Microwave dispersion and absorption for a rotational transition in methanol

ClfEMfCAL PHYSICS LETTERS

Voluruc 38, number 2

MlCROWAVE DiSPERSiQN AND ABSORPTION FOR A ROTATIONAL TRANSITION IN METHANOL

Received 17 October 1975

A metbad for dispIaying 3 micsowavc rotaticmal transition in the dispcrsioll xuode is described and applied to the J = 4 +- 3, K = -1 + 0, E-&W transition in methanol. The effective linewidths in the absnrption and dispersion nMes z.110 the SCIIIIC and dvjp = 18.9 f 0.3 hIIIz/torr at 297 K.

The application of a microwave electric field of ampiitudc “0, frequency o, and wave number k, C = fo

COS (of

to a gaseous

- kZ)

expression

,

for the ord&ary

absorption

coefficient

f2]

sample induces a macroscopic palarizaIt occurred to us that it may he of use to check these expressions and recently derived theoretical

tion P=P,cos(wr

42) - 4 sin(wt -kz) ,

with 311in-phase component P, and an in-quadrature component Pi. FIygarc and his co-workers [ I] have shown that in a conventional microwave spectrometer with a sample cell in the microwave line the microwave electric field at the detector (z = 0) is given by E = Eo COSWt + (?TWf/~) (Pi CQSWr f P, sin az) )

where I is the length of the sample cell, c is the velocity of the radiation, and the other quantities ore 3s pEcviously dekined. The typical microwave detector is an

approximately square-law device followed by a lowpass filter. As a consequence of this fact and the fact that in most casts e. % Pi or P,. the detector current is given by i = @[ci + (27T4C)

Co Pi]

,

is a constant. The chang in ~rptal as a result of the presence of the sample is

wficie

prom these equations it is apparent that absorption by or emission from the sample gives rise to B ~ig~?d which is proporiiona~ to the irl-quadrature component of the polarization. Further analysis leads to the usual

p

hi = (2T@Wl,C)

EOPi *

current

expressions for pr and Pi by arranging the microwave system such that the change in crystal current as a result of polarization of a sample would be proportional to the in-phase component P,. The in-phase component of the polarization of the sample is related to the dispersion,

the

so what we have done is to arrange

microwave system such that the spectrometer

records the spectrum of the dispersion rather than of the absorption. The purpose of this RMC is to describe the microwave system and our comparison of absorption and dispersion spectra for the J= 4 f 3, K = -1 +- 0, E level transition in methanol.

2. Experimental

details

To convert an absorption microwave spectrometer to one for recording dispersion spectra it is only ncccssary to add a bridge arm which bypasses the sample cell. The bridge arm must contain an a ttenuator and a phase shifter and rejoin the main microwave 297

fine just before the detector. With this system the microwave field at the detector wifl be of the form E = q, coswt f eucos(wr - cjj

effects from the Siark components and the microwave frequency WE scanned. The Sa (v) values, the amp]& ficr output in the absorption mode, were fit by least squares to a Lorcntz line shape, s:, (v) = ---’ (Y

where eR and rparc the ~mpiitu~ie rind relative: pilitsc, rcspcctivciy, of the contribution to the field from the bridge arm, and the other quantities are as previously defined. If the phase is chosen to satisfy the CX[lWSSiOIl co3~

and

the

= -qJe~

,

if CL3> EQ, then the f?eIrt 3t the detector takes fm-ll

and

.JI:,(Av)~ - --- f D . v*y

+ (Av)”

In this expression p. is the line center, Av is the fine width, and Aa is the lint height. The micrownvc field in the cell was kept low enough to atsure that iinebroadening soturntion effects were neglligiblc, To obtain spectrn in tl~c dispcrsiolt rnorlc the attenuation in the bridge arm \viS reduced to some value such that erS > Q. The microwave frcqucncy was then set to v. and the phase shifter WDSadjusted until S:i(~o) = R, where S, is tI1e ar~2plifrcr output in the dispersion mode. This n~cthod of adjustiag the phase was ndoptcd because it may be shown by sofulion of the differcrltial equntiuns for Pi and Pr [3] or by the use of Kramers-Kronig type relations 14) that if Pi is lorent;r.i:m,

Therefore, ,y&g

=

_ .-

we expect that

..cw_ _??__ f B

*

(v-vo)’ -f (Av)~ To test these expressions P~ckartl Model 8460A an K-band (26.5-40.0

WC

used :1Hewlett--

l??icr~w~v~ spcctromctcr

witfl

Wz) system :ind il microwave bridge. This instrument is Stark-rnoduiatcd at 33.3 kHz and the s~~tr~~l~l~t~r output is obtained from a lock-in amplifkr operating ilt this frcc~ucncy. The voltage at the output of the nmplif&r IS proportional to Ai; that is, S(v)=GAi+-N, where S(P) is the v&age af the output of’the amplitier, G is a griin Victor, and B is the amplifier voltage in the absence of 3 sample, For these expetimerits the microwave frcqucr?cy of the spcctrornctcr WE c~~ntro~l~dby a Digital ~qujp~l~i?t ~~rpo~tion PDPEI/Ecomputer and the output of the lock-in amplifier was rcr?d by the computer and stored for later analysis. To collect spectra i?l :he absorption mode (cB = 0) the Stark field was set high enough to eliminate 293

The a~l~plitl~d~s~~ znrf .4d are cquai only if eB = CQ,. In any c3sc, however, Sd(flo) = U. After adjustruerlt of fiD and the phssc, the spectrum in the dispcrsioa anode was recorded and frt by Icsst-squares rc~ne~lent ofp(), .Lw,Ad.andB The gas pressures in dais work were measured by II~IIS of an MKS Baratron type 77 pressure meter with ~1type 77Hl pressure-measuring head. The rnctI~~~lu1was obtained from J-T. Baker {An~yti~l Grade purity >99.9%) and used as reccivcd.

3. Results and discussion Spectra were recorded in the absorption ancl dis-

persion modes at several pwssurcs for the transition in methanol which occurs at 36169.2 MNL. The microwave region from 36 t 59 MHz to 36 170 MHz was scanned at 100 kHz intervals. AR oscilfoscope trace of the recorded data points of u typical spectrum takccn in the dispersion mode is shown in fig. 1.

Volu1nc 38, number 2

CHEMICAL PHYSICS LETTERS

I March 1976

WC have taken wit11 rcccnt measurements of linewidths in the absorption mode for the J = 2 c- 1 transition in OCS [ 51. The purpose was to provide a precise test of the theory. However, it soon became apparent that measurements in the dispersion mode arc considerably less satisfactory than absorption measurements. There are at last two reasons for this. First, even with a well-rnatchcd microwave system there is a slight

Fig. 1. Plot of spcctrometcr output in the dispersion rnodc vasus frcqucncy for ihe / = 4 <- 3, R 7 - 1 6 0, Iz-stntc transition in mcth~~ol. 11x frcqucncy spxing bctwecn the points is 100 kIlz. 2OOOf

-7

-T _-

r

-7-

-r

-.

7- -

r

-T--‘T’T

1600 -

.r _ 0

L

_,___

20

A

_

L_.L-_L~I~ 40

GO

80

variation of the phase of the radiation in the bridge arm rclativc to that in the sample arm :IS the microwave frequency is varied. Second, the u--vu factor in the relation between P, and Pi causes the effects of nearby transitions to be greater in the dispersion mode than in the absorption mode. As a consequcncc of these difficulties, WC had to be satisfied with the cornprison shown in fig_ 2. Nevertheless, the results were gratifying; it is apparent that within the estimated precision of tilt measurements (+ 3%) the linewidths obinined in the two modes are the same. Also, from the data in fig. 3, Av/p = 18.9 k 0.3 MHz/torr at 297 K for the J = 4 <- 3, K = -. 1 + 0 E level transition in methanol. In fig. 2 the intercept of the least stpares line is 62 f G ktiz. Ordinarily, in a plot of lincwidth versus prcssurc the intercept is a measure of wall collision broadening. However, in this case, as a result of the rapid Stark effect, the intercept is more probably a mcasurc of the zero-basing of the Stark squxe wave. A zero-basing error of several tenths of ;1 volt per centimeter would be sufficient to broaden the iinc to 62 kllz.

100

p/mrorr I:& 2. Plot of lincwidtli VerSuS prCSSUre for the J = 4 ‘- 3, # = -1 c 0, I+state tmnsltion in nxthnnul. ‘1%~C~O~FC~ are for rncasLIrCnv_mts in the dispersion mode, the circles in the absorption mode. ‘lb2 wlid line is from ;I le:lrt-squares fit of the dntn.

Fig. 2 is a plot of linewidths, Av, ohtidncd from Icastsquares fits of the data, as :I function of the gas prcssure. Our original intent was to make these mcasurzIIIC’II~S with tllc smnc care :1nc1attention to detail thzt

References [I [ .I.(:, RfcC;urk, ‘T.G. SCIIIII~IL and W.11. Flygarc, J. Chcm. Phys. 60 (1974) 4181. [a] J.C. hIcC;urk, T.G. SchnxrlR :md W.H. Fly~:rre, Acivan. Chcm. Phys. 25 (1973) 1. [3] li.11. Scbwendtm:m ;lnd H.M. Pickctt, J. Chcm.

(1972) 3511. (41 C.P. Slichtcr, Principles 0f’ni:ignetic

r~SWlilllW

I’hyS.

57

(Ilarpcr

and Row, New York, 1363). [S] R.A. Cruswcll, S.R. Brown und R.I!. Schwendcman, Chcm. I’hys., to bc publishccl.

J.

299