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A study of submillimetre atmospheric absorption using the HCN maser
J. Quant. Spectrosc. Radiat. Transfer. Vol. 9, pp. 809 824. Pergamon Press 1969. Printed in Great Britain
A STUDY
OF SUBMILLIMETRE
ABSORPTION W. J.
USING
BURROUGHS,
ATMOSPHERIC
THE HCN
MASER
R. G. JONES and H. A. GEBBIE*
Division of Electrical Science, National Physical Laboratory, Teddington, Middlesex, England (Received 28 October 1968)
Abstract--A study of water vapour absorption at two submillimetre wavelengths (337 ,am and 311/~m) has been made as a function of foreign gas pressure using A, CH4, N2 and CO 2 as the broadeners in order to explain excessive absorption in the atmospheric "window" regions. As an extension of this work the absorption coefficient of water vapour alone was measured as a function of pressure and temperature. From an analysis of the ratio of the absorption coefficients at the two wavelengths, the anomalous absorption has been explained in terms of three contributions. 1. A background absorption which is independent of foreign gas broadening. This is ascribed to two-body collisions in water vapour which may be explained in terms of a dimeric form of the water molecule having a binding energy of (5-2 + 1.5) kcal mol - 1. 2. A modification of the line shape in the far wings which is dependent upon the foreign gas pressure and quadrupole moment. This effect is consistent with a two body quadrupole coUision-induced background absorption, 3. A three-body effect which is related to the quadrupole moment of the foreign gas used to broaden the water vapour lines.
1. I N T R O D U C T I O N
A NUMB~ of studies of atmospheric absorption in the submillimetre and millimetre regions have clearly shown that the experimental values in the "window" regions exceed those predicted by theory by a factor of 1.5 to 2. t l - 4 ) In this work we have attempted to examine the variation of absorption due to water vapour as a function of both water vapour and foreign gas pressure using a number of specially dried non-dipolar broadening gases (A, CH4, N2 and CO2) at the two principal HCN maser wavelengths 337/am (29.712 cm t) and 311/am (32-166 cm-1),t5~ by measuring the magnitude of the absorption coefficients at the two wavelengths and their ratio as a function of foreign gas pressure. It will be shown that the discrepancy between theory and experiment can be explained in terms of molecular collision processes not usually considered in standard theoretical line-broadening studies. An analysis of these results shows that the principal contributions are an absorption in water vapour that is independent of foreign gas pressure and an absorption which is proportional to the square of the foreign gas pressure (p 1) and is dependent upon the gas having significan t quadrupole moment. In order to investigate the anomalous absorption in water vapour alone, a temperature and pressure analysis was carried out to determine the nature of the collision processes involved. In general, the analysis of the effects will be of a qualitative * Now at National Bureau of Standards, Boulder, Colorado, U.S.A. 809
810
W
J . B U R R O U G H S , R . G . JONES a n d H . A . G r ! m m
nature, but an attempt has been made to relate the observed effects to, in the first case, the binding energy of the dimer of the water molecule, and, in the second case, to the quadrup'31e moment of the foreign gas employed. The choice of foreign gases was restricted to readily available non-dipolar gases which had a range of quadrupole moments. The reason for not using dipolar gases was to avoid any dipole~tipole collision-effects which would probably mask any quadrupole effects. The emphasis on quadrupole effects is based on the fact that since nitrogen has an appreciable quadrupole moment [Q ~ 1.4 × 10-26 eSU cm 2 (6)] and is the major source of atmospheric line-broadening, any discrepancy between theory and experiment may possibly be bes! explained in terms ofa quadrupole-induced effect} ~' Carbon dioxide was chosen on account of its even greater quadrupole moment [Q ~ 5"2 × 10 2e. eSU cm2(6)], and argon and methane on the basis of their negligible quadrupole moments. It is thus hoped to explain the anomalous behaviour of atmospheric absorption in the submillimetre "window" regions by a study of water vapour absorption broadened by these four foreign gases. 2. T H E O R Y
To facilitate the theoretical analysis of the absorption measurement we must first emphasize the position of the two H C N maser lines with respect to the absorption transitions in water vapour (Fig. 1). At 29.712 cm 1 over 85 per cent of the absorption coefficient is attributable to transitions in excess of 3 c m - I from this wavenumber, whilst at
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F I G . I. T h e o r e t i c a l s p e c t r u m o f air at 20°C w i t h a n a b s o l u t e h u m i d i t y o f 13.5 g / ' m t, s h o w i n g the
relative p o s i t i o n o f the H C N m a s e r lines, with respect to the a d j a c e n t w a t e r v a p o u r a b s o r p t i o n lines, 2
2~2oat25'085cm-X,32-~4oat30"556cm-1
42_~5
2at32'365cm-X,10-)2-zat32"951cm
1.
A study of submillimetre atmospheric absorption using the HCN maser
811
32-166 cm-1 the contributions to the absorption from the nearby transitions 1o --* 2 2 (32.951 c m - ') and 4z ~ 5-z (32"365 c m - 1)(8)are respectively ~45 and ~ 35 per cent. Hence a comparison of the absorption coefficient at these two wavenumbers will provide a measure of variation of the specified line-shape between the near and far-wing regions. The importance of such an analysis is enhanced by the observations in near infra-red work on HC1,19) that significant deviations from the Lorentz line-shape are only observed when absorption measurements are made more than 1 cm -~ from line centre. In order to theoretically predict the pressure dependence of these absorption coefficients we will first carry out a simple analysis, based on the most elementary line-shape, in order to define the expected ratio of the absorption coefficient at 337 pm(c%~7) and 311/am (c%11), /-) : 3(337/~311 as this is the most convenient way to consider the experimental results (see Section 3). We will then give a quantitative analysis in terms of a more complete line-shape, so that a comparison between the theoretical and experimental results may be made in terms of the molecular parameters of the broadening gases used in this work. 1. (i) Qualitative Analysis: We assume that the line-shape of a given water vapour transition (i --, j) may be given by a Lorentzian form :
O~.ij(0.)
Aij
A0.ij
0.if +A0.
=
(I)
where A~j is the line strength of the transition at wavenumber (a~) and is a constant for a given value of Po and the half width A0.~j is given by :
A0"ij = poAa'ij + P, Aa'i'~
(2)
where Po is the pressure of water vapour and Pl is the pressure of the broadening gas, both in torr, and Aa'i~ and A0.'i~are the pressure-broadened half-widths at 1 torr for water vapour and the broadening gas respectively. If we can now assume that : A0.ij <~ l a - 0 . J
(3)
then by inserting equations (2) and (3) into equation (1) we obtain the approximate absorption coefficient : O~iJ(0.) :
Ai: 7"[(0"- -
,
~ij) 2 (P°A0"iJ+ P , A 0 " i j )
,, •
(4)
We may now simplify this by replacing poA0"'~j by p'oAa'~} where :
Aa'~j
po':
(5)
where Po' is the equivalent foreign-gas broadening pressure of Po torr of water vapour. Inserting equation (5) into (4) we get : A ij A 0"'i'j .
e,j(0")- r r ~ 2 t P o
.
.
.
.
-epl~ = k~j(0")[po +p~].
(6)
8t2
W . J . BURROUGHS, R. O. JONES and H. A. G~Bm~!
Now if we consider the values of can evaluate the ratio :
eu(0-) at two wavenumbers al and 0-2 (i.e. ~ and a21 wc p
'~1 --
:~2
=
(0"2 -- 0-ij) 2
(al - o-ii)2"
(7)
The important property of this ratio is its independence of both P0 and p~. If we now extend the analysis to include a large number of absorption transitions then :
~ AijAalJ =k(a)[po,+Pl ] ~(0-) = (po' +Pl) .. re(a- aii)2
IS)
where aijAoij
from which it can be seen that the value of ~1/~2 is still independent of the pressures Po and Pl. Hence, by observing the value of the ratio p as a function Ofpo and Pl we can measure any deviations from the simple line shape [equation (l)], and relate these to the molecular collision processes involved. (it) Quantitative analysis. In order to make a quantitative analysis, both of the values ~337 and ~311 and also of the ratio p, a more exact form of the line-shape must be used. Moreover, we need to compare our results with the numerical predictions of some accepted model. The majority of the theoretical values of a(a) quoted here have been derived directly from the work of ZHEVAKIN and NAUMOV(3) who used the kinetic line-shape : ~0(0") --
4A ij
02 A0"ij
n
(0-2 -- 0"2)2 + 4 0 - 2 A 0 2 "
(9)
Two important points should be noted concerning this expression : (a) Equation (9) reduces to equation (1) if0-+0-ia _~ 20- so that for values o f f ~ 30 cm the difference between equation (9) and equation (1) for [0"-0"~j[ < 1 cm ~ is less than 3 per cent. (b) The simple analysis in the preceeding section is not altered if we use equation (% instead of equation (1) since equation (6) is still applicable if A0"u ~ [0--0-J. The reason that any quantitative analysis need be given is that despite the extensive theoretical work carried out by ZHEVAEIN and NAUMOV(3) their results are only in graphical form and hence the value of ~3~ cannot be derived directly from their work with any degree of accuracy. An approximate value of ~a,~ was obtained by using the values of ~(a) given by ZHEVAKIN and NAUMOV(3) in the adjacent window regions at 31-1 and 34-1 c m -1. The values of ~iy(a) at 32-166cm i and 31-1 and 34-1 cm -1 for the 1o -~ 2_ 2 and 42 -~ 5_ 2 transitions were then recomputed from the known line-strengths (4) using the Nz-broadened halfwidths given by BENEDICT and KAPLAN. (1 l) From these values the background contribution ~h due to all other transitions at 3 l-1 and 34"1 cm- i was obtained and by interpolation the value of this contribution c% at 32'I 66 c m - t was estimated, then the value of 0~311 was obtained by combining this value with the computed contributions from the lo ~ 22 and 42 --* 5 _ 2 transitions at 32"166 cm-1. The value of~337 c a n be obtained directly from the published results (3) as in the region of 29-7 cm ~ ~(0") is a slowly varying function of a. In computing ct31 ~ the theoretical
A study of submillimetre atmospheric absorption using the HCN maser
813
values of Aals for N2-broadening given by BENEDICTand KAPLAN are used/1°) To compute values of~337 and ct311 as functions of Pl we have taken the atmospheric values of ZHEVAKIN a n d NAUMOV (3) to be equivalent to p~ = 675 torr of Nz, since throughout their work they have assumed that (Aais),ir is 0"9 (Aai~)N2 for equal pressures. Thus by taking the value of ~(a) at 675 torr of N2 and from this evaluating the values of 0~337 and ct3~x for Pl = 0 and Po = 13-5 torr using a mean value of Aa~j of 9 × 10 -2 cm -1 (derived from BENEDICT and KAPLAN'S H 2 0 - H 2 0 broadening data) t~ ~ it is possible to derive approximate expressions for the p~-dependence of c~33 v and 0~311. These are (expressed in the form of a secondorder polynomial, see Section 4): ct311 = 63.61 +0-834pl - 9 . 9 × 10-Sp 2 db k m - 1 (10) ct337 = 11"45 +0"150pl db k m - 1 The presence of a negative p2 term in ct3~ ~ arises because the assumption in equation (3) is no longer valid for the transition 42 ~ 5_2 when p~ > 250 torr. For this reason the value of p is also not quite constant but varies from p=0"180+_0"018
at
Pl = 0 t o r r
to
(11) p = 0.196 ± 0 - 0 2 0
at
Pl = 760torr.
However, this variation is much less than is observed experimentally (Section 4) indicating that an even more detailed theoretical consideration is necessary to account for the observed results.
3. E X P E R I M E N T A L
DETAILS
The equipment used for this work is shown diagrammatically in Fig. 2. The 2.3 m CW operated maser had a plane-parallel mirror cavity and the radiation was coupled out through a 6 m m diameter hole in the centre of one mirror. The power output of this system was approximately 0.1 m W at 337 iLm and 0-01 m W at 311 Itm. The CW radiation was modulated at 13 Hz by a mechanical chopper and the output of the monitor and cell detectors were both passed through narrow band filters and their relative phase adjusted so that both signals were in phase (Fig. 2). The size of the two signals was then compared using a Tektronix (1A7) differential amplifier; and a null condition obtained by attenuating the signal from the monitor detector, which was always greater than that from the cell detector, using a voltage dividing box. The attenuation could be measured to four figures, though in practice only three figure reproducibility was achieved. The value of the attenuation of the monitor signal required to obtain the null condition was measured as a function of the absorption path length, which was varied from 10 m to 50 m in 10 m increments, thus enabling the absorption coefficient to be determined. In the case of the weaker radiation i.e. 311 pm, the dynamic range of the attenuation of the monitor signal was of the order 103 with a minimum signal to noise ratio of 10. This means that accurate measurements of the absorption coefficient could be made up to 1000 db k i n - 1.
814
W..1. BURROU(ilIS, R. ( } . . l o x l S a n d It. A. Ol BIIll
PUMP l
~1~
2;2
13 Hz DIELECTRIC CHOPPER BEAM-DIVIDER ~
J [ ~ A ' A "X PRESSURE
NI
Q2) GAUGE
t2OOV
GOLAY / DETEOToR ] 13Hz ] [FILTER J •
. i 13 Hz i L FILTER ]
FOREIGN GAS
r V~'~Ri;B LE /
IATTENUATORj ~-
-
"
....
~-DIFFERENTIAL / AMPL F ER I / <
.
.
.
.
[
NULL
SIGNAL
[l{;. 2. S c h e m a t i c d i a g r a m of the e x p e r i m e n t a l syslem. The m u h i p a s s cell ,<'.as hL'alcd to 5{}' (' h., ineaT]s of healing tapes. The cell din]cnsions arc 3 111e 40 cm arid lhe nlit'l'or,, ~', :lilt] A,I , ;il-e I q cn] in d i a l n e t e r atld J]2 is 20 c m in d i a m c t c i ; all 3 illillOlS h a v e a 2"5 Ill r:.tditl>, O1 ctlrValtllc [ h e ca'~iiy a d j u s i m e n l on the m a s e r a l l o w e d 337 Hm a n d 311 ira1 r a d i a l i o n to be o b t a i n e d a h c r m i t c l y b ; mean-, of t u n i n g the cavity lenglh.
The Inultipass W h i t e cell was a 2.5 m system c a p a b l e of giving path lenglhs flom l/} m to 60 m in increments of 10 m. The metal cell could be p u m p e d d o w n to 0-1 l o n using a r o t a r y p u m p or pressurised to lO00lorr. Since {hc r a d i a t i o n froln the maser ~xas not focused in line with the surface of ,~12 but wits allowed l,,} diffracl from the m a s e r H p c F I t u c to fill M , , the focussing of the r a d i a t i o n within the W h i t e cell was not perfect, l t o w c x c r . since the Rayleigh distance for the exit a p e r t u r e is - 12 cm an a p p r o x i m a t e focus can he formed in the region of the front surface of the m i r r o r M e. F o r this reason, the geometrical losses did not exceed 15 db k m ~, and the system was regularly c a l i b r a t e d so that 1]it m e a s u r e d a b s o r p t i o n coefficients could be corrected for these s y s t e m a t i c losses. [ urthermore, it should be noted that these losses were very much less than most of the wducs of thc a b s o r p t i o n coefficients m e a s u r e d (Fig. 3). The e x p e r i m e n t a l technique was, after c a l i b r a t i n g the cell under v a c u u m c o n d i t i o n s , to fill the cell with water v a p o u r to a pressure of t3 to 14torr, in the case of the r o o m t e m p e r a t u r e ( T - 20°C) studies. The p r o b l e m of a v o i d i n g changes in water v a p o u r conc e n t r a t i o n d u r i n g o b s e r v a t i o n s , due to a d s o r p t i o n o n t o the walls of the cell, was largely o v e r c o m e by t h o r o u g h l y wetting the system. "It was found that m a i n t e n a n c e of a relative h u m i d i t y of a b o u t 80 per cent p r o d u c e d a stable c o n d i t i o n t h r o u g h o u t a range of b r o a d e n i n g gas pressures. As will be seen later, the values of ~311 are in quite close a g r e e m e n t with theory, and hence can be used to m o n i t o r the water v a p o u r content. However, d u r i n g most of the work it was found that within e x p e r i m e n t a l e r r o r the water v a p o u r presstlre r e m a i n e d c o n s t a n t if the initial c o n d i t i o n s a l r e a d y q u o t e d were obtained. O n e p r o b l e m with having such a high h u m i d i t y in the cell was to ensure that no water c o n d e n s e d o n t o the m i r r o r s as this would have a m i s l e a d i n g effect on the results obtained. This was a v o i d e d both by
A study of submillimetre atmospheric absorption using the HCN maser
815
checking that no condensation was visible and by observing that no apparent change in absorption took place on heating the mirrors.
8oo
++/EH4 /
/
Na/
/
+
/
//
70C
/~//311}J
600-
t
/
i
E 500
u
40C
°
¢
°
/
0
g aoo<,,
0#
20C
-
//%-'~"
I~
Na
9.9"~
CH~
au ~ 1
,oo
0
200
400
600
800
I000
Pressur~ p, (torr) F'I(;. 3. Results obtained for N 2 and CH,, using 13.5 tort (Po) of water vapour, and varying the pressure (Pl) of N2 and CH4.
The absorption coefficients at the two wavelengths were measured for a range of foreign gas pressures (Pl) and from the values of c(33v and ~(311 obtained the ratio P(Pl) could be recorded. Examples of the measured values of 0~337 and ~31~ for N2 and CH4 are shown in Fig. 3. To check that all the observed absorption was due to water vapour broadening alone, the absorption due to the pure broadening gases was measured and
816
W.J. BURROtJGHS, R. G. JONES and H. A GEBBIIq
found to be negligible for all the values of Pl considered. This result indicated that the amount of water vapour remaining in these dried gases was negligible and showed that collision-induced quadrupolar absorption in the quadrupolar gases (9"1°) was insignificant. This agrees with the result spectroscopically obtained for CO2 (1°) in that the absorption due to 400 torr of pure C 0 2 should be ~ 5 db km i, i.e. less than the errors quoted for this work (Section 4).
4. E X P E R I M E N T A L
RESULTS
Using the techniques outlined in the previous section, a series of absorption coefficients was obtained using argon, methane, nitrogen and carbon dioxide as broadening gases. The results were fitted, by means of a least squares analysis, to a second order polynomial of the form" c~ = a l + b l P l
+tip 2
(12)
and the values of the coefficients a~, bt and Cl obtained when the results are normalized to an absolute humidity of 13.5 gm 3 are given in Table 1.
TABLE I
bl(dbk m t t o r r
l)
Standard error in,~ (dbkm t)
337 337 337 337
A N2 CH4 CO 2
27"50 27"64 26"98 27"95
0'0514 0"179 0"167 0"493
0"50 3"4 - 1"3 6"8
4"47 5-35 358 6"73
311 311 31 I 311
A N2
77"00 74-59 70-61 74"31
0"253 0"834 0"91 I 1-920
4"2 2"8 12"7 71"0
7"44 12"26 13-76 861
CO2
1)
2)
Gas
CH 4
al(dbkm
clldb k m 1 torr xl05
2(pm)
From these least squares fits the ratios (p = 0 ~ 3 3 7 / ( x 3 1 1 ) as a function of pressure have been computed and are shown in Fig. 4. The standard errors in Table 1 indicate that the uncertainties range from + 5 d b k m ~ at low values of a to _+20dbkm ~ at large values of c~, and this is reflected in the increased errors in the values of ~3~ at high values of px, though as proportional errors they are in general smaller than those occurring in c%37, and the latter tend to provide a measure of the upper limit of the accuracy obtainable. The values of c~3~ and c~337 have also been measured as a function of temperature 7" and pressure Po in water vapour alone. The cell could be heated up to 50°C, and P0 varied from 0 to 40 torr. From these measurements it was found that both ~3av and ~31~ showed a close agreement with a simple p0z dependence (Fig. 5), and from this that p is independent of P0- The temperature dependence of p is shown in Fig. 6.
o o
~~ ~K
0 0
0 '¢
0 ~
0 ~
0
0
0 0
o
¢)~,-
cn
o ~0
: ' - ,.b,
I
I
u'~,
I
I
÷,¢ I I
//
/
,,
~')
~
j
/
i / I
iI
i//
..o"
0
0
o
o
1
¢
/ /'
I1÷
,.~
0
o
6
:
l° 0
6
IL E ~ ._
t:~lj ~
0
> .~_~
W . J . BURROUGHS,R. G. JONES and H. A. GEBBn~
818
40
\1 O
.35
'30
.25
-20
J 2'o
3'o
do
s'o
T (°C) - - ' -
FIG. 6. The temperature dependence of the ratio p
5. D I S C U S S I O N
= ~337/~311
OF
obtained for pure water vapour.
RESULTS
(i) Qualitative analysis. It is immediately obvious that these results, especially the ratios of p = 0~337/~311, do not agree with those predicted on the basis of the simple theory. The discrepancy between theory and experiment can be qualitatively explained in terms of two anomalous contributions : (al A background continuum due to dimeric water. If such a contribution exists the initial anomalous drop in p which occurs with all the gases as Pt is increased (Fig. 4) can be explained if we assume that the dimer contributes a pressure-independent attenuation ~e (this assumption will be justified in the quantitative analysis of the temperature study). The ratio is then given by P(Pl) -
0~337(Pl) + 0~a
(13)
where ~ 3 7 and c~;1t are the contributions that may be attributed to monomeric water vapour, and me is a pressure-independent, slowly-varying function of frequency so that ea at 337 pm can be assumed to be approximately the same as en at 311 pro. Then p(p~) will tend asymptotically to p' = c~37/c~;11 with increasing Pl, as found for A and CH4 (Fig. 4). This property of the dimer is in agreement with certain theoretical predictions, ~14) and also spectroscopic analysis of an atmospheric feature observed at 7.5 c m - t / l 5,16)
A study of submillimetre atmosphericabsorption using the HCN maser
819
Further qualitative information concerning the spectrum of this dimer may be obtained from the poZ-dependence of~337 and ~311. If we consider equation (4) for pure water vapour we obtain : A~j O(ij(O') -- 7[(0" -- O'ij) 2 P°AtriJ"
(4a)
Now in the case of the monomer Aij is proportional to the number of absorbing molecules per unit volume and hence to Po and therefore : c~(~r) = ~ ct/j(~r) = k(c0p 2.
(8a)
This is just the dependence that has been observed in Fig. 5 but if we are postulating the presence of a dimer the concentration of which is dependent on p(](16) (i.e. A~j for the dimer is dependent on the number of water molecules per unit volume squared) then ~d(a) = kd(~Y)p3.
(14)
The absence of any appreciable p3 term in the observed absorption must be taken to indicate that either the lines are so numerous or the line widths are so great that it is improbable that pressure-broadening of discrete lines will be observed or that the dimer does not exist. Since the temperature dependence of p (Fig. 6) is consistent with a relatively strongly bound dimer (see next Section) it must be assumed that the failure to observe pressure broadening of the dimer features is due to a multiplicity of absorption transitions. This result would appear to be consistent with the fact that low energy vibrational states ( ~ 100 c m - 1 ) ( 1 4 ) will have appreciable populations at ~ 300°K and hence the pure rotation spectrum will be exceedingly complicated and effectively a continuum at the values of Po used. It is not considered plausible that the existence of a continuous background can be explained in terms of a short lifetime, which would result in broad absorption features, as such a lifetime is not easily reconciled with the value of the binding energy obtained from the quantitative analysis of the temperature study. (b) Pressure-broadening by non-dipolar gases shows interesting properties. First, the gases without quadrupole moments (A, CH4) show a variation of p with Pl consistent with the form: c(337 +~d
(13)
P - - ~ 3 1 1 -~-O~d
where t 0~337 =
k'l(P'o+Pl)
t
t
!
o~311 = kz(Po + P l ) and r
/,'1
P =~.
If one evaluates c(d to satisfy this condition one finds (Fig. 7) : c(a = 17.0+5.0db km -1
(6a)
820
W.J. Bt'RRI)UGHS, R. G. JONES and H. A. GI!BBK
which leads to P'
k;
k', = 0.194+0.010.
The value of p' is in good agreement with the theoretical value given in equation (Ill. Thus, it can be seen that apart from the contribution due to dimeric water vapour l~,) the pressure-broadening effect of nonquadrupolar gases is, within experimental error, in agreemenl with the theoretical predictions based on the standard line-shapes. Secondly, the quadrupolar gases (N2 and CO2) show effects that are Pl dependent, but can be explained only if we replace ~,~3: and ~3~1 in equation (6a) by the expanded form ~;~v -- k'l(P; +P, )+clP~
(6b)
~'311 = k 2 ( P o + P l ) + c z p l where ('1 and c 2 are constants at constant temperature. For the pressure range considered in this work
P = k'2 k'2 P{)q-Pl
l(2+1(2 pl
since
ki(p'O +Pl ) >_ clp~ k2(Po +Pl) >~ c2p 2.
(15)
Hence if we p l o t / / a g a i n s t p~ we should obtain a set of straight lines (Fig. 7). The displacement of the line in the case of CO2 is possibly due to adsorption of the gases onto the walls of the cell. The/)2 term must arise as a result of 3-body collisions, revolving two molecules of the broadening gas and a single water vapour molecule. As was noted in Section 3 this absorption could not be explained in terms of collision-induced absorption in N 2 and CO2 alone 112"131 as at the pressures considered this is negligible, as was shown experimentally !Section 3). The existence of such an effect is unexpected at such low pressures, and hence indicates that the influence of dipole-quadrupole multiple collision effects may be of greater importance than previously anticipated and should be given further theoretical consideration. (ii) Quantitatice amdysis. (a) The dimeric contribution :~a at T = 20°C has already been introduced in the previous analysis in order to evaluate the pl-dependence of p' tFig. 71. If a similar analysis is carried out on the values of p obtained in the variable temperature study the values of 7a that are obtained can be plotted as loge :~a against T - ~ (T in °K) at constant pressure as shown in Fig. 8. This is an Arrhenius type plot from the gradient of which the value of 5.2+ 1.5 kcal tool 1 of the binding energy of the dimer is obtained. This value is in agreement with the submillimetre spectroscopic work {l~'~ and also with the theoretical prediction of VIK rOROVA and Zm~VAKINJ~4-~ (b) In order to make a quantitative analysis of the values of c%3v and :z,~ obtained experimentally we must compare them with those obtained theoretically in section 2(ii)
A study of submillimetre atmospheric absorption using the H C N maser
821
0
,
i
I O
0
O
0
~
Ol
4. eb
,
•
0
t-
0
~
Q
P~o ~5Ol !
4-
i
1
~g 2~
0
~
o
~
2.=
I t~
0
~
0I'N
6
6_.~.
6
6
6
I:::u
822 using
W.J. BURROUGHS,R. G. JONESand H. A. GEBBIE
N 2 as a broadening gas. For ct311 the theoretical value was : c(311 = 6 3 . 6 1 + 0 . 8 3 4 p l _ 9 . 9 x 1 0 - S p 2 d b k m
1
as compared with experimental value : c%11 = 74"59+0-834pl +2"8 x 10-5 p~ d b k m - I The coefficients show good agreement with the results already obtained in the qualitative analysis. The difference 10-98 db kin- 1 between the constant terms is, within experimental and theoretical error, in agreement with the value ofctd evaluated for 7-' = 20°C. The closest agreement is for the coefficient of the Pl term, indicating that the theoretical values of the simple pressure-broadened line-widths Aaij are substantially correct. This result is a little surprising as work on the 10.85 and 12.67 c m - 1 lines(17 ~8) suggests that under atmospheric conditions the theoretical values of Aa;i are up to 20 per cent low. It should be noted that any discussion of such agreement should be qualified by the fact that all the coefficients are dependent on the absolute measurement of P0 which was accurate only to the order of _+ 10 per cent. Moreover, the ratios of the Pl terms for the other gases do not show such agreement (see later). Finally the discrepancy between theory and experiment in the p2 term corresponds to the suggested 3-body collision effect already discussed. Similarly for 5337 we get : Theory:
~337 = 11"45+0"150p1 d b k m
1
Experiment :
ct337 = 27-64 +0.179 Pl + 3.4 x 105 p~ db kin- 1.
The numerical differences here can again be explained in the same manner as for the ct311 result. It should further be noted that the difference in c~ (the p2 term) in both cases is of the same order, hence justifying this assumption in the earlier qualitative analysis [equation (15)]. It is not possible to extend the analysis to the other broadening gases, as no theoretical work exists on the broadening coefficients of these gases with water vapour in this spectral region. Furthermore, in the case of CO2 the complication of adsorption of both H 2 0 and C O : onto the walls occurs, and explains the large negative p~ term in ~3~1 for this broadening gas. Thus the only results that may be obtained from the coefficients must be in terms of the relative magnitude of these for the various gases and also the ratios p and p' as has been done in the qualitative analysis. We note that : 1. There is good agreement between the values of ~337 and ~311 obtained using CH4 and those predicted on the basis of simple N2-broadening apart from the background contribution of ~ . The general agreement of the form of the absorption coefficients again supports the hypothesis that for non-quadrupolar gases there is close agreement between theory and experiment. 2. The ratio of the coefficients of the p~ terms in the cases of N2 and CO2 broadening, derived from the gradients ofp' (Fig. 7) is 4"2 and does not equal the ratio of the squares of the quadrupole moments (Q). This would appear to indicate that a simple Q2 dependence of the 3-body collision effect is not an adequate explanation, but the accuracy of this ratio is such (Fig. 7) as to make any definitive comment on the nature of the collision effects exceedingly difficult.
A study of submillimetre atmospheric absorption using the HCN maser
823
3. The ratios of the coefficients of the p~ terms of CO2 against N 2 and of N 2 against A are considerably greater than would be expected on the basis of microwave broadening results, tt9~ This indicates that there is also an excess quadrupole effect in the Pt term which is in agreement with other broadening results in the millimetre and submillimetre region, tt7'~8) This result also agrees with microwave work on foreign gas broadening in HC1. (7) In this work, the ratio of the Pt terms for N 2 and CO2 broadening was 4.58, 20 c m - ~ from the nearest HC1 line. In our results the ratio of these two terms is 2.76 at 29.7 cm-1 and 2"30 at 32'2 c m - i , whilst for microwave results in close proximity to the 6.12 cm-1 water vapour line it is 1-60.tt9) This increasing ratio with distance from a given absorption feature indicates an excessive absorption due to two-body collisions and possibly a broad-band quadrupole collision-induced absorption of the type proposed by FRENKEL. (2°) It should be further noted that throughout this work the effect of higher multipole moments, octupole and hexadecapole are assumed to be negligible. This conclusion is not entirely supported by FRENKEL (20) but we feel that the difference between the values of p' obtained for N 2 and CH 4, and the marked similarity in p' for CH4 and A clearly indicate that the octupole moment of C H 4 is not making a significant contribution to absorption effects in the submillimetre region. However, our results do not eliminate the possibility that in the very far wings of pressure broadened dipole rotation lines (7) the effect of the higher multipole moments is not negligible, t2°) CONCLUSIONS We have confirmed the existence of an extra contribution to the usual Pl dependent broadening coefficient due to quadrupolar gases. This is complementary to previous microwave absorption measurements. (7'x9) We have also observed absorption due to two distinct and previously rarely considered effects. (i) The presence of the dimer of water vapour which results in a background contribution to atmospheric absorption. This appears to be of considerable importance in the "window" regions and can explain approximately half of the excessive absorption observed in these regions. (ii) The existence of a significant quadrupole-dependent 3-body collision effect, which was previously considered to be negligible. This effect accounts for most of the remaining anomalous absorption in the "window" regions. We may therefore conclude that these results provide a qualitative explanation of the excessive absorption in the submillimetre atmospheric "window" regions.
Acknowledgements--We wish to acknowledge the valuable assistance of Mr. D. W. E. FULLERin the preliminary stages of this work. We would also like to thank Dr. J. CHAMBERLAIN,Dr. C. C. BRADLEYand Dr. G. BIRNBAUM for helpful discussions. Note added in proof--We have recentlyreceivedtheoretical calculationst2l) of ~t337and ~3t ~from Dr. R. J. EMERY of Queen Mary College, London that remove certain errors in earlier works, t22) This gives a slightly different value ofp which is lower than used here i.e. p =0"157 at Pl =0torr p = 0"173 at Pt = 760tort.
(lla)
These valuesdo not alter the analysispresented here, but add support to our conclusionsconcerningthe discrepancy between theory and experiment.
824
W . J . BURROUGHS, R. G. JONES and H. A. GEBB1E REFERENCES
1. 2. 3. 4. 5. 6. 7. ~. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22.
J. H. VAN VLECK,Phys. Rev. 71,425 (1947). N. I. FURASHOV,Optics Spectrosc. 20, 234 (1966). S. A. ZHEVAKINand A. P. NAUMOV,Radiofiz. 6, 674 (1963). W. J. BURROUGHS, E. C. PYATT and H. A. GEBBIE, Nature. Lond. 212, 387 (1966L L. O. HOCKER, A. JAVAN and D. RAMACHANDRARAO, App[. Phys. Letters 10, 147 (1967). KRISHNAJI and VINOD PRAKASH, Rev. Mod. Phys. 38, 690 (1966). A. A. MARYOTT and G. BIRNBAUM,J. Chem. Phys. 47, 3200 (1967L R. T. HALL and J. M. DOWEING, J. Chem. Phys. 47, 2454 (1967). W. S. BENEDICT, R. HERMAN, G. E. MODRE and S. S1LVERMAN,Can. J. Phys. 34, 850 (1956). W. S. BENEDICT and L. D. KAPLAN, J. Chem. Phys. 30, 388 (1959). W. S. BENEDICT and L. D. KAPLAN, JQSRT4, 453 (1964). H. A. GEBBIE and N. W. B. STONE, Proe. Phys. Soc. 82, 543 (1963). H. A. GEBBIE, N. W. B. STONE and D. WILLIAMS, Mol. Phys. 6, 215 (1963). A. A. VIKIOROVA and S. A. ZHEVAKIN, Sol'. Ph.vs. Doklaclv i!,, 1065 (1967) H. A. GEBBIE and W. J. BURROUGHS, Nature, Lond. 217, 1241 (1968). J. E. HARR1ES, W. J. BURROUGHSand H. A. GFBBIE (see this issue). V. YA. RYADOV and N. I. FURASHOV, Radiofiz. 9, 1073 (1966). V. YA. RYADOV and N. I. FURASHDV, Optics" Spectrosc. 24, 93 (1968). J. R. RUSK, J. Chem. Phys. 42, 493 (1965). L. J. FRENKEL, Molec. Spectrosc. 26, 227 (1968). R . J . EMERY, Ph.D. Thesis, London University (1968). R. J. EMERY, Appl. Optics 7, 1247 (1968).
A STUDY
OF SUBMILLIMETRE
ABSORPTION W. J.
USING
BURROUGHS,
ATMOSPHERIC
THE HCN
MASER
R. G. JONES and H. A. GEBBIE*
Division of Electrical Science, National Physical Laboratory, Teddington, Middlesex, England (Received 28 October 1968)
Abstract--A study of water vapour absorption at two submillimetre wavelengths (337 ,am and 311/~m) has been made as a function of foreign gas pressure using A, CH4, N2 and CO 2 as the broadeners in order to explain excessive absorption in the atmospheric "window" regions. As an extension of this work the absorption coefficient of water vapour alone was measured as a function of pressure and temperature. From an analysis of the ratio of the absorption coefficients at the two wavelengths, the anomalous absorption has been explained in terms of three contributions. 1. A background absorption which is independent of foreign gas broadening. This is ascribed to two-body collisions in water vapour which may be explained in terms of a dimeric form of the water molecule having a binding energy of (5-2 + 1.5) kcal mol - 1. 2. A modification of the line shape in the far wings which is dependent upon the foreign gas pressure and quadrupole moment. This effect is consistent with a two body quadrupole coUision-induced background absorption, 3. A three-body effect which is related to the quadrupole moment of the foreign gas used to broaden the water vapour lines.
1. I N T R O D U C T I O N
A NUMB~ of studies of atmospheric absorption in the submillimetre and millimetre regions have clearly shown that the experimental values in the "window" regions exceed those predicted by theory by a factor of 1.5 to 2. t l - 4 ) In this work we have attempted to examine the variation of absorption due to water vapour as a function of both water vapour and foreign gas pressure using a number of specially dried non-dipolar broadening gases (A, CH4, N2 and CO2) at the two principal HCN maser wavelengths 337/am (29.712 cm t) and 311/am (32-166 cm-1),t5~ by measuring the magnitude of the absorption coefficients at the two wavelengths and their ratio as a function of foreign gas pressure. It will be shown that the discrepancy between theory and experiment can be explained in terms of molecular collision processes not usually considered in standard theoretical line-broadening studies. An analysis of these results shows that the principal contributions are an absorption in water vapour that is independent of foreign gas pressure and an absorption which is proportional to the square of the foreign gas pressure (p 1) and is dependent upon the gas having significan t quadrupole moment. In order to investigate the anomalous absorption in water vapour alone, a temperature and pressure analysis was carried out to determine the nature of the collision processes involved. In general, the analysis of the effects will be of a qualitative * Now at National Bureau of Standards, Boulder, Colorado, U.S.A. 809
810
W
J . B U R R O U G H S , R . G . JONES a n d H . A . G r ! m m
nature, but an attempt has been made to relate the observed effects to, in the first case, the binding energy of the dimer of the water molecule, and, in the second case, to the quadrup'31e moment of the foreign gas employed. The choice of foreign gases was restricted to readily available non-dipolar gases which had a range of quadrupole moments. The reason for not using dipolar gases was to avoid any dipole~tipole collision-effects which would probably mask any quadrupole effects. The emphasis on quadrupole effects is based on the fact that since nitrogen has an appreciable quadrupole moment [Q ~ 1.4 × 10-26 eSU cm 2 (6)] and is the major source of atmospheric line-broadening, any discrepancy between theory and experiment may possibly be bes! explained in terms ofa quadrupole-induced effect} ~' Carbon dioxide was chosen on account of its even greater quadrupole moment [Q ~ 5"2 × 10 2e. eSU cm2(6)], and argon and methane on the basis of their negligible quadrupole moments. It is thus hoped to explain the anomalous behaviour of atmospheric absorption in the submillimetre "window" regions by a study of water vapour absorption broadened by these four foreign gases. 2. T H E O R Y
To facilitate the theoretical analysis of the absorption measurement we must first emphasize the position of the two H C N maser lines with respect to the absorption transitions in water vapour (Fig. 1). At 29.712 cm 1 over 85 per cent of the absorption coefficient is attributable to transitions in excess of 3 c m - I from this wavenumber, whilst at
,i Ii )1 IO ~
JI f
IL ,i
i
I r ~f t
a,
1
fi i .!
, \\
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I "i
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,
,
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z
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,
30 WAVENUMBER
,l
,
,
] 35
<7 (Crn " l )
F I G . I. T h e o r e t i c a l s p e c t r u m o f air at 20°C w i t h a n a b s o l u t e h u m i d i t y o f 13.5 g / ' m t, s h o w i n g the
relative p o s i t i o n o f the H C N m a s e r lines, with respect to the a d j a c e n t w a t e r v a p o u r a b s o r p t i o n lines, 2
2~2oat25'085cm-X,32-~4oat30"556cm-1
42_~5
2at32'365cm-X,10-)2-zat32"951cm
1.
A study of submillimetre atmospheric absorption using the HCN maser
811
32-166 cm-1 the contributions to the absorption from the nearby transitions 1o --* 2 2 (32.951 c m - ') and 4z ~ 5-z (32"365 c m - 1)(8)are respectively ~45 and ~ 35 per cent. Hence a comparison of the absorption coefficient at these two wavenumbers will provide a measure of variation of the specified line-shape between the near and far-wing regions. The importance of such an analysis is enhanced by the observations in near infra-red work on HC1,19) that significant deviations from the Lorentz line-shape are only observed when absorption measurements are made more than 1 cm -~ from line centre. In order to theoretically predict the pressure dependence of these absorption coefficients we will first carry out a simple analysis, based on the most elementary line-shape, in order to define the expected ratio of the absorption coefficient at 337 pm(c%~7) and 311/am (c%11), /-) : 3(337/~311 as this is the most convenient way to consider the experimental results (see Section 3). We will then give a quantitative analysis in terms of a more complete line-shape, so that a comparison between the theoretical and experimental results may be made in terms of the molecular parameters of the broadening gases used in this work. 1. (i) Qualitative Analysis: We assume that the line-shape of a given water vapour transition (i --, j) may be given by a Lorentzian form :
O~.ij(0.)
Aij
A0.ij
0.if +A0.
=
(I)
where A~j is the line strength of the transition at wavenumber (a~) and is a constant for a given value of Po and the half width A0.~j is given by :
A0"ij = poAa'ij + P, Aa'i'~
(2)
where Po is the pressure of water vapour and Pl is the pressure of the broadening gas, both in torr, and Aa'i~ and A0.'i~are the pressure-broadened half-widths at 1 torr for water vapour and the broadening gas respectively. If we can now assume that : A0.ij <~ l a - 0 . J
(3)
then by inserting equations (2) and (3) into equation (1) we obtain the approximate absorption coefficient : O~iJ(0.) :
Ai: 7"[(0"- -
,
~ij) 2 (P°A0"iJ+ P , A 0 " i j )
,, •
(4)
We may now simplify this by replacing poA0"'~j by p'oAa'~} where :
Aa'~j
po':
(5)
where Po' is the equivalent foreign-gas broadening pressure of Po torr of water vapour. Inserting equation (5) into (4) we get : A ij A 0"'i'j .
e,j(0")- r r ~ 2 t P o
.
.
.
.
-epl~ = k~j(0")[po +p~].
(6)
8t2
W . J . BURROUGHS, R. O. JONES and H. A. G~Bm~!
Now if we consider the values of can evaluate the ratio :
eu(0-) at two wavenumbers al and 0-2 (i.e. ~ and a21 wc p
'~1 --
:~2
=
(0"2 -- 0-ij) 2
(al - o-ii)2"
(7)
The important property of this ratio is its independence of both P0 and p~. If we now extend the analysis to include a large number of absorption transitions then :
~ AijAalJ =k(a)[po,+Pl ] ~(0-) = (po' +Pl) .. re(a- aii)2
IS)
where aijAoij
from which it can be seen that the value of ~1/~2 is still independent of the pressures Po and Pl. Hence, by observing the value of the ratio p as a function Ofpo and Pl we can measure any deviations from the simple line shape [equation (l)], and relate these to the molecular collision processes involved. (it) Quantitative analysis. In order to make a quantitative analysis, both of the values ~337 and ~311 and also of the ratio p, a more exact form of the line-shape must be used. Moreover, we need to compare our results with the numerical predictions of some accepted model. The majority of the theoretical values of a(a) quoted here have been derived directly from the work of ZHEVAKIN and NAUMOV(3) who used the kinetic line-shape : ~0(0") --
4A ij
02 A0"ij
n
(0-2 -- 0"2)2 + 4 0 - 2 A 0 2 "
(9)
Two important points should be noted concerning this expression : (a) Equation (9) reduces to equation (1) if0-+0-ia _~ 20- so that for values o f f ~ 30 cm the difference between equation (9) and equation (1) for [0"-0"~j[ < 1 cm ~ is less than 3 per cent. (b) The simple analysis in the preceeding section is not altered if we use equation (% instead of equation (1) since equation (6) is still applicable if A0"u ~ [0--0-J. The reason that any quantitative analysis need be given is that despite the extensive theoretical work carried out by ZHEVAEIN and NAUMOV(3) their results are only in graphical form and hence the value of ~3~ cannot be derived directly from their work with any degree of accuracy. An approximate value of ~a,~ was obtained by using the values of ~(a) given by ZHEVAKIN and NAUMOV(3) in the adjacent window regions at 31-1 and 34-1 c m -1. The values of ~iy(a) at 32-166cm i and 31-1 and 34-1 cm -1 for the 1o -~ 2_ 2 and 42 -~ 5_ 2 transitions were then recomputed from the known line-strengths (4) using the Nz-broadened halfwidths given by BENEDICT and KAPLAN. (1 l) From these values the background contribution ~h due to all other transitions at 3 l-1 and 34"1 cm- i was obtained and by interpolation the value of this contribution c% at 32'I 66 c m - t was estimated, then the value of 0~311 was obtained by combining this value with the computed contributions from the lo ~ 22 and 42 --* 5 _ 2 transitions at 32"166 cm-1. The value of~337 c a n be obtained directly from the published results (3) as in the region of 29-7 cm ~ ~(0") is a slowly varying function of a. In computing ct31 ~ the theoretical
A study of submillimetre atmospheric absorption using the HCN maser
813
values of Aals for N2-broadening given by BENEDICTand KAPLAN are used/1°) To compute values of~337 and ct311 as functions of Pl we have taken the atmospheric values of ZHEVAKIN a n d NAUMOV (3) to be equivalent to p~ = 675 torr of Nz, since throughout their work they have assumed that (Aais),ir is 0"9 (Aai~)N2 for equal pressures. Thus by taking the value of ~(a) at 675 torr of N2 and from this evaluating the values of 0~337 and ct3~x for Pl = 0 and Po = 13-5 torr using a mean value of Aa~j of 9 × 10 -2 cm -1 (derived from BENEDICT and KAPLAN'S H 2 0 - H 2 0 broadening data) t~ ~ it is possible to derive approximate expressions for the p~-dependence of c~33 v and 0~311. These are (expressed in the form of a secondorder polynomial, see Section 4): ct311 = 63.61 +0-834pl - 9 . 9 × 10-Sp 2 db k m - 1 (10) ct337 = 11"45 +0"150pl db k m - 1 The presence of a negative p2 term in ct3~ ~ arises because the assumption in equation (3) is no longer valid for the transition 42 ~ 5_2 when p~ > 250 torr. For this reason the value of p is also not quite constant but varies from p=0"180+_0"018
at
Pl = 0 t o r r
to
(11) p = 0.196 ± 0 - 0 2 0
at
Pl = 760torr.
However, this variation is much less than is observed experimentally (Section 4) indicating that an even more detailed theoretical consideration is necessary to account for the observed results.
3. E X P E R I M E N T A L
DETAILS
The equipment used for this work is shown diagrammatically in Fig. 2. The 2.3 m CW operated maser had a plane-parallel mirror cavity and the radiation was coupled out through a 6 m m diameter hole in the centre of one mirror. The power output of this system was approximately 0.1 m W at 337 iLm and 0-01 m W at 311 Itm. The CW radiation was modulated at 13 Hz by a mechanical chopper and the output of the monitor and cell detectors were both passed through narrow band filters and their relative phase adjusted so that both signals were in phase (Fig. 2). The size of the two signals was then compared using a Tektronix (1A7) differential amplifier; and a null condition obtained by attenuating the signal from the monitor detector, which was always greater than that from the cell detector, using a voltage dividing box. The attenuation could be measured to four figures, though in practice only three figure reproducibility was achieved. The value of the attenuation of the monitor signal required to obtain the null condition was measured as a function of the absorption path length, which was varied from 10 m to 50 m in 10 m increments, thus enabling the absorption coefficient to be determined. In the case of the weaker radiation i.e. 311 pm, the dynamic range of the attenuation of the monitor signal was of the order 103 with a minimum signal to noise ratio of 10. This means that accurate measurements of the absorption coefficient could be made up to 1000 db k i n - 1.
814
W..1. BURROU(ilIS, R. ( } . . l o x l S a n d It. A. Ol BIIll
PUMP l
~1~
2;2
13 Hz DIELECTRIC CHOPPER BEAM-DIVIDER ~
J [ ~ A ' A "X PRESSURE
NI
Q2) GAUGE
t2OOV
GOLAY / DETEOToR ] 13Hz ] [FILTER J •
. i 13 Hz i L FILTER ]
FOREIGN GAS
r V~'~Ri;B LE /
IATTENUATORj ~-
-
"
....
~-DIFFERENTIAL / AMPL F ER I / <
.
.
.
.
[
NULL
SIGNAL
[l{;. 2. S c h e m a t i c d i a g r a m of the e x p e r i m e n t a l syslem. The m u h i p a s s cell ,<'.as hL'alcd to 5{}' (' h., ineaT]s of healing tapes. The cell din]cnsions arc 3 111e 40 cm arid lhe nlit'l'or,, ~', :lilt] A,I , ;il-e I q cn] in d i a l n e t e r atld J]2 is 20 c m in d i a m c t c i ; all 3 illillOlS h a v e a 2"5 Ill r:.tditl>, O1 ctlrValtllc [ h e ca'~iiy a d j u s i m e n l on the m a s e r a l l o w e d 337 Hm a n d 311 ira1 r a d i a l i o n to be o b t a i n e d a h c r m i t c l y b ; mean-, of t u n i n g the cavity lenglh.
The Inultipass W h i t e cell was a 2.5 m system c a p a b l e of giving path lenglhs flom l/} m to 60 m in increments of 10 m. The metal cell could be p u m p e d d o w n to 0-1 l o n using a r o t a r y p u m p or pressurised to lO00lorr. Since {hc r a d i a t i o n froln the maser ~xas not focused in line with the surface of ,~12 but wits allowed l,,} diffracl from the m a s e r H p c F I t u c to fill M , , the focussing of the r a d i a t i o n within the W h i t e cell was not perfect, l t o w c x c r . since the Rayleigh distance for the exit a p e r t u r e is - 12 cm an a p p r o x i m a t e focus can he formed in the region of the front surface of the m i r r o r M e. F o r this reason, the geometrical losses did not exceed 15 db k m ~, and the system was regularly c a l i b r a t e d so that 1]it m e a s u r e d a b s o r p t i o n coefficients could be corrected for these s y s t e m a t i c losses. [ urthermore, it should be noted that these losses were very much less than most of the wducs of thc a b s o r p t i o n coefficients m e a s u r e d (Fig. 3). The e x p e r i m e n t a l technique was, after c a l i b r a t i n g the cell under v a c u u m c o n d i t i o n s , to fill the cell with water v a p o u r to a pressure of t3 to 14torr, in the case of the r o o m t e m p e r a t u r e ( T - 20°C) studies. The p r o b l e m of a v o i d i n g changes in water v a p o u r conc e n t r a t i o n d u r i n g o b s e r v a t i o n s , due to a d s o r p t i o n o n t o the walls of the cell, was largely o v e r c o m e by t h o r o u g h l y wetting the system. "It was found that m a i n t e n a n c e of a relative h u m i d i t y of a b o u t 80 per cent p r o d u c e d a stable c o n d i t i o n t h r o u g h o u t a range of b r o a d e n i n g gas pressures. As will be seen later, the values of ~311 are in quite close a g r e e m e n t with theory, and hence can be used to m o n i t o r the water v a p o u r content. However, d u r i n g most of the work it was found that within e x p e r i m e n t a l e r r o r the water v a p o u r presstlre r e m a i n e d c o n s t a n t if the initial c o n d i t i o n s a l r e a d y q u o t e d were obtained. O n e p r o b l e m with having such a high h u m i d i t y in the cell was to ensure that no water c o n d e n s e d o n t o the m i r r o r s as this would have a m i s l e a d i n g effect on the results obtained. This was a v o i d e d both by
A study of submillimetre atmospheric absorption using the HCN maser
815
checking that no condensation was visible and by observing that no apparent change in absorption took place on heating the mirrors.
8oo
++/EH4 /
/
Na/
/
+
/
//
70C
/~//311}J
600-
t
/
i
E 500
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40C
°
¢
°
/
0
g aoo<,,
0#
20C
-
//%-'~"
I~
Na
9.9"~
CH~
au ~ 1
,oo
0
200
400
600
800
I000
Pressur~ p, (torr) F'I(;. 3. Results obtained for N 2 and CH,, using 13.5 tort (Po) of water vapour, and varying the pressure (Pl) of N2 and CH4.
The absorption coefficients at the two wavelengths were measured for a range of foreign gas pressures (Pl) and from the values of c(33v and ~(311 obtained the ratio P(Pl) could be recorded. Examples of the measured values of 0~337 and ~31~ for N2 and CH4 are shown in Fig. 3. To check that all the observed absorption was due to water vapour broadening alone, the absorption due to the pure broadening gases was measured and
816
W.J. BURROtJGHS, R. G. JONES and H. A GEBBIIq
found to be negligible for all the values of Pl considered. This result indicated that the amount of water vapour remaining in these dried gases was negligible and showed that collision-induced quadrupolar absorption in the quadrupolar gases (9"1°) was insignificant. This agrees with the result spectroscopically obtained for CO2 (1°) in that the absorption due to 400 torr of pure C 0 2 should be ~ 5 db km i, i.e. less than the errors quoted for this work (Section 4).
4. E X P E R I M E N T A L
RESULTS
Using the techniques outlined in the previous section, a series of absorption coefficients was obtained using argon, methane, nitrogen and carbon dioxide as broadening gases. The results were fitted, by means of a least squares analysis, to a second order polynomial of the form" c~ = a l + b l P l
+tip 2
(12)
and the values of the coefficients a~, bt and Cl obtained when the results are normalized to an absolute humidity of 13.5 gm 3 are given in Table 1.
TABLE I
bl(dbk m t t o r r
l)
Standard error in,~ (dbkm t)
337 337 337 337
A N2 CH4 CO 2
27"50 27"64 26"98 27"95
0'0514 0"179 0"167 0"493
0"50 3"4 - 1"3 6"8
4"47 5-35 358 6"73
311 311 31 I 311
A N2
77"00 74-59 70-61 74"31
0"253 0"834 0"91 I 1-920
4"2 2"8 12"7 71"0
7"44 12"26 13-76 861
CO2
1)
2)
Gas
CH 4
al(dbkm
clldb k m 1 torr xl05
2(pm)
From these least squares fits the ratios (p = 0 ~ 3 3 7 / ( x 3 1 1 ) as a function of pressure have been computed and are shown in Fig. 4. The standard errors in Table 1 indicate that the uncertainties range from + 5 d b k m ~ at low values of a to _+20dbkm ~ at large values of c~, and this is reflected in the increased errors in the values of ~3~ at high values of px, though as proportional errors they are in general smaller than those occurring in c%37, and the latter tend to provide a measure of the upper limit of the accuracy obtainable. The values of c~3~ and c~337 have also been measured as a function of temperature 7" and pressure Po in water vapour alone. The cell could be heated up to 50°C, and P0 varied from 0 to 40 torr. From these measurements it was found that both ~3av and ~31~ showed a close agreement with a simple p0z dependence (Fig. 5), and from this that p is independent of P0- The temperature dependence of p is shown in Fig. 6.
o o
~~ ~K
0 0
0 '¢
0 ~
0 ~
0
0
0 0
o
¢)~,-
cn
o ~0
: ' - ,.b,
I
I
u'~,
I
I
÷,¢ I I
//
/
,,
~')
~
j
/
i / I
iI
i//
..o"
0
0
o
o
1
¢
/ /'
I1÷
,.~
0
o
6
:
l° 0
6
IL E ~ ._
t:~lj ~
0
> .~_~
W . J . BURROUGHS,R. G. JONES and H. A. GEBBn~
818
40
\1 O
.35
'30
.25
-20
J 2'o
3'o
do
s'o
T (°C) - - ' -
FIG. 6. The temperature dependence of the ratio p
5. D I S C U S S I O N
= ~337/~311
OF
obtained for pure water vapour.
RESULTS
(i) Qualitative analysis. It is immediately obvious that these results, especially the ratios of p = 0~337/~311, do not agree with those predicted on the basis of the simple theory. The discrepancy between theory and experiment can be qualitatively explained in terms of two anomalous contributions : (al A background continuum due to dimeric water. If such a contribution exists the initial anomalous drop in p which occurs with all the gases as Pt is increased (Fig. 4) can be explained if we assume that the dimer contributes a pressure-independent attenuation ~e (this assumption will be justified in the quantitative analysis of the temperature study). The ratio is then given by P(Pl) -
0~337(Pl) + 0~a
(13)
where ~ 3 7 and c~;1t are the contributions that may be attributed to monomeric water vapour, and me is a pressure-independent, slowly-varying function of frequency so that ea at 337 pm can be assumed to be approximately the same as en at 311 pro. Then p(p~) will tend asymptotically to p' = c~37/c~;11 with increasing Pl, as found for A and CH4 (Fig. 4). This property of the dimer is in agreement with certain theoretical predictions, ~14) and also spectroscopic analysis of an atmospheric feature observed at 7.5 c m - t / l 5,16)
A study of submillimetre atmosphericabsorption using the HCN maser
819
Further qualitative information concerning the spectrum of this dimer may be obtained from the poZ-dependence of~337 and ~311. If we consider equation (4) for pure water vapour we obtain : A~j O(ij(O') -- 7[(0" -- O'ij) 2 P°AtriJ"
(4a)
Now in the case of the monomer Aij is proportional to the number of absorbing molecules per unit volume and hence to Po and therefore : c~(~r) = ~ ct/j(~r) = k(c0p 2.
(8a)
This is just the dependence that has been observed in Fig. 5 but if we are postulating the presence of a dimer the concentration of which is dependent on p(](16) (i.e. A~j for the dimer is dependent on the number of water molecules per unit volume squared) then ~d(a) = kd(~Y)p3.
(14)
The absence of any appreciable p3 term in the observed absorption must be taken to indicate that either the lines are so numerous or the line widths are so great that it is improbable that pressure-broadening of discrete lines will be observed or that the dimer does not exist. Since the temperature dependence of p (Fig. 6) is consistent with a relatively strongly bound dimer (see next Section) it must be assumed that the failure to observe pressure broadening of the dimer features is due to a multiplicity of absorption transitions. This result would appear to be consistent with the fact that low energy vibrational states ( ~ 100 c m - 1 ) ( 1 4 ) will have appreciable populations at ~ 300°K and hence the pure rotation spectrum will be exceedingly complicated and effectively a continuum at the values of Po used. It is not considered plausible that the existence of a continuous background can be explained in terms of a short lifetime, which would result in broad absorption features, as such a lifetime is not easily reconciled with the value of the binding energy obtained from the quantitative analysis of the temperature study. (b) Pressure-broadening by non-dipolar gases shows interesting properties. First, the gases without quadrupole moments (A, CH4) show a variation of p with Pl consistent with the form: c(337 +~d
(13)
P - - ~ 3 1 1 -~-O~d
where t 0~337 =
k'l(P'o+Pl)
t
t
!
o~311 = kz(Po + P l ) and r
/,'1
P =~.
If one evaluates c(d to satisfy this condition one finds (Fig. 7) : c(a = 17.0+5.0db km -1
(6a)
820
W.J. Bt'RRI)UGHS, R. G. JONES and H. A. GI!BBK
which leads to P'
k;
k', = 0.194+0.010.
The value of p' is in good agreement with the theoretical value given in equation (Ill. Thus, it can be seen that apart from the contribution due to dimeric water vapour l~,) the pressure-broadening effect of nonquadrupolar gases is, within experimental error, in agreemenl with the theoretical predictions based on the standard line-shapes. Secondly, the quadrupolar gases (N2 and CO2) show effects that are Pl dependent, but can be explained only if we replace ~,~3: and ~3~1 in equation (6a) by the expanded form ~;~v -- k'l(P; +P, )+clP~
(6b)
~'311 = k 2 ( P o + P l ) + c z p l where ('1 and c 2 are constants at constant temperature. For the pressure range considered in this work
P = k'2 k'2 P{)q-Pl
l(2+1(2 pl
since
ki(p'O +Pl ) >_ clp~ k2(Po +Pl) >~ c2p 2.
(15)
Hence if we p l o t / / a g a i n s t p~ we should obtain a set of straight lines (Fig. 7). The displacement of the line in the case of CO2 is possibly due to adsorption of the gases onto the walls of the cell. The/)2 term must arise as a result of 3-body collisions, revolving two molecules of the broadening gas and a single water vapour molecule. As was noted in Section 3 this absorption could not be explained in terms of collision-induced absorption in N 2 and CO2 alone 112"131 as at the pressures considered this is negligible, as was shown experimentally !Section 3). The existence of such an effect is unexpected at such low pressures, and hence indicates that the influence of dipole-quadrupole multiple collision effects may be of greater importance than previously anticipated and should be given further theoretical consideration. (ii) Quantitatice amdysis. (a) The dimeric contribution :~a at T = 20°C has already been introduced in the previous analysis in order to evaluate the pl-dependence of p' tFig. 71. If a similar analysis is carried out on the values of p obtained in the variable temperature study the values of 7a that are obtained can be plotted as loge :~a against T - ~ (T in °K) at constant pressure as shown in Fig. 8. This is an Arrhenius type plot from the gradient of which the value of 5.2+ 1.5 kcal tool 1 of the binding energy of the dimer is obtained. This value is in agreement with the submillimetre spectroscopic work {l~'~ and also with the theoretical prediction of VIK rOROVA and Zm~VAKINJ~4-~ (b) In order to make a quantitative analysis of the values of c%3v and :z,~ obtained experimentally we must compare them with those obtained theoretically in section 2(ii)
A study of submillimetre atmospheric absorption using the H C N maser
821
0
,
i
I O
0
O
0
~
Ol
4. eb
,
•
0
t-
0
~
Q
P~o ~5Ol !
4-
i
1
~g 2~
0
~
o
~
2.=
I t~
0
~
0I'N
6
6_.~.
6
6
6
I:::u
822 using
W.J. BURROUGHS,R. G. JONESand H. A. GEBBIE
N 2 as a broadening gas. For ct311 the theoretical value was : c(311 = 6 3 . 6 1 + 0 . 8 3 4 p l _ 9 . 9 x 1 0 - S p 2 d b k m
1
as compared with experimental value : c%11 = 74"59+0-834pl +2"8 x 10-5 p~ d b k m - I The coefficients show good agreement with the results already obtained in the qualitative analysis. The difference 10-98 db kin- 1 between the constant terms is, within experimental and theoretical error, in agreement with the value ofctd evaluated for 7-' = 20°C. The closest agreement is for the coefficient of the Pl term, indicating that the theoretical values of the simple pressure-broadened line-widths Aaij are substantially correct. This result is a little surprising as work on the 10.85 and 12.67 c m - 1 lines(17 ~8) suggests that under atmospheric conditions the theoretical values of Aa;i are up to 20 per cent low. It should be noted that any discussion of such agreement should be qualified by the fact that all the coefficients are dependent on the absolute measurement of P0 which was accurate only to the order of _+ 10 per cent. Moreover, the ratios of the Pl terms for the other gases do not show such agreement (see later). Finally the discrepancy between theory and experiment in the p2 term corresponds to the suggested 3-body collision effect already discussed. Similarly for 5337 we get : Theory:
~337 = 11"45+0"150p1 d b k m
1
Experiment :
ct337 = 27-64 +0.179 Pl + 3.4 x 105 p~ db kin- 1.
The numerical differences here can again be explained in the same manner as for the ct311 result. It should further be noted that the difference in c~ (the p2 term) in both cases is of the same order, hence justifying this assumption in the earlier qualitative analysis [equation (15)]. It is not possible to extend the analysis to the other broadening gases, as no theoretical work exists on the broadening coefficients of these gases with water vapour in this spectral region. Furthermore, in the case of CO2 the complication of adsorption of both H 2 0 and C O : onto the walls occurs, and explains the large negative p~ term in ~3~1 for this broadening gas. Thus the only results that may be obtained from the coefficients must be in terms of the relative magnitude of these for the various gases and also the ratios p and p' as has been done in the qualitative analysis. We note that : 1. There is good agreement between the values of ~337 and ~311 obtained using CH4 and those predicted on the basis of simple N2-broadening apart from the background contribution of ~ . The general agreement of the form of the absorption coefficients again supports the hypothesis that for non-quadrupolar gases there is close agreement between theory and experiment. 2. The ratio of the coefficients of the p~ terms in the cases of N2 and CO2 broadening, derived from the gradients ofp' (Fig. 7) is 4"2 and does not equal the ratio of the squares of the quadrupole moments (Q). This would appear to indicate that a simple Q2 dependence of the 3-body collision effect is not an adequate explanation, but the accuracy of this ratio is such (Fig. 7) as to make any definitive comment on the nature of the collision effects exceedingly difficult.
A study of submillimetre atmospheric absorption using the HCN maser
823
3. The ratios of the coefficients of the p~ terms of CO2 against N 2 and of N 2 against A are considerably greater than would be expected on the basis of microwave broadening results, tt9~ This indicates that there is also an excess quadrupole effect in the Pt term which is in agreement with other broadening results in the millimetre and submillimetre region, tt7'~8) This result also agrees with microwave work on foreign gas broadening in HC1. (7) In this work, the ratio of the Pt terms for N 2 and CO2 broadening was 4.58, 20 c m - ~ from the nearest HC1 line. In our results the ratio of these two terms is 2.76 at 29.7 cm-1 and 2"30 at 32'2 c m - i , whilst for microwave results in close proximity to the 6.12 cm-1 water vapour line it is 1-60.tt9) This increasing ratio with distance from a given absorption feature indicates an excessive absorption due to two-body collisions and possibly a broad-band quadrupole collision-induced absorption of the type proposed by FRENKEL. (2°) It should be further noted that throughout this work the effect of higher multipole moments, octupole and hexadecapole are assumed to be negligible. This conclusion is not entirely supported by FRENKEL (20) but we feel that the difference between the values of p' obtained for N 2 and CH 4, and the marked similarity in p' for CH4 and A clearly indicate that the octupole moment of C H 4 is not making a significant contribution to absorption effects in the submillimetre region. However, our results do not eliminate the possibility that in the very far wings of pressure broadened dipole rotation lines (7) the effect of the higher multipole moments is not negligible, t2°) CONCLUSIONS We have confirmed the existence of an extra contribution to the usual Pl dependent broadening coefficient due to quadrupolar gases. This is complementary to previous microwave absorption measurements. (7'x9) We have also observed absorption due to two distinct and previously rarely considered effects. (i) The presence of the dimer of water vapour which results in a background contribution to atmospheric absorption. This appears to be of considerable importance in the "window" regions and can explain approximately half of the excessive absorption observed in these regions. (ii) The existence of a significant quadrupole-dependent 3-body collision effect, which was previously considered to be negligible. This effect accounts for most of the remaining anomalous absorption in the "window" regions. We may therefore conclude that these results provide a qualitative explanation of the excessive absorption in the submillimetre atmospheric "window" regions.
Acknowledgements--We wish to acknowledge the valuable assistance of Mr. D. W. E. FULLERin the preliminary stages of this work. We would also like to thank Dr. J. CHAMBERLAIN,Dr. C. C. BRADLEYand Dr. G. BIRNBAUM for helpful discussions. Note added in proof--We have recentlyreceivedtheoretical calculationst2l) of ~t337and ~3t ~from Dr. R. J. EMERY of Queen Mary College, London that remove certain errors in earlier works, t22) This gives a slightly different value ofp which is lower than used here i.e. p =0"157 at Pl =0torr p = 0"173 at Pt = 760tort.
(lla)
These valuesdo not alter the analysispresented here, but add support to our conclusionsconcerningthe discrepancy between theory and experiment.
824
W . J . BURROUGHS, R. G. JONES and H. A. GEBB1E REFERENCES
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