- Email: [email protected]
Energy ordering of the B and C states in XeCl, XeBr, and KrCl, from temperature dependence of emission spectra
Volume 72, number
CHEMICAL
I
ENERGY OZDERiNG FROM TEMPERATURE Joel TELLINGHUISEN
PHYSICS
OF THE b AND C STATES IN XeCI, XeBr, AND KrCI, DEPENDENCE
CF EMISSIGN SPECT%
and Mark R. McKEEVER
*
Department of Chemistry.
Zlnderbrlt Umrersrty, Nashzvlle. Tennessee 37235.
Recervcd 31 January
m final form 29 February
1980,
15 May 1980
LETTERS
USA
1980
Inert-gas hahde emtssron spectra from a Tesla drscharge are studred as a functron of pressure and temperature From the temperature dependence of the mtimte pressure ratro of broad-band (C - A and B - A) emrssion to B - X emisston, the energy separattons, TeC - T eB, are found to be -130 cm-t (XeCI), -80 cm-’ (XeBr) and 375 cm-’ (KrCI). Estrmates of the (C - A)/(B - X) spontaneous emrssron branchmg rattos agree well with thcoretrcal predtctrons
1. Introduction The discovery and development of the Inert-gas halide lasers over the last five years has inspired much basic research on the spectroscopy and kmetrcs of these systems. One question of recent Interest IS the energy ordenng of the two lowest ron-parr exerted states m the IgX molecules [l-6 j _These states are commonly labeled 3 and C by experimentahsts [7] and have Hund’s case (c) designahons S2 = l/2 and z2 = 3/2, respectively Detarled theoretical calculattons [6,8,9] predict these states to have practrcally the same electromc energies (TeB and T<), with C lying slightly higher than B. However experimental compansons of total spontaneous emissron in the broad C + 4(3/2) band with that in the sharply peaked B + X system indrcate that C hes about 600 cm-* below 9 m XeF [l-3,10] Thus result is supported by studies of XeF laser performance as a function of temperature, which show that the B + X laser unproves as the temperature IS increased to ==SOOK, whrle the C + A laser operates better at lower temperatures [ 11,121. Relative mtensrty measurements for other IgX species [2,4] suggest that the reversed ordermg may be a general feature of these molecules, although the Indicated separations for the other igF l
Present address: Photo Products Department, E I du Pont de Nemours. Inc. Towanda, Pennsylvama 18848, USA
94
and IgCl specres are less than the 600 cm-t value obtamed for XeF. With the exceptlon of the temperature-dependent studtes of XeF laser performance, all the experunental evrdence for the reversed ordermg of the R and C states comes from relative intensity data at a single temperature (300 K), interpreted with the aid of the theoretical estunates [8,9] of the (C + A)/(C + X) spontaneous emission branching ratio. While the evidence is overwhelmmgly in support of the near degeneracy of the B and C states, the splittings, & = Te TeB, and indeed the ordenngs deduced in these studies could be in error rf the theoretrcal branching ratios are not correct. Also, the theoretical calculations Suggest that the B + A( l/2) transition has appreciable mtensrty m the non-Iluonde IgX molecules, and this transttion has been clearly identtfled ln some IgGr and IgI molecules [ 131. In the IgCl molecules the B + A and C + A transitions overlap so badly in the h&-pressure spectra as to be unresolvable (see below). Stdl the B -+ A contnbutlon to the broad-band emlsslon must be somehow taken mto account to avoid systematrc error in the resultant AE values. To address the above mentioned deficiencies, we have investrgated the temperature dependence of the relatrve intensities for broad-band (B + A and C + A) emission and B + X emrssron m XeCl, XeBr, and KrCI. The expenments utilize our thermally controlled Tesla discharge [14,15], operated near 360 K and
800 K at pressures in the 100-750 Torr regrme. In the data analysrs the C + A transitron is taken into account. and experimental estimates are obtamed for both the energy separation & and the spontaneous emission branching ratio, A, = AC _ A/‘1 B _. X_ The results for AE bear out the earlier indications of reversed B/C ordenng m XeCl and XeBr, but yield a “correct” ordenng m KrCl.
