calculated values of K0 in a given spectral n-nion

agreed, within experimental error, with the observed values. We thin

assumed that the lunciion represented by the table which gi.ve sat is Iactory

agreement was appropriate. More detailed Iniormatiop about the methods

used to determine the line parameters is given in the lollowitiK sections,

along with a discussion 01 t lu imiuemc that errors in the line parameters

have on the derived values oi v.

10

SPECTRAL CURVES AND LINE PARAMETERS

I

Representative spectral curves of the three regions investigated are

shown in Figs. I, 2, and 3. The shapes ot the extreme wings ot thi- lines

occurring below the band head at 69H8ob cm were investigated by measur-

ing the absorption above the band head by sampl'-s such as those represented

in Fig. 1. No absorption lines of any significance occur in the region

between the band head and 7100 cm . Essentially all the absorption in

this region is due to the extreme wings of the lines oi the 00 J band and

the weaker 01 M)l 0 band whosi head can be seen near 6950 cm

Curve B in Fig. 1 represents a 2 aim sample with sufficiently lar^e

u to produce signllleant absorption above th» band head. Curve C, which

represents a sample at iV.h atm, is relatively smooth below bfOQ cm

since the individual lines have hern broadened suitiiuntly at tht hi«her

pressure to smooth-out the striutun. It is ol inUrest that S.impl» B

absorbs more than Sample (" below h90l) cm sime th. absortur thiikness

11

u

^ o T3 O 1 01

c u 0> s: re

4-1 JO o

M u 0) 3

i

1) D D.

IM O

V) a*

a E ä

'S > « ■i u 10 H 3 w: o o o u ac E «N o o c y m 1—1 CI i •rH ». •

x: 3 E W r^ r^

^^

f« 0 X »t

o • 0 ■ ^^^ c ^^^ o

^•--^ p 1 0

M :=~- u

0 ^■v ^^^ 1^ 1/1

T 1 D C o

E y i

& £

•

^j o a E »t »t ***' o

o ■ la

ÜJ CD

X.

E o

c c ■ E O 3 ■ X 1

O • B • •

-'J 8 Z >

u -i II M

U o fS 4

»4

dsr 0> -< (0 ^

p4

a« — c.

•J 1 < oc u J E « a. B V) 1 . ■ > >, M -- M & w c 1 i c a ■

E ■il X 0 E a a «A

i CD •

o o

001 xx

12

I I

of B is considerably larger. However, above th? band head, the absorption

coefficient is due to the extreme wings of the lines and is proportional

to pressure. Therefore, in this region Sample C absorbs more than the

lower pressure Sample B, although B has the larger absorber thickness.

On the basis of the equations in the previous section, we expect the

absorption above the band head to be a function of the product (up). In

contrast to this, in regions where most of the absorption is due to nearby

lines, it is nearly independent of p for constant u when p is sufficiently

high to broaden the lines and smooth-out the structure. Thtnlorc, as

seen in Fi^. 1, the increase in p and decrease in u shilt the center of

absorption, although the centers and strengths of all the lines remain

i i xeci.

Figure 2 shows three spectral curves in tht- region of Interest near

3800 cm . Of primary interest is the contribution to the absorption

above 3760 cm by the lines which occur below this wavenumber. It is

apparent from the structure in the curves that several wi-ak bands occur

in the region where tht- absorption by the extreme win«« of tht- distant

lines is being measured. In ordt-r to determine the quantities of interest

we attempted to account lor thr absorption bv the weak, nearbv bands;

the broken curves represent the transmlttan^e that we would expect il the

weak bands were not present. In accounting lor the m .irhy lim s we

Investigated samples covering a wide MMSt of .>reKsures ,ind .mide use ol

the «inference in the pressure dependenct ut tht contributions by the

nearby lines and by the distant lines.

I)

4-1 • p-4

3 (0

i r^ i i i i —i— 4_l

• H •a 0) •o c o •)-l ■l

. .o (TJ

M c

1\

^ o

h

!

H

E

E m 4-' •

2.3

50

7,3

00

»f

the

str

<

b> The

cu

rv

ainple

s:

3 <•

| 0

•J 3 X m4 \c o tfl >*N k.

1 o o c c O «4

h

4-i ri

y c

vC o

11 ^- — i U • 4

i \ ^,,^ M o E X 00 CN -3

i • h —< *-• •»1 Oi

E o

J \ ' E | y

W (T u x: ■

\

ÜJ

2 Q o

50 c

ip4 fj 4/ 4

\ 3 | c •^3 n = -1 - ■ tl • M ! A

\ ^ 4 o M C o

L* fcj «^

. \ 8 ÜJ >

j. E sc

3 ^TJ

a x \ u

— 0> < L •3 u

c nj

N rh ^ ■ O

1- T3

0 c u

X = C "c X • «11

|W

\

\

it «

Ü 3

4-* 1

n t -. -4 <

■ X O 4- \>X « *-*

\ 1 \ \ / )

v. —«

■ E t 3 O 0 *

CD § - i

- B

u

m 0 <t

O X '4- "J

^ .* 0 C

-« ■ 4-. C C

•2 g r 8 O n

K U C t 4-.

<

1 r

^

c : |

- E

■ <

t/.

: . 1 O u

—• a.

0 n X (/

3 O O E i : U^ 1

001 «I

14

I I

I I

i I I I

Absorption by pressure-induced bands exhibit the same pressure

dependence as absorption by extreme wings of lines. Therefore, it is

more difficult to determine the contribution by pressure-induced bands

such as the 22 0 band for which there is evidence between 4040 and

4100 cm in Curve C of Fig. 2. The broken portion of this curve repre-

sents our best estimate of the transmittance without the influence of the

pressure-induced band. It seems unlikely that the contribution by the

pressure-induced band is significantly less than W« have estimated; it

may be an even larger part of the absorption observed in this region.

Therefore, the absorption attributed to the extreme wings of thf distant

lines probably represents a maximum; it seems unlikely that it is

significantly more than our estimatf.

Table 1 contains a listing ol the absorption bands ol interest in the

three spectral regions studied. Part A provides information about the

bands which occur below the band heads and contain the lines whose shapes

are studied. Pan B contains information about the relatively weak bands

which occur in the spectral regions where the absorption coetlicient is

measured. Contributions by these bands are accounted lor in order to

determine the i onlrilml Ion due to the bands listed in Part A.

Curves A and B in KIK. 2 repn s» nt two samples with tin MM CO,

pressure and the MM path length. Ileliun has been added to the (0, in

Sample A to produce a total pressure ol I ♦.<> atm while S.i: ph | contains

enouKh N9 to produce the same total pressure. Sin. t ( urvi I', Mils below

Curve A, it is apparent that i_ is more i Mective than lie as a iorei>;n-

IS

TABLE 1

IDENTIFICATION, POSITIONS, AND STRENGTHS OF BANDS

Part A - provides information about the bands containing the lines whose shapes are studied.

Part B contains information about the relatively weak bands which occur in the spectral regions where the absorption coefficient 1« measured. The contributions by these bands are subtracted from the observed absorption to determine the contribution due to the bands listed in Part A.

BAND

IDENTIFICATION

Gl1 3-«110

00" 3

Part A

BAND CENTER (cm-;)

STRENGTH

(atm"1cm" STP cm

- ' )

7000 (-■III-1 lU'^ion (1.^ ,,}

6935.05 C

6972.49 c

Jhoo

0.00 3 3

0.0083 at '4)1 K

0.041 0.059 at 431 K

cm' Kt'Kion (-'.7 . )

OJ1!-or-o ic/H0. 30 C 2.3

02 1 3612.Hi c 29.0

10 I »714.7h C 44.9

in-oi'o 3723.21 C 3.r)

REMARKS

Band In .ul at R40, h9K8.5b cm-1. Stronnost line, Rib. .it h9H2.94 cm'

Stronufst line, Hlh, ••l 1727.10 cm"1

oiU.oi'o

00° 1

2400 cm-1 Region (4. 3 . )

2336.7 210

2349. i 2700 Mad lund at R122, 2)97,1 cm"1. Strongest 1 itu , Hlh, nt 2 361,5 cm"

Ih

TABLE 1 (Continued)

IDENTIFICATION, POSITIONS, AND STRENGTHS OF BANDS

Part B

BAND IDENTIFICATION

BAND CENTER Ccm-1)

REMARKS

20 I-02n0

I4o0

0I,2-02o0

00o2«-0I10

22o0 PI

04o0 (18)

12 0 (IK)

20o0 (IK)

04o0 (17)

12o0 (17)

20 0 (17)

04n0 PI

04 "0 PI

nw PI

12 "0 PI

20 0 PI

7000 cm'' Region (1.4 u)

No absorption lines were observed between band head and 7100 cm-1.