2. Theory
kc-(+kQc
WIB)_
= k&kCB
= Keg = exp (-Ae/kT),
(4)
where Kq is the equihbrium constant for the process, lg( M) + IgX( B) * Ig( hl) f &X(C), and the second approximation is obtained by neglecting any differences m the rotational and vrbrational partition functions for the B and C states. The Infinite-pressure ratio of spontaneous emission intensities (quanta/s) in the C + A and B * X transitrons is 1, = [I(C + A)/I( G * X)],
We revrew bnefly the steady-state kinetrcs scheme whrch is pertinent to the data analysrs [ 1,2] _Stnctly speakmg the Tesla drscharge is not a steady-state source [ 151. However one can readdy show that the relative mtensrties obtamed from a transient source wrll equal those obtamed m steady state in the hrghpressure hmit. For the decay of the exerted states we mclude spontaneous emrssron, colhsional quenchmg, and collisronal couphng via the buffer gas. Representmg the B- and C-state concentratrons and the buffer gas concentration by B. C, and Al, respectively, we have in steady state,
kg-($
15 hfay 1980
CHEhlICAL PHYSICS LEI-I’ERS
Volume 72, number 1
+kQs bf + k,&f)B
+ k&fC
= 0,
(1)
III + k&f)C
+ k&fB
= 0,
(2)
in which the quenchmg constants are denoted kQB are kcB (for C -, R) and kqc, the couphng constants and kg=, the total radrative decay rates are 7;’ and 7:‘, and the productron rates are k, and kc_ (The production mechanism in our drscharge IS not understood m detarl, but both the broad-band and B + X intensities depend only weakly on total buffer gas pressure for the discharge mrxtures investigated here; hence the production rates are approxrmated as independent of hf_) Solving for the concentration ratio, we obtun
A body of accumulated data indicates that for hl = He, Ne, and Ar, kQB = kw
=(AC_.A/A~__X)(~/&,,
=+exp(-Wk’l?.
(5)
Thus If I, IS known at two temperatures, one can determine AE and the branching ratio A, from AE = kT1 T2(T2 - T,)-’ In Ar = (T2 - TI)-‘(T2
In(lr2/lrl). Infrz - Tr hfrl).
(6) (7)
In the experiments we measure the total broad-band emasion, which includes a contribution from the C + A transition. Hence the desired I, values are obtained by subtractmg the B j A contribution, I, = [f(broad-band)/f(B
+ X)],
- A,_,/A,_x
For XeBr we are able to obtain an experimental estimate of the branching ratio B, in eq. (8) from an approxunate resolution of the broad-band emission into the two components. However for XeCl and KrQ we must fall back on the theoretrcal estimates of this raho. In all cases the uncertainty in B, represents a srgnificant source of error in our determination_
3. Experimental
spectra
For our spectroscopic source we used the Tes!a discharge described m detll elsewhere [15]. Spectra were recorded at two temperatures - “room-T” and 500°C - giving estimated heavy-body discharge temperatures of 360 K and 800 K, respectively [ 14]_ The emission was dispersed through a McPherson model 218 0.3 m monochromator and detected with a Hammamatsu R456 photomultiplier. The average dc current was measured with a Keithfey picoammeter and
Volume
72. number
1
CHEhllCAL
recorded on a chart recorder. The spectrometer was intensity calibrated from 2000 to 3700 X wnh a D, standard lamp from Optronic Laboratories, and from 3300 to 6000 W with a tungsten stnp filament lamp. The calibration ytelded a response functton whrch was flat wnhm 2% from 2800 to 3600 A, so no mtensny correctrons were needed for the XeCl and XeBr spectra. However the response functron dropped appreciably at shorter wavelengths, necessitating a 20% reductron m the raw I&l,, ratios for KrCl. Spectra were recorded as a function of total pressure m the range 100-750 Torr. The discharge mixtures typically contained less than 1 .O Torr of halogen, about 20 Torr oi Xe or Kr, and Ar as buffer gas In the KrCl experunents we checked for possible dependence on the halogen-beanng reagent and buffer by using PC!, and Ccl, as alternative Cl sources. and Kr as a buffer. These expenments gave intensity ratwos which were consistent with those obtained with Cl,/Kr/Ar mixtures However we did observe a shght Increase (==lOZ) in the f&1,X ratio m the room-?. experiments when the drscharge was operated m open arr Instead of mstde the oven. We tentatrvcly attnbute thus effect to a higher discharge temperature m the open-an discharge, which was more vrgorous, as mdrcated by a five-fold stronger emission signal. Wth the oven in place the radiant output was comparable to *hat observed u-t our OH temperature determmatron [l-l], so we believe our stated temperatures of 360 K and 800 K are reliable within 20 K. Typical spectra are shown for XeCl at two pressures in fig 1, and for XeBr and KrCl at two temperatures m figs. 2 and 3. For each molecule both the B - X band and the broad band are broader at low
PHYSICS
15 May 1980
LETTERS
-B-X
BilA
C-A
3000
3500
x(A)
FIN 1. XeCl spectra recorded for a Tesla discharge of mwtures contammg 0 06 Torr CL2, 18 7 Torr Xe, and Ar to the lrdlcated total pressures Esumated dlschargc temperature was 360 K.