3800 cm"1 Region (2.7 u)

3814.26 C

3856.72

3980.6

4005.9

4064.0

2400 cm'

Evidence in Curve C, Fig. 2.

Region (4. i . )

2500.4

2614.2

2757.0

2 524.2

2641.1

2775.4

2543.3

2585.1

2670.9

2 760.7

2797.0

(Ih) bands are prominent in Fig. K

(17) bands are expected to be very weak and overlapped by stronger bands. Possible evidence of 20 0 (17) band in Curve B, l-ig. J.

Not observable.

Probably obscured by 12 0 (IK) band.

Evidence in Curve B, Fig, J.

Probably obscured by 20 0 (1M) band.

Probablv obscund bv 12 0 (IK) band.

'Lower level Is OOnQ unless indicated otherwise. (17) and (IM) r« lei to C1 O1 0- and C" 0 0 molecules; othtr bands are C 0* . PI denotes a pressure-Induced band.

Values followed by C are from Courtoy; all others are calculated from energy levels given by Stull, Wyalt. and Plass,

17

broadening gas. Since the bands between 3600 and 3800 cm"1 are consider-

ably stronger than those studied in the 7000 cm"1 region, we have been

able to measure the absorptance much farther from the centers of the

absorbing lines than in the higher-wavenumber region.

The 2400 cm region is shown in Fig. 3. The continuum portion of

the absorption above the band head near 2400 cm"1 is mostly due to the

very strong 00 1 band whose center occurs at 2349.2 cm"1. Most of the

structure above 2400 cm"1 is due to three bands of C1 W8 which arise

from transitions that are forbidden in the symmetric C12016 molecule.

However, these transitions Ar« allowed in the isolopic molecule because

of the asymmetry introduced by the presence of the ()lH atom. The corres-

pond in^ bands of c: 0 0 7 are much weaker since' the. asymmetry of the

molecule is hss and the abundance of the ()17 atom is unlv approximately

one-1 itth thu ot Q h. The contribution by the isolopu bands as well as

I lew pressure-induced bands above 2400 cm"1 were accounted tcr in order

to determine the absorption bv the extreme, win^s oi the strong lines

whose centers occur below .''♦()() un" .

The strenuth ni the Ml band near 2400 em"1 uas taken trom WSH;*

their value is also in |Md agTMMnt with the results ol other workers.

StrePKths ol the bands listed in Part A ol Table 1 tor the ISM u;,"l and

7000 cm • r«gi«M were determined trom spectral curves ot samples at

approximately 13 atn. At this pressure t h. spe.tral lines are suliuientlv

broad, n.el that t h. Mriutur. within t h. band is smoot heel out, an.l t h.

iransmittance- measure.! with the spectron.ter elos.lv approximates the

IH

i 1 1 r

E o

HI c

ja O

v u OJ

3

01 j: H

8 S CM

UJ

m

ÜJ

i 8

8 J 1 I I I

o m J i

HI

8 OJ

3 a

ai i—« a E US

on c

3 O

g -l 0 o

•r-l U-i 00 01 0J I* -C

H o o rn O

00

•o c o a

c

.c

0> CT^ '^

^ a. i ■ CM >

u in

4-« -j ra 4-1 >. c —4 OJ D OJ ■-4 U) U a 0J t F h h « a tn OJ y. M 0

U a. a ^ 1

-t

3^1-1 E

r -

O

001 xi

19

true transmittance. Methods described previously8 were used to determine

the strengths of each of the separate bands in regions of overlapping.

Strengths of individual lines were calculated from the band strengths by

use of the appropriate theoretical expressions.6,7

The half-widths, -, of self-broadened C0„ lines at 1 atm were

assumed to vary with quantum number J according to Fig. 4, which is based

on empirical equations derived by WSB4 from 15 a CO data obtained by

9 Madden. In order to check the validity of Fig. 4, we have used the

curve-of-growth technique to measure the half-widths of several CO lines

in various regions of the spectrum lor values of J less than approximately

25. Our results are generally in good agreement with the curves shown

in Fig. 4. No significant difference in the hall-widths of the lines

having the same J value for different bandi has been observed. We will

show later that our results on shapes of the extreme wings of the lines

are not influenced strongly by modifications in the relationship between

o a and J, particularly for large .1.

The ratios, o^/a^ ot the half-widths of foreign-broadened lines to

those of self-broadened lines are given in Table 2. The ratios for H,

and N2 have been determined as part of the present investigation. The

results lor A, He, and 02 are based on the present N measurements and

ratios given by Hurch, Singleton, and Williams10 lor N,, broadening and

broadening by these gases. Results of quick checks of the relative

broadening abilities agree well with those of BSW. No significant dif-

ferences in the ratios lor a given gas have been observed in the three

different spectral regions«

20

10 01 > kl • 3 in u u

01 u <u 4-i 0 M B IM H

>> X H X) 8 w T3 •^ 3 01 (0 > i i o. & •H ^1 a 01 u •—i m > u i

-a B H ""0 H 'rj

u U) ~E X. W n E 4-t 3 'oa 0 o i*4 f-* X i 4-1 Gu u 3 E X tr 4J 3 o. 01 ra X ». 01 n

t—* B 0

■r-l X

4-1 •H 1 H i 4->

■ 3 IN , <u er <t X c 0) ^3 o u

• r^ • o E f—* —^ B 19 n 01 o b

IN u •a X O •H ■a 1 u U 1

T. 0.

■v & i <u >, E X B V X 4J |

T3 M ■a 10 E 19 B 01 4-4

0 •-< B . —i h 3 ■p4 o *~ 1

xi 0 rj 1 i E i r-* 4-1 ü

U-i i-H X ^-1 0 0 a m

<U U-i X E e w ID 01 u 4-1 T! O (*-( X ■ IN E 0 4-1 •a "< C

0 (/) c g O • 0 0

h 1 X u

x: -a IM E — 4-i i) o rj OJ XJ « -a in u E

X 3 1! B O 3 i

x i o SS w

't-d 0) - + 19 *-* u 4-1 01 '0 11) 'J X 0J X

n "0 4-1 3

1 0J 1 ^v E i X B ^-^ •H o N 'J 0) 1 in

■w c m E »—< m u »—i / IT! u -o E X E 0 H i "^ E n! 0 0 *": U

Sr. 1 > 0

i- o u. 4-,

(..UiO),,^

21

TABLE 2

RELATIVE HALF-WIDTHS OF C09 LINES BROADENED BY VARIOUS CASES

Broack-niriK Gaa

O ) o

s CO.,

co2 1.00

H2 0.81

A 0. b 5

IK' 0.49

Ü, O.hH

ll2 1.17

-

22

• >

I I I

Figure 5 contains portions of four speitrai curves which illustrate

the technique used to determine the ratio of foreign broadening to self

broadening. Curve A represents a sample ol pure CO with the pressure and

path length indicated. After obtaining Curve A, the path length ol the

multiple-pass absorption cell was changed to approximately four times its

original length, and the C02 pressure was adjusted to provide the same

absorber thickness as lor Sample A. Nitrogen was then adiled to the sample,

and spectral curves B, C, and I) were scanned with the sample at the total

pressures indicated. We note that Curves A and C are nearly coincident

near the centers of the lines, while D approximates A n.ar the transmittance

maxima between the lines. Since the spectral slltwidths and absorber

thicknesses are the same lor all the samples, we conclude that the shapes

ol the N2-broadrneH linos are ditierent from those ot the seii-broadened

lines as close as 0.9 cm" to the line centers. (Two lines are s.u-i to

have the same shape il l( , .-.^ (Eq. (j)) is the same at all (- ) when

the pressures are adjusted so that the hall-widths are equal.) Tin r.suits

discussed in I ol lowing sections make it char that N,-broadened lines

have quite different shapes from sei I-broadened lines when ( - ) is more o

than a lew cm ; however, the method used to obtain those results is not

applicable lor ( - o) l«M than approximately } cm'1. ih.nlore, the

method indicated by Ki*. S can provide additional imormation about I he

shapes ol lines nearer their centers. Because ot the unite spe.tral

slitwidtli ot the spectrometer, the true shapes ol the lim s c.innot be

determined near the enters where the t ransmi t lance ili.iiu.es rapi.llv with

wavenumber.

23

1 r. ■ •- I I

I

■o

o 001 Xi

I

■

~ - i-

3

-

I •

*

.

— - -t -

Since the half-widths of the lines shown In Flg. 3 are considerably

less than the spectral slitwldth of the spectrometer, we cannot determine

the half-widths directly from the curves. However, we can determine the

o / o ratio (^ Id If we assume that the shapes of the N -broadened and self-

broadened lines are similar over a region near their centers that is

comparable to the spectral slitwldth. Since Curve C nearly matches Curve A

near the line centers, we assume that the half-widths of the lines are the

same for the corresponding samples since the absorber thicknesses and

spectral slltwldths are identical. Therefore, -„ /- can be determined 'Ms

by use of the following equation:

„(A) n(C) (C) o / o P P PN2 'N/'S' WJ

where the superscripts (A) and (C) refer to the correspondinK samples, and

p and p are the CO and N- pressures, respectively. By substituting tlM

appropriate pressures into Kq. (12) for several sets of measurements, we

have determined that ■ l O.MJ - O.Oh. This value compares favorably

♦• 11 wit» 0.75 - 0.04 obtained by Patty, Manning, and Card—K with a CO., laser

as a radiation source. The measurements of Patty et al repr»sent the

absorption at the center ot the P20 line of the 10 IMN 1 band. Since

our value represents an average over the region within 0.J - ().J cm oi

the center, any difference in the shapes of the N^-broademil ami sell-

broadened lines within this interval would produce a dttference between

our results and those ol Patty et al.

25

From the portions of the curves between the lines, we can show that

N2 broadening is only approximately 0.77 times as effective as self broaden-

ing; i.e., the absorption coefficients are identical when the pressure of

a pure CO^ sample is 0.77 times the pressure of a very dilute mixture of

C02 in N2. This is approximately 77 less than the value 0.83 obtained

near the line centers. Although this difference is small, we believe it

is significant sinct- results consistent with Fig. 5 were observed in dif-

ferent spectral regions and ior a variety ot samples. Hurch, Singleton,

and Williams have measured the ratio of N broadening to self broadening

ol C02 lines with a spectrometer having low enough resolution that the

Individual lines were not resolved. Since most of their samples produced

considerable., absorption, thev were nearly opaque near the line centers

and most ol tin increase in absorptance due to increasing pressure occurred

near the absorptance minima between the lines. It is, therctore, not

surprising that their value, 0.7/ - 0,05, for the ratio ol the broadening

abilities agrees with the 0.77 obtained in the r.resent investigation lor

the regions near the absorptance minima.

2h

NORMALIZED ABSORPTION COEFFICIENTS

i i I I

Curves of the normalizetl absorption coef tic lent« have bten obtained

tor several broadeninn «ases by substituting; into Eq. (11) values oi

transmittance from curve« which represent samples coverinK verv wide

ranges of absorber thickness and pressure. Pigim I shows K , th«

normalized absorption coefficient lor CO self broadeniiiK in the 7000 cm

rcKlon. The solid curve represents the experimenlnl results, and the

various geometrical symbols represent data from samples at dillerent

pressures. We note that throuKhoul the rewion Irom 7010 to 70M) cm

there is very good agreement between results obtained Irom samples whose

pressures vary trom less than 2 atm to approximatilv IS atm. This result

confirms the assumption that the absorption (.oeliicitnt is proportional

to pressure when ( - ) " as indicated by Eqs. (10) and (11).

The upper curve in Pig« '> represents values ol K calculated by

assuminn that all o( tin lines have the Lorentz line shape. The lower

27

1>

■

3 O -

>

H

•I

c c

•a

« — x l

M M .* Q 4» <» 3 O H 3 V w .. C

"' —i ■ ■ i i... "•."•.—; 1 « «0 K a) L • I i 2 O o o

I _(dlSUU0 UUP) s>j

c

«I

3t c •«4

c 41

•o o

o tj

3 « i a« >

o /.

ig . w j, 0 O w u

1 § I a

— b

0 1 * x

I ■ x I " X

B •st C in

> c ig 4, X l/l

I » k. 1 a -^ «,

0 3 *•> u

■g N: § i & M 1 ac '■■> O

«i «i B -o i« 4, ^ w C

-4 "O 3 C B <«

-^ x I U >-4

o A O I 0 ■ x i w i a u 3« O b <M

l< t > X u u 3 B

X

— c -

•o c

• c V IB O- E IB u X I in >

-I (/) C

O u -j a< ■ ■ c X ■•• ■ i u

3 •J w > X

u 4< U 3 ■

\ <3

X T3 C

•n 3 * O c -

a w <B

X X

c c

•o

IB l>

X

1 c IB X

X

I -

§ - s ■ IB "

o

.-

1

I I

curve represents calculated values based on the modified line shape

derived by WSB from absorption measurements in 'Ke 2400 cm region

(4.3 n band). It is apparent trom these curves that the absorption lines

In the 7000 cm region are sub-Lorentzian, but their wiriKS are consider-

ably stronger than the lines in the 2400 cm region. The shapes ol the

absorption lines in the different spectral regions are compared in more

detail below.

Figure 7 shows similar results for broadening by Hk and N0 with a

portion of the C02 curve from the previous figure repeated tor comparison.

We note that at 7010 cm , K is only approximately one-tenth as great

for N2 as for self broadening. From this result it is apparent that the

absorption by the wings of ^-broadened lines is much K;,* than that by

self-broadened lines. We also see that the wings of the He-broadened

lines are even less absorbing than N -broadened ones. Since K° and

o K are so small, we were able to measure these quantities onlv over the

2 spectral regions indicated.

A few measurements on broadening by A, 0,,, ami M, were also made in

this region. I'pon redueiiiK tin data, we found that t h. results were not

as consistent as those for N and He; thereiore, tluv have not been

included in Fig. 7. However, values of K° agreed to within 10 or Ml 2

percent with corresponding values ol K" Similarlv, v.ilm s lor A .ind

02 apparently a«ree with those for N, to within approximately tin same

accuracy. Broadening bv A, 0,,, and H, in other speitr.il rcgiOM is

discussed below.

29

r

|H M I I I 1 |llll I I |—I |ll| | |

O o

c 10

o eh

c

■ u 5

• c o IK

•*4 u m a E o u u O

«

c

.^^UJD UJiD)0>|

^ £

C O

O a

■o

T3 ■ C a ■

r. x:

r - o

•t c — o

■ o Q.

■3 ■-' v <? C £ O ^i «J

X «5 /. 0 I

'— k- »j

li U (fi ••- wi

-• t; | c

o I

"3 I

M ■

£ H

JU

Figure 8 shows the results for self broadening and N. broadening in

the 3800 cm' region. We recall from Fig. 2 that several weak bands in

the region of Interest had to be accounted for before we could determine

the contribution by the lines below 3760 cm . Reliable measurements were

limited to wavenumbers where the contribution by the weak, nearby bands

was considerably smaller than that by the distant lines. We have assumed

that K0 can be represented by a smooth curve drawn through the data points.

As pointed out in the discussion of Fig. 2 the portion o». the absorplance

between approximately 4000 and UOO cm that we have attributed to the

extreme wings of the strong lines probably represents a maximum. There-

fore, the curve In Fig. 8 also is believed to represent maximum values

throughout the same region. Values of KN could not be determined above Mm

-1 ' 3900 cm since the additional absorplance due to liunasinn the N,,

pressure in CO- + N mixtures was too small to measure.

o -1 Plots of K versus . In the 3800 cm reKion are shown tor various

broadening gases In Fig. 9. The curves corresponding to N,, 0,, iiml A

are close to each other near khe band head, as they are near 7000 cm

Also, as In the 7000 cm region, values represenU-d by the He curvi- are

only approximately one-tenth those represented by the sei I-broadeniiiK

curve. Data on H,; broadeninK are limited to the region between J770 ;iinl

3780 cm where the ah orpl ion by the 00. lines is larg« «.ompared to the

absorption by an H,, pressure-induced band. At higher wavenumbers t he

absorption by the II, band is too larne to be tCCOWItwl lor .uiuialely.

il

H'll I I I 1111111 I I jlllll | ' | mm i - '—fTTTTT

b o t

o To

c o IA •w U 0* n 01 £ 3 £ w X « c i ■ hi OJ c V M V 0> T3 c J3 > «0 I ■0 E U (A

«0 3

(A | JC <■) s

J: fl! o m

1 (fl tt E u u c <J C u I •#•4 u ■ o 0 IN

o —< a o

0. vt n V ♦J OJ u ■o m £

c ■o 4N

»i <B V c c > Q 0 •tN

IN X 3 p^ •o tA u rn 0*

(A O V C w E £ V J3 h H

3 ■ 0/

4J E • • 01 nj — «4 X- X ^^* i U) ---<

B E «j 0* IA 1 B 01 > (A p e u o H o —* 3 a ^ o —4 o

M '*- o: vt 01 1 o

^U T3 4-1 H ■ ^n C (A «pj AS *4-< 3 ^5 o • flj

ID a c C

u 0) •

Z o •r4

1 •P4

CO -4 1

ÜJ *-» u E

^ C ■ 3

U3 '»4 IM

• u

1 V •■-I U4 —4 B s b 0» <0 3 il 4J o E T- 0 c u (A (»1 X o

u c (A 01 50 o ••-4 > e ■ -H C

•H JC u (A X. c w a ■ «J 1 L c

T3 • » O •^4 o rj - -< (A ^-i oc o i .a u E e « ^. i

J3 o u

(N o E B M ■ ao > «* .^ r» b

T) r^ Oi H C •X >^ > HJ U JO X IN

o o 3 IM i-4 C u ^N 1 1 0

01 X JC •••4 o (fl «4 || X (« a w l- 0) p u 0 c Q o e

IM •-4 H I •M •—* '»4 x

0 ^t ^ M ■ T; «-*

£ I o c 4-t w £ —1

• o 4J ^3 X o ra |i

M E O IN 1 w u '-<

c a» £• 1 U HN 3 '_ X 1 fe "U ■ ^ a

I (diSUJ0 US\Ü)\\

32

I

•

^(^IJUO ujp)0>j

33

c (0

o

c o

y o

E U

o

00

-a ■

b

c •H c

■o

0

c

_ e

a E 0

■a | — 3

C 111 « 3 u it

^2

C | -a

u c

■ OJ c

o u

a u o m

4 ^^ .K -o y j W c 01 B H X ■^i

L| E V 0

k II £ H] o 3 01

m 3 O

•--l N ifl >

0

u:

10

c o •H 00 01 h

o

-a

H

a b o in

to -C

I u

00

c 10

I I

Figure 10 contains the curves of K in the 2400 cm region for C0?,

N„, and A. As in the 3800 cm region, the N9 and A curves are nearly

coincident near the band head. However, at higher wavenumbers, these two

curves diverge, with the N curve occurring above the one corresponding

to A. Also, as in the 3800 cm region, the N- curve approaches the CO

curve when the distance from the edge of the absorption b."nd is approxi-

mately 100-150 cm . The portion of the absorption due to the nearby bands

is ioo large to be accounted for accurately above 2570 cm . However,

from Curve B of Fig. 3, we can set upp«r limits on K of approximately

-8 -1 -1 -9 -1 5 x 10 (atm cm ) at 2710 cm and 5 x 10 ' (atm cm ) at

2830 cm'1.

I I I

..

34

I I I I

1

I

H 10

f E O

o

!400 2500 2580

WAVENUMBER IN CM x

FIG, 10. K for C02, $ , and A in the 2400 cm" region, The curves

represent the contribution of lines below 2400 cm* . Above 2570 tin''

it is difficult to account lor the contribution ol the nearby bands;

however, from Curve B of Fig, 3, we can set

Vrp

upper limits on K of -8-9 Is

5 x 10 and 5 x 10 ' (atra cmemw) at 2710 and 28J0 cm . respectively

35

CURVES OF X VS (VV ) o

Curves of* versus (v-.o) for several dlff«r«ttl l-roacUn i n« /ases are

shown in rtgl. il-14 lor the three dillerenl spectral regions investiKaled.

The curves have been derived 1rom experimental values oi K0 by tlM trial-

and-error method described previously. In most cases, values 01 k" calcu-

lated by substituting values I rom the \ curves into Bq. (11) av;ree with

the experimental values ol K0 to within two or three pei.enl. Plgur« 11

shows curves for sell broadening in the 7000 cm"1 rogiOO. Curve A

represents samples at room temperature, 296 K. while Curvis | and (

correspond to samples at 451 K. We had to assume values lor the hall-widlhs

of the lines at 431 K since this quantity was not measure.I. Curve | was

obtained Ironi the 431 K data by assuming that the hall-Udths ot t he

sell-broadened absorption lines vary inversely with temperature when the

pressure is kept constant. Curve C was derived iron, the same data as

Curve B, but the normal i/.ed half-widths were assumed to vary inversely as

the square-root ol the temperature.

36

I I I

s 3

o c H fl o

1- w ■ •o 01 •- •o 41 a 3 I 10 E o «0 a» >, c A *J — I 4i ■ IA 4* « u •H «J h< u 3 4» o ■ d > I O C

a» •-• i • ja > u t >, i r fa 3 f*4 X <o ■ w >

**4 u 3 (A 1 o X Q. *^ >. w ■ p4 "O 3 1 « 3 ■ 0 u 1 X a 4« w- H (A > ^ o •

4« fa

C fl

o •*< 0 Q - X

fl3 ^ M ■ o p

i- 1 ■ 3 i

^—N, ■4

i 1 c

••4 —

| I ec — X 1 o <« -

IT.

> -3 U 1 — c — o r^

U 3

1 c ■3 a

"^■^ U IB «9

o u ■

M • X —

^0 C

■ü 0 ■C

1 •- u it

1 ■ 1

^J 1 w c

^

C

—4

• II E

« 1 O w

o P^ 3 w

V. c X 0

ID 2 «0 fa V

•a ~3 a 3-1- ii E 1 C U C s ~ — 3 1 •-f —rf fQ W

"3 !3 w O 1« 1 X C U 0 'S 4< fa o i) <t CL

1 E X E p

'•-■ w IA W m^ <« *j «4 | | •" | - X v O

fa «5 3 wi 0 F fif

IM V,

0 ^. 0 «« # fa

y C

, E fa

5 - to p4 ir 1A X 3 P4 u

3 • ■ c U «B k • t

D - E

XXX M 9 M

o

t

Figure 12 shows the curves of \ versus (v-v ) for broadening by He,

C09, and N at room temperature and by N at 431JK. Calculated values

o cf K are only slightly dependent on the values ol X assumed for very

small and for large (v-. ). Tht-refore, the uncertainty of the end portions

of the curves of \ is greater than for the center portion. The regions

between the vertical dashed lines in Figs. 11-14 are probably accurate

to - 10 to 20 percent; outside the interval bounded by the lines, the

uncertainty may be considerably greater. Lines in all three spectral

. i

regions were assume«! to he Lorentzian (\ 1) when ( - ) • i cm lor o

sell broadening and when (.- ) < 0.5 cm lor loreign-gas broadening.

Figure li contains curves oi v versus (.-. ) lor sell broadening

and broadening by N and A in tin IMP m region. Since measurements

were made over a wider spectral r«giM tor pure 00. th.m lor mixtures,

the CO curve extends to larger ( - ) th.in do the otlur curves. W» / o

recall that tlu K cu ve in Fig. « is believed to represeiU maximum

values above jWO Lm . Siiut ■ lor ( - ) ureater th.m anproxim.Uelv o

200 ca is strongly dep.ndint upon K0 lor the I900»4t00 Oi" region,

the curve of "- lor (,- ) between 200 and 400 cm also prob.iblv repre-

sents maximum v.ihus ol this quantity, Figur« I ^ shows the turves oi •

for CO^, N , and A lor the 2400 cm region. The cinrv« lor sil I bro.iileninn

compan-s i.ivoribly with th< an.il vt ic.il cxpnssion |iv«n hv MSB lor the

same quant ity.

M I I

I I I ii 11 i i i—r ii i i i i i—r

u J 1 l_i_J L

o

LO

CVJ I

O

E

i

at c

c IT. o u

o E

> w 3 'J

«

C o

u

o o c

—< u ■ o b i -3 > I c -o — 3 >* u

C

C K I

III

-a i

u. c

it > u 3 o

-J O (J

c n -C — E «-

E | 0 '~ X c o

V II G C .JZ o «B «-' •-*

r< (5 0 sr x c

O 0 0 -

c

—

o u X !/. I c

u 0

a i-

If. «0

■

I ■/,

X

-

E

B B

u - 3 cr /

- J —'

c o •y.

u D.

O

I I I

r

i H 1 L

— i

e § OC M .

M | C £ O u -p

«1 c y

•«- c •** M O

X u T3 >, C -. fl —

»8 n «i <«-^ | w

M X C 1 1 E o O 1

—i —

•> o < u

^ 1 ■ i ri w.

& • N a o 3

D < >.

JO T3 c

T3 1 ■ C r 1 O

•P «i H 0 X u w £

■/. —

ft 1 C E

—• J —J

O V- '1 0 —

— o

.u

I I I

IN i i i i—r ["iii i i—| 111 ii i i ■]—r

E u

i

.1 G

CN

U 0

c u.

w

Before discussing further the results shown in Fins. 11-14, we will

consider some of the factors that influence the shapes of these curves.

Since all of the curves are based on half-widths given by Fig. 4, it is

of interest to determine how the X curves would be changed if we assumed

different values for the normalized hall-w.dths ol the absorption lines.

The solid curves in Fig. Ir) are the same as the corresponding curves lor

self broadening shown in Figs. 11 and b. The plus signs represent calcu-

lated values of K which are based on values of X given by the upper panel

and on line widths I rom Fi^;. 4. The squares plotted in the lower panel of

Fig. 15 correspond to calculated values ol K hased on the solid X curve

in the upper panel and on lines whose normalized half-widths, , are s

0.092 cm , the mean value based on the curves ol Fig. 4. Hi note that

the squares deviate signitleantly Irom the plus ligni only in the region

near the band head sinci a BigaiflcMl p.ul ot t hi .ihsorpt ion lu.ir tin

band head is due to nearby lines whose hal I-wiilt lis wt re assumed to be

approximately O.OM cm when calculating I be values representi I by plus

signs. A good portion ol the absorption in tins region is also due to the

much stronger lines. I " 10 to I " 20, whnh are « or > Oi* below the

band head. However, luvond approximately 1r) cm I rom the band head,

nearlv all ol the absorption is due to tbe Itroogcf lines whose ball-

widths art approximatelv the sain lor both .. a h ul.it ions.

Tbe broken portion ol tin curve in t lu upper panal Ol Fii;. I'j

represents the modiIii at ion in the ) eurve that is required to provide

agreement with the experimental values ol K il we assume that

.J

I I

X

10 -5

icr6i-

V icr7

10 -8 7000 7050 7100

\AAVENUMBER (cm'1)

FIC. 13. Intlucm« ol nssumcd lin«' wirlth on calculated CUfVCI

oi \(.-. ) nd K (v) in th«- /ooo sm region« Hi« curv< Ln th.

lowtr p;int I ri'prrs«nts I hi rxpor imi'nt nl n suits lor K < ). Thi

► •■ represent ihv v.ilues calculated on tlM basil ol lines whos.

X Is niven by the solid curve in the upper p.ini 1 iin<l whose li.iit-

widlhs arc |lVM hy Ki«. 4. ih« I- '• r» presi nt v.ilms calculated

on the basis of the s.ime "■ but with (».f)'».' lor .ill lines.

Values of K (.) based on lines with 0.042 ca and ■ Mldified s accpr«IinK to tke tlashetl curve agree with t h« < >;p« i ivient .il < urve

to within - 2 percent.

4J

o -1 a9 0.092 cm for all of the lines. The effect on the X curve for other

modifications in the values of r can be inferred from this curve. If all

values of ^ were increased by 107, for example, the carve of X would, of

course, be shifted down by the same factor.

We see from Table 2 that the band head in the 7000 cm"1 region occurs

at R40, which is only 5.6 cm" from Rib, the strongest line in the band.

By comparison the band head in the 2400 cm" rtgion occurs at R122 which

is more than 35 cm from llu strongest line Therefore, many weak lines

of high ,1 value contribute significantly to the absorption a lew cm'1

above the 2 597 cm band head since they are much closer than the strong

lines. Consequently, the shapes of the "■ curves lor the J4()() cm" region

are probably more dependent th.in the one lor the 700(1 cm'1 region upon the

hall-widths , ssumed 'or hiKh .) lines. Ihis is also true lor llu MOO on"1

region since the strongest lines are several cm" irom the region where

K has been ■•Mitred* s

The curves in !'ig. lb provide information about the ilependence ol

tin calculated values ol K on . (om-erselv, it also shows the variations

introduced in the curves ol > by errors or chMgM in the values ol K0

which are being matched. Curv.- A in the low. r panel oi lig. lh thtmt the

experimentally determined curv.' ol K" , whuh also app. a I n Kig. B lor

th. 1000 cm region. The circles in the lov.r panel whith lit the experi-

mental curve very Well lepr. •-. nt t lie valu.s ol K° caKulated on t h.

basis of the N curve «iven by A in t li. upper panel. Curve | in t h.

upper panel repr.sints | modiiication ol a portion ol Curve A In, ( - )

44

10"'EA

lO"2

IQ" 100 200

f-V.fenr) 300

i—i i i,

3800 3850

WAVENUMBTR (cm')

3900

FT«:. lh. Curvs of •> and K^ showing Indu.n, r ol .Tssum. ,1 lino

fihnpc on Ihr c .il, ul flted absofption cMfftctwM in tlM MQO . m''

r.'Kion. Curvr A in MM low.r p.tn.l t .pr.s.n. s . h.. .xprr i.mnt ..I

r.Milts lor KN . Thr ctrclM r.'pr.'s.-nl th». valu.s C«le«Ut«l on

Ihr I... is of a'line shapo whosr V !„ Klv<.n l)y rurV(1 A JM , h(

upp.r pantl. Varlallons in l hf I i n«. sh.ipr Riv.n l-v Curves H. C,

P. .ind K in Ihr upp.r pan.-l MMT« assum.-.l, «ml I hr . or rrspoml i n«

MlCMUt«^ curves of K° an shown in th,- low.r p.-.n.l. 1 h. six

vrtical lin.s f., ihr l^w. r panel In.licnt,. Ihr wav.numb.rs at which

••xprr imental mcasurcmrnt s MM made.

Ub

r

' 60 cm ; Curve B In the lower panel represents the resulting calculated

values of K . We see that the modification to lh>' line shape for (v-v ) Mm O

leBu then 5 and 60 cm produces only a relatively small change In the

calculated values of K° between 3770 and 3780 cm" . Krom this result we 2

conclude that much of the absorption in this region is due to lines more

than 60 cm away, although many lines -»ccur within this distance. Above

-I 3800 cm the modification represented by Curve B in tin upper panel

provides no ■Ignificant chanue in the K curve.

Similarly, the curves marked "C" in both panels of Fig. lh indicate

the influence ot I f|uitc different modi i icat ion to the Y curve lor ( - ) o

• 60 cm . Ot course, mod i I ic.it ions li and (' do not affect the calculated

. o - j values ol K^ more than 60 cm above the lughest-wavtnumber lines being

considered. The rather major ciuinge Indicated by Curve C provides a

sizable change in the calculated values ot K° between i77() and )7H() c«

since the relative contribution ol 1 hi ne.irbv, weak lines is increased.

The C curves are based on a Lorentl line shape lor ( - ) ■ l() cm with 0 —

I sudden decrease in the absorption coefficient as ( •■ ) increases. 1 he

quite lignificent difference between curves A ami c in tin lower panel ol

fig» lb is evidence thai ll.>broadened linei arc lub^Lorentsian within

l" CM ol tlu i r centers.

The modification represented by curve D for 60 cm* • ( - ) ■ ISO cm* o

is seen to Influence the calculated values ol K fron epproximately i790

-1 H2 to 1880 cm , K'e believe that the difference between Curvei A and D in

the lower panel is less than the uncertaint) oi tin evp.r iment.il K"

46

values obtained in this region. Curve E illustrates the effect of quite

a large change in X for large tv-V#>. We see that the calculated values

o -1 of K^ below 3800 cm are not influenced significantly by this modifica-

tion, indicating that most of the absorption in this region is due to

lines within 60 cm

We see from Fig. 16 that errors of 15 or 20 percent in the values of

KN might cause a significant change in the shape of the resulting curve

of X, although X at any value of (v-vo) might not be changed greatly. For

example, if the measured values of K^ fell on Curve B at 3770 and J780 cm'1

-I2

and on Curve D at 3815 and 3850 cm , the corresponding X curve would fall

on Curve I in the upper panel for (v-v ) • 60 cm"1 and on Curve D for

60 < (v-Vo) ■ 150 cm" . Beyond (v-vO 150 cm"1, the derived curve would

fall on the existing Curve A. Thus, relatively small errors in the

measurement of K° may cause quite a difference in the shape ol the X

curve. Therefore, we must be careful not to place too much significance

on the shape of the X curve, although the KVcrage value of the curve over

relatively wide ranges can he considered reasonably accurate.

We will now return to a discussion of the results shown in Flgt, 11-14.

In Curve A ot Fig, 11, which represents self broadening ol CO in the

7000 cm ' region, X appears to reach a minimum when (.- ) ^ 1.' cm"1 and o

to increase slightly before attaining I maxiniuin at epproxlmately 60 cm"1.

In view of the discussion of Fig. 16, we conclude, that the minimum near

12 cm and the maximum near 60 cm" may or may not be reel. However it

is signiticant that the average X throughout this region is between 0.5

and O.d.

o

4 7

According to the simple, classical theory, the half-width of a

collision-broadened line is proportional to collision frequency and,

therefore, inversely proportional to the square-root of temperature, 9,

-1/2 if the pressure is constant. This 0 ' dependence is usually regarded

as approximately correct for foreign broadening; however, various experi-

mental and theoretical results indicate that for self-broadening the

dependence on temperature may be as strong as 0

Curves B and C of Fig. 11 show the N functions we obtained by

— 1 -1 /? assuming a 0 and 0 " dependence of 1 . The Influence of temperature

s '

on line strengths was accounted for in the calculations. Values on

Curve B, which corresponds to a 0 dependence, an- only about 0,6 as

large as the room temperacurc values (Curve A) for the same (v-V ). If o

a weaker temperature dependence is assumed, the deviation Irani Curve A

is even greater. Thus, it is apparent that increasing temperature changes

the line shapes witli a marked decrease in the extreme wingB,

The curve corresponding to N at 43l0K in Fig. 12 also falls well

below the room temperature curve. The Vil'K curve is based on the 0 '2

. , . o -1 dependence ol . No curve corresponding to the 8 ' relationship is shown

for N2 broadening, since this relationship is expected to apply to sell"

broadening only. Because of turbulence in the samples at high pressure and

431°K, we were limited to somewhat smaller samples than at room temperature,

Consequently, we could not make reliable measurements &e far above the

band head at the elevated temperature, and the > curves are limited to

smaller (v-. ). o

48

I I 1

Ife

i I I

A few measurements at elevated temperatures were made in the 3800 cm

region. However, the absorption by the nearby weak bands increased so

rapidly with increasing temperature that the contribution by the extreme

wings of the distant lines could not be measured accurately. Most of the

lower energy levels involved in the weak bands above 3760 cm are excited,

so that their populations, and, in turn, the band strengths increase with

increasing temperature. However, in spite of the increased absorption by

the weak bands, the absorption near 3850 and 3900 cm' remained approxi-

mately constant. From this result we concluded that the absorption by the

extreme wings of the strong lines decreased with increasing temperature,

as in the 7000 cm region.

We note that the N2 curve in Fig. 12 drops very rapidly to approxi-

mately 0.06 at (V-V ) 25 cm . In accordance with the discussion of

Fig. 5, we have assumed that the Lorentz line shape was valid (X 1) for

N2 for (v-Vo) < 0.5. Our results do not enable us to determine reliably

the curves of X for 0.5 « CwJ < 3 cm" , and conversely, our calculated

values of K are relatively insensitive to the values of > assumed for

this region. However, it is apparent from our data that X is as low as

approximately 0.3 for (v-v ) 5 cm' . Although the curve lor sell

broadening is sub-Lorentzian, it does not decrease as quickly as the curve

corresponding to N,, broadening. The He curve decreases even faster than

the N curve, reaching approximately 0.08 for (■,-'. ) 5 cm" . Both the z o

He and N9 curves appear to have an approximatelylevel portion after the

first sudden decrease, although these level portions do not cover as large

49

a range of values of (v-v ) as does the level portion of the self-broadening o

curve. Evidence for the large difference between the wings of He- and

N -broadened lines was mentioned in the discussion of Fig. 2.

As in the 7000 cm region, the N? curve falls well below the self-

broadening curve for the 3800 cm region in Fig. 13. However, the two

curves tend to approach each other for very large (v-v ). This phenomenon

was not observable in the 7000 cm region, possibly because N9 measurements

could not be made for sufficiently large (v-v ). The curves for A, 0 , and

N„ are similar for (v-v ) • 100 cm , but for larger values the N„ curve I o I

falls above the other two. Also, as in the 7000 cm region, the He curve

falls well below the N„ curve and is similar to the K. curve, which is

based on limited data. Thus, H,,, which is a relatively efficient broadener

near the line centers (Table 2), is verv inefficient 'or (.-. ) more than o

a few cm

Figure 14 contains similar curves lor the 2400 cm region. As in the

7000 cm the N curve ialls considerably below the CO., curve then approaches

it as (v-v ) increases. The apparent crossing ol these two curves near

(v-v ) 230 cm may not be signiticant because of the large uncertainty

in the curves near and beyond the crossing point. However, the sudden

increase and the gradual decrease in the separation ot the CO and N9

curves is probably significant. The relative shapes of the N9 and A curves

are also similar in the JK0O and 2400 cm regions. Ihe A curve lies above

the N curve throughout most of ' !■ region for ( -, ) • 90 cm , but bevond

this point their jositions are reversed.

SO

I 5

I I

I

I

I i

i

i

It is of Interest that the curves corresponding to the two light

molecules, He and H_, are similar and both are quite different from those

representing the heavier molecules. The broadening by these two gases

appears to be similar in the extreme wings, although H2 is a diatomic

molecule and He is monatomic. It is apparent from the great divergence

of the X curves corresponding to the various gasts that the mechanism

involved in the broadening of lines several cm from their centers is

quite different from the mechanism producing the broadening near the centers.

The broadening of the extreme wings is more strongly dependent upon the

broadening gas.

The results for He and H suggest that broadening in the extreme

wings may result from collisions with relatively slow-tnovinv molecules

since the number of slow H- and He molecules is much less than lor heavier

molecules at the same temperature. Further support lor this sugnt'Stion is

provided by the decrease in absorption by the wings oi the lints as the

temperature increeses and the nui.iber of slow-moving molecules dein.ises.

Of course, there are insufficient data lure to prove conclusively thiil the

extreme wings are due to collisions with slow molecules; however, the

widely accepted belief that they result trom the very hard collisions does

not appear to be justified. II broadening in the extreme wings is, in

fact, due to slow molecules, the amount of broadening may depend strt ,>;ly

i on the amount ol tine the two colliding molecules remain within a certain

. distance, rather than on the distance 01 closest approach.

I I I

H

Argon was investigated s'nce it is monatomic and heavier than either

N2 0r 02* In vlew of it8 fl"1'6 different physical characteristics, it is

surprising that its hehavior as a broadening gas is so similar to that of

02. Since the molecular weight of A is approximately the same as that of

C02, it is apparent that the broadening mechanism in the extreme wings

cannot be explained by the molecular weights alone. It is well known12

that the half-widths of lines depend on the dipole and quadrupole moments

of the colliding molecules, so that a knowledge ol th. masses and shapes

of the molecules is not sufficient to predict the broadening characteristics.

However, most ol the present theories deal with half-widths ; nd shapes ne.-.r

line centers; very little work has dealt with thr shapes 01 the extreme

wings.

In order to compare the shapes of the lines in the ditierenl spectral

renlons and to show tlM line shapes lor sever.il diffcTMl broadening gases.

we have constructed the curves in Figs. 17 and lH. The quantllv k is ma x

the absorption coefficient at the center ol | Lorenl/ line with 0.1 cm"1.

which Is typical o! | sei I-broadened CO^, lim at slightly more than I atm.

Log-log plots have been used in order to represent the UNTMU shape by a

straight line when (vv#) X . Kach decade has been made twice as Ion«

on the abscissa as on the Ordinate so that the curves are not as steep as

they would be otherwise. Fach curve was obtained by multiplying the

Lorcntz curve by the appropriate value of • fron» Ptg«, 11, 1J. .md U.

Figure 17 shows the- ratio k/k^ plotted versus (.- J for sei I-broadened

lines in the three spectral regions indicated. Mt see that the curves

52

f max

10-3

IQ"4

10-5

10-6

10-7

10-8

IO-9

lO-K)

^ SELF

\\N BROADENING

^ N\^\r 7000 7000 N\V

_ (43i'K) \^V \ LORENTZ

10 100

p-U (cm-') FTC. 17. Ratio k/k vorsus (.-, ) for sol t-broatlcnnl

max o lint-s In thriT spinlral nylons. Th«- turves corrcsporul

to a Lort-ntz line ind to lines in the wavenumh» r regions

imliiat eil. The absorption coefliiient at the tenter of

a Lorent/. line with 1 0.1 cm is represented by k

The curve which represents a sample at -• U "K is based on

a line whose strength is the same at 4 U ^K as at ^SJb'K

with k equal to the absorption coeffitient at the max

center ot the line when the sample is at 29h*K.

51

I I 1

10-3

lO"»

10-5

N2 \\ \ BROADENING

7000

Ar '

Nv\v BROADENING

k max

t IS 10-6 (- 7000 \s (43I0K)

10-7

10-8

10-9

lO-'O 10

v-Po (cm-1) *'-H (cm-' )

flQ, 18. Ratio k'k^^ versus (v-V0) tor N,- «ad A-hrondcn. .1 li.us in

three spettr.il rewions. The curves corr. sporn! to a Lor.nt/. lin, ..ml to

lines in the w.ivenumber regions indicated. k is the ■bMrvtioa max i i «ii

coefficient at the center ol a Lorentz line with 0.1 en

Preceding page blank

i

r

the order of increasing wavenumber. This phenomenon may be based on the

ratio of the period 01 the electromagnetic waves to the time the collidinK

molecules are within a certain distance.

,h

INFLUENCE OF * ON CALCrLATEI) LINE STRENCTH

It is apparent that if X is l(?ss than unitv lor all ( - ), Ea. (4) o

cannot he satisfied exactly, ami the line strenWth S «iven hy Eq. (r)) will

depeml on pressure and on the hroadenin« «as. Experience has shown us

that line strengths are not functions ot pressure or broadening gas;

therefore, we must consider the valiiiity 01 the method used to derive the

curves of \ versus (vv0) with respect to the condition 01 COMtMl line

strength. If pressures are low and is many times less than the minimum

value ot ( -,o) for which ■ • 1. the integral ol the right hand side ol

Eq. (8) is barely changed whin the non-unity values 01 X are included.

However, il is larger, the inlluenceol subst i l in i,^ v i11to |.:ij# (H) is

not negliKible.

This phenomenon is illustrated in Fig, 19, where ( urve A represents

a LOTMtl line with 1 em , which corresponds to a tvpual seit-

broadened line at a pressure ol anproximatelv 10 atm. Curve | r.presents

V

V

1.0

o E

-^ 0.5

—i 1 r T ! i 1 "T I

■ 1 -

" 1 " 1° " i ' M ■ A\

\

r ! i [ p - v - \\

c\\\ \ \ \ * *

0 (V-K)cm-'

10

FIT,. 14. k plotted versus (.-. ) to s'ov, lnfluenc< oi > on /lui loi

a sin^lr line. Curvci A and B riprisnt ■ l,i>r.iii. Line ■nd I CO., lii

in thf 7000 cm itv;ion, n spte t i VTIV, With I i in and

k l(atni im,,.,,) . Curve C was obtained by multiplyina A bv max S11' '

valui's ot v ^iviti in Pig. 12 tor N. lints. Curv« I' was obtained

by multiplvinn (' by the appiopri.it. laitor. 1 . >. so that tin ai . a

is tin' satm- under Curvea A and !'. The curvci are shown I or

(\—v ) ■ 1" cm onlv. but Larger ( - ) were considered when o — o calculating the areas und« r the curves«

r)8 ■i

i

the absorption coefficient of such a line after it has been modified accord-

ing to the curve of X versus (w ) for a self-broadened CO line in the

7000 cm region. Curve B is coincident with Curve A for (v-v ) < 3 cm'1. o

We see that the area under Curve B, which represents the Jkd >, is not

greatly different from that under Curve A, so that the factor / in Eq. (8)

has only a moderate influence on the line strength. Approximately 0.065

of the total /kdv for a Lorentz line occurs for (v-v > 10 ., the distance

to which the curves in Fig. 19 have been drawn. Curve C represents an

N2-broadened line with , 1 cm'1 after it has been modified according to

the curve of X for N,, broadening in the 7000 cm"1 region. The area under

Curve C is only two-thirds the area under Curve A. Therefore, it is

apparent that the profile over all values of (vv#) cannot be «iven by

Eq. (8) with X a function of (vv#) only if the strength of the line is

independent of pressure.

Since Eq. (8) is not appropriate for all conditions, we will consider

the applicability of a slightly more complex relationship to a wider range

of - and (v-v ). We define o

TO, -) /kdv/jk. ■■(■.'-•• )d., L O

where ^ corresponds to ■ LorcU^ line. For | BivM ■unction and ■ Kivcn

t, the afsorption coefficient due to a sin^le 1 in. is «iven bv

kL(''' ^-V- (13)

59

r

The quantity •. O, ,) is adjusted so that /k(v) is independent of pressure

or broadening gas. Since v i 1, q» must be > I and increase with increasing

n. In the example of the N^-broadened line given in the preceding paragraph,

qp is 1 T 2/3 1.5, and k is represented by Curve I), which was obtained by

multiplying the values in Curve A by 1.5.

A test of the validity of F.v. (13) lor a region including strong lines

was made from measurements on several samples in the R-branch of the 10 1

band from approximately 3720 to 3740 cm" . The integral ol the observed

absorption coefficient, /kdv, over this region was found to be the same,

within 2 or 37 experimental error, whether the lines were self-broadened,

N2-broadcned, or He-broadened. Furthermore, this quantity was essentially

the same for samples at | atm as at 13 atm, induating that the sum ol the

strengths of all ol the lines is independent oi the brMdmlng |M or the

pressure, as assumed.

We assumed that Kq. (13) was valid and caKul,-)ied k and /kd-. over the

3720-3740 cr.i region lor sample parameters torri spondiiiK to the samples

of pure CG2, CO,, • N., and CO,, I He stuff i'd. V.üues ol • i rom Pig, 13 were

included in the calculati :. and the appropriate values ol (•, ) were

determined for substitution into Kq. (13) by the procedure followed in

obtaining Curve 1) of Pig, 19. The agreement between the MlcilUUd and

observed values was good, indicating that Kq. (li) could be jsed in •

region where the .ihsorpt ion is due to nearby, strong lines. The calculnted

values were also essentially the same as those cnKul.ited lor the s.ime

samples on the assumption that the LOTMItl shape was valid. This amvirent

bO

lack of dependence on line shape occurs because essentially all absorption

in this region (3720-3740 cm ) is due to nearby lines and, therefore,

independent of the shape of the extreme wings, provided /kdv within a few

cm of the center for each line remains constant.

If the relationship given by Eq. (13) is valid, the absorption coef-

ficient in the extreme wings of lines must increase more than linearly

with pressure. For example, - for a typical N -broadened line at 1 atm,

is approximately 0.08 cm , and the Lorentz line shape is valid for (v-v ) o

less than approximately 7 .. Therefore, the modification brought about by

multiplying by ' for (v-V#) v 0.5 cm" causes only a small change in /kdv,

and fa 1. But, as we have shown immediately above, at approximately

12 atm the half-width is 1 cm' and r 1.5. Therefore, if Eq. (13) is

valid, k in the extreme wings of the line is 1,5 x 12 = 18 times as great for

12 atm as for 1 atm. We have .ii^asured the absorption coefficient for both

self and N2 broadening for samples covering wide ranges of pressure and

have found no such super-linear relationship between absorption coefficient

and pressure. All of our results indicate that the absorption coefficient

increases linearly with pressure when the absorption is due to lines whose

centers occur at a distance of several half-widths. Thereiore, we conclude

that the absorption coeffii icnt in the wings cannot be represented properly

by Eo. (13).

Most of the discussion in this section has applied to situations in

which - is not a small fr.'ction ol the minimum value ot ( -• ) at which o

there is significant deviation from the Lorentz shapi. Inder these situa-

tions we find that Eq. (8) is not valid if we assume that "• is a I'mction

hi

of (v-Vo) only. We have found further that the shape of the extreme wings

cannot be represented by Eq. (13). More information than can be obtained

by the methods used in the present study are required before the shapes of

lines within approximately 5 cm of their centers can be understood.

However, it should be noted that Eq. (8) is applicable with X a function

of (v"v0) when this quantity is more than a few cm" and pressures are

less than 1 or 2 atm. As the pressure increases this relationship is still

appropriate if (v-v ) is several times as great as ,.

b2 i t

i

SUGGESTED FURTHER WORK

The need for several additional expcrimcnts is apparenl from the

results and the conclusions which can b« drawn ahout t lie shapes ol 00,

absorption lines. Similar experiments ihould In done for absorption

bands of gases such as CO or N^O which have tuffli ienils ihcrp band luails

that wing absorption can be measured without i Kctllive Interference by

nearby lines. Additional inlormalion could be obteined from simiiar

measurements near (^-brandies ol sever.;l Kases, Including 00, near 570 cm'

The stronger-tban-expected dependence ol wing absorption on tempera-

ture needs further investigation over wider temperature raiiKes, above ami

below room temperature. Additional knowledge about the influence ot

temperature is required in order to make reliable calculations ol heat

transfer in atmospheres which contain considerable ('07, such as Mars and

Venus. Measurements of the absorption near H7 5 cm by the extreme wingl

of lines at lower wavenumbers lor luKh-pressure samples night also provide

I I

63

additional information about the previously unexpected dependence of wing

absorption on wavenumber. On the basis of comparisons made in Figs. 17 and

18, we expect the wings of the distant lines contributing to the absorption

near 875 cm to deviate even further than the lines included in the present

study from the Lorentz shape. The very weak absorption by the wings of

lines broadened by H- and He is surprising and should be investigated

further in other spectral regions and with other absorbing gases.

The present investigation has provided little more than qualitative

information about the shapes of lines between 0.5 and 5 cm" from their

centers. The region near tht- band head at 6988.56 cm" could provide

additional information for this portion of the lines if measurements were

made with spectra] slitwidths less than approximately 0,03 cm"1, which is

considerably narrower than we could attain. Wavenumber accuracy of approxi-

mately 0.01 cm would also be required. With these experimental conditions

the half-widths of the lines very near the band head could be measured and

their contribution to the absorption just above the band head could be

determined much more accurately than has been done in the present study.

Spectral scans made with very good resolution over regions containing

lines could also provide valuable information about the relative shapes of

lines within a few tenths of a cm from their centers when broadened by

different gases. The method illustrated by Fig. 5 in which two samples

with different broadening «ases, but the same absorber thickness, are

employed can provide a direct comparison of the shapes of lines broadened

by different gaici without accounting lor the distortion of the spectr;il

curve because of finite spectral slitwidth.

64

All of the results obtained in the present study for the extreme

wings of lines relate to the high-wavenumber side of the line centers

(v > vo). Since band heads are formed on the high-wavenumber sidus of

C02 bands, regions where most of the absorption results from distant

lines occur above the line centers. There are no places in the spectrum

where most of the absorption is due to the extreme wings of lines at

higher wavenumbers. However, by making careful measuremcnls on the low

wavenumber sides of some ol the bands for samples at several ntm pressure,

one could probably account for thu nearby lines with sulficitnt accuracy

to estimate the contribution due to stronger, distant lines. The shapes

of the low-wavenumber sides of the lines (v • V ) could not be detcrmimd o

as accurately as the high-wavenumber sides have been; however, certain

limits on the possible asymmetry of the lines could be established.

Measurements of this type might be made more accurately with .jmples

containing a single isotoplc species In order to reduce the contribution

of weak isotoplc lines which occur where the absorption would he measured.

19 1 h Since the most common Isotope, C 02 , Is lighter than tin other isotopes

of significant abundance, the Isotoplc bands usually occur on the low-

wavenumber side of the stronger C 0« bands with the same transitions.

Cooling the samples to reduce the contribution hy dillerence hands mid

by high J value lines would probably make more accurate measurements

possible.

65

RF.FERKNCKS

1. A. A. Michelson, Astrophys. ,1. 1, 2 51 (1H95).

2. W. S. Benedict, R. Herman, C. E. Moore. woA S. Silverman. Can. ).

Phys. _}4, 830 and 850 (19%).

3. W. S. Benedict, R. Herman. Gt E. Moore, and S. Silverman. Astrophys.

,1. 13S. No. 1, 277 (IM2).

4. B. H. Winters, S. Silverman, ami W. S. Benedict, I. ouanl. Spectry

Radiative Transfer 4, 527 (19h4).

5. I). E. Burch, I). A. Cryvnak, and K. K. Patty. I. Opt. Soc. Am. _57,

885 (1967).

6. G. Herzberg, Molecular Spectra and Molecular St rue tun 11. Infrared

and Raman Spectra ol Polyatomic Molecules (I). Van Nostr.ind ( o. . Inc.,

Princeton, New Jersey, Ninth Printing 1960).

7. L. I). Cray and .1. E. SdvldgC, .1. Quant. Spcctrv Radiative 'IransUr

j>, 291 (1965).

8. I). E. Burch, 1). A. Cryvnak, and R. R. Patty, I. Opt. Soc. Am.

33 5 (1968).

66

I I I I

I I

REFERENCES (Continuetl)

9. R. P. Madden, J. Chem. Phys. 35, 2083 (1961).

10. D. E. Burch, E. B. Singleton, and I). Williams, Appl. Opt. 1. 359 (tM2)t

U. R. R. Patty, E. R. Manrln«, and J. A. Gardner, J, Opt. Soc. Am. (In press).

12. P. W. Anderson, Phys. Rev. 2^, 647 (1949).

67

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I ONICINATINC ACTIWI'V ^Corporal« «ufhor;

Advanced Developirent Operation Aeronutronlc Division Philco-Ford Corporation

<• nCPOHT ((CUK'TV C l.*t«IFtC«TION

Unclassified 16 snouP

1 HiPOUT TITUB

The Shades of Collision-Broadened C0? Lines

« DCSCMIPTIve NOTES iTvp» ol npori mnd Inclutlv daimt)

Scientific Report

I AUJHOn(S) (Lm»i nam«. Urn nmm* Inlllml)

Burch, jarrell E. Gryvnak, David A.

Patty, Richard R. Bartky, Charlotte E.

• MC PORT DATE

31 August 1%H 7* TOTAL NO OF PASES

67 • • CONTRACT OH CHANT NO

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12

fa oniaiNATon-i REPORT NuMacnrSj

U-320 3

t6 OTHin REPORT NOCJ; (Any oihttnumbmn Mat may 6a aaaftfiad ihli impo'O

11 SUPPLEMENTARY NOTES 12 SPONSORING MILITARY ACTIVITY

13 ABSTRACT

The shapes of the extreme wings of seif-hrcadened CO lines have been investigated in three spectral regions near 7000, 38o0, and 2400 cm"1. Absorption measurements have been made on the high wavenumber sides of band heads where much of the absorption by samples at a few atm is due to the extreme wings of strong lines whose centers occur below the band heads. Considerable new information has been obtained about the shapes of self-broadened CO- lines as well as C0„ lines broadened by ti , 0-, A, He, and U . Beyond a few cm"1 from the line centers all the lines absorb considerably less than Lorentz-shaped lines having the same half-widths. The deviation from the Lorentz shape decreases with increasing wavenumber in going from one of the three spectral regions to the next. The absorption by the wings of H-- and He-broadened lines is particularly low, and the absorption decreases with increasing temperature at a faster rate than predicted by existing theories.

DD FORM I JAN 64 1473

-68< UNCLASSIFIED

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UNCLASSIFIED Secunty Classification

i« KEY WORDS

co2

Line Shape

Line Broadening

LINK A

>LE ' MT

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of .^o!1J'A1?NG A",V,rY: E"'" 'he n.me .nd address of the contraclor, tubcomractor, «rantee. Departmenl of De- fenae activity or other orgamiation (co^o.ale ,u,ho,) ,»sUi„K me rrport. ■

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GPO B66.S5I

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■

I I

PHILCO PHILCO-FOHD CORPORA riON

Aenonutnonic Division

Newport Beach, Calif. • 926B3