cXeBr
B-X
rBr2
O-A
P and HughT, where excited vlbratlonal levels make greater relative contrtbuttons to the total emtsston. In the KrCl and XeBr spectra, the broad-band emrssron IS overlapped by a halogen system. The halogen concentratrons m the discharge were kept below 0 5 Torr to muumize the relative mtensrty of the halogen band (and m the case of KrC!, the Ar,Cl emission [ 161, which was easily observed m Ar/Cl, discharges). The broad-band spectra were corrected for the spectrometer response function (in the case of KrCl) and, with the aid of quantum spectral simulations [ 171, were extrapolated to long and short wavelengths, through the regions of overlap with the halogen bands and the B + X band. These resolved spectra and the 96
Fig. 2. XeBr spectra recorded for discharge mtxtures of 0 55 Torr Brz, 18.7 Torr Xe, and 683 Torr Ar at 360 );; and 1.13 Torr Br2.19.9 Torr Xe, and 629 Torr Ar at 800 li
Volume 72. number
1
CHEMICAL
PHYSlCS
15 May L980
LETTERS
narrow B --f X bands were then integrated to obtain the intensity ratios shown as a function of I/P in fig. 4. Least-squares fits were used to obtain the desired infinite-P intercepts from these data. For XeQ and XeUr the high-T intercepts were smaller than the low-T values, indicating that the C state lies lower than the B state in these molecules_ The opposite dependency was observed for KrCl. These results are analyzed in more detail below.
4. Discussion 4.1. XeCl
2200
2500
AlAl
Fig 3 KrCl spectra recorded for drscharge mrxtures of 0.23 Torr Cls, 19 2 Torr Kr. and 624 Torr Ar at 360 K; and 0.14 Torr Cla. 21.1 Torr Kr. and 718 Torr Ar at 800 K. (These spectra not corrected for spectrometer response )
048 XeBr
t
016
The intercepts and their standard errors from the least-squares fits of the XeCl data were 0.2 10 + OIlO7 at 360 K and 0.174 f 0.006 at 800 K. Using eqs. (6 j (8) we calculated AE and A, for a range of assumed Br values. Results are shown in fig. 5. At the theoret~cal value, B, = 0.065 [9], we obtain AE = -128 C 35 cm-l and A, = 0.087 f 0.009. The latter value is in perfect agreement with the theoretical branching rauo [9]. Our AE value is considerably smaller in magetude than the estimate of -230 t 30 cm-1 given by Brashears and Setser [4] _ However the latter authors based their determmation on an assignment of all broad-band emission to the C + A transition alone. On reprocessing theu data with allowance for the B + A contrrbution, we obtain Ae = -165 cm-l,
1
OD8 -
. .
.
.-
. I
I
I
0
I
I
10
P-‘(lo-3 tort+ Frg 4. Ratros of broad-band to B - X mtensrty for XeBr, XeCI, and KrCl at 360 K (sohd potnts and hnes) and 800 K (open pomts and broken lures). The hnes represent leastsquares fits of the data - quadratrc for XeCl at 360 K. lmear m all other cases
I 0
I
I
I
I
I
I
a10
Fig. 5. Calculated A, and de values for XeCl as functions of El,.'The dashed lines indicates the errors (10)). and tie dotted hnes mark the theoretical branching ratios from ref. [9] _
97
Volun-s-72,
number
1
which agrees reasonably
well with our value. Of course
both values depend strongly on the assumed value of B,. With allowance for a possible 20% error m the theoretIca estimate of this quantity, the error in & increases to 50 cm-l _ The curvature m our 360 K data (fig. 4) resembles that observed by Rrashears and Setser at 300 K but 1s not as pronounced_ These authors explained the curvature in terms of a vibrational dependence of the Crj conversion rates, with lower rates for the low u’ levels which dominate m the near-Boltzmann vlbrational distnbutions achieved at high P. Our weaker curvature at 360 K and evident lack of curvature at 800 K can be taken as consistent with thus explanation, since the vIbratIonal dlstnbutlons shift toward higher u’ at these temperatures_ Of course there is no guarantee that the initially prepared vibrational and electronic distnbutlons are the same m our expenment as in that of Brashears and Setser, so no reason to expect perfect agreement m the pressure dependence. 4.2. XcBr The XeBr ratios showed a slight mcrease with mcreasing P at 360 K but no obvious curvature_ At 800 K there was virtually no P dependence m the ratios. Linear fits were used for both data sets, yieldmg infbnte-P ratios of 0.438 f 0 01 1 at 360 K and 0.413 2 0.008 at 800 K. In the XeBr spectrum the broad band IS asymmetncal and can be resolved mto two peaks, as shown in fig. 2. From theoretical considerations the B + A peak 1s almost surely the one at longer wavelength. Our resolution of the 360 K spectrum indicates that 65 + 7% of the broad-band emission is B --f A, from which we calculate B, = 0.285 f 0.030. Using this value m eqs (6)-(8) we obtain & = -80 -C40 cm-l and A r = 0.112 + 0.025. Here again a maJor source of uncertainty (particularly for _-Ir) IS the residual uncertainty m B,. Our estimates of A, and B, are 9Pr, and 17% greater, respectively, than the theoretical values [9] _ 4.3. KrCI Both data sets for KrCl show a slight decrease in IB~/I~x with increasing P. The infinite-P ratios of 0.057 f 0.003 at 360 K and 0.122 + 0.004 at 800 K 98
15 May 1980
CHEMICAL PHYSICS LETTERS 1000 -
I
1
I
I
/L
i’0 /_
500AC
-loo-
----_-I
--_-__-_-_ 1 1
I
01
FIN 6. A, and & for &Cl, as functions of f3,. Note loganthmlc ordmate scales.
mdlcate clearly that C lies above B in KrCl. The calculated & and A, values are shown as functions of B, m fig. 6. Note that AE IS particularly sensitive to B, in tlus case, but that A, is not. Thus situation 1s the reverse of that for XeC1 and XeCr, where the C state was found to lie beiow B. We could locate no pubhshed estunates of the branching ratios for KrCI. However from the trends evident m the theoretical calculations on the IgF and XeX molecules, we expect these ratios to be simdar to those for XeCI. Takmg B, = 0.06, we obtain & = 375 + 70 cm-t and ii, = 0.12 2 0.02. Our value for &z disagrees with the prehmmary indlcatlon of -100 cm-t by Brashears and Setser [4]. The neglect of the B + A emission m the latter work cannot account for such a large discrepancy, so we can offer no explanation for it
5. Conclusion From a study of the temperature dependence of relative emission intensities in a Tesla discharge, we have determined the energy separations of the B and C states m XeCl, XeBr, and KrCI. The results venfy earlier indications of a reversed ordering of these states m the XeX molecules, but an alphabetic ordenng is found for KrCI. Our experimental estimates of the spontaneous emission ratios are m good agreement wth theoretlcal predlctlons. Our treatment has neglected any differences III the
Volume 72, number 1
CHEMICAL PHYSICS LETTERS
rotatronal and vrbrational partitron functions for the B and C states, as was noted in conjunction with eq. (4). Because we use temperature dependence, this neglect has no effect on the & determmation, but it could lead to errors in the branchmg ratro A,. Taking XeCI as an example, If the C-state internuclear distance Rd is smaller than R,, by 0.1 A, as seems reasonable from the observed [ 181 0.09 A drfference between ReD and R,,, the true A, would be larger than the value we obtain by a factor (R,B/ReC)2, which 111 this case IS 1.07. In vrew of the lack of detailed spectroscop~c mformation about the C states, such corrections do not appear to be warranted at thus time. From the trends evident m the C/B separations for XeF, XeCI, XeBr, and ICrCl, rt seems hkely that the C state lies withm a200 cm-l of the B state in XeI, KrF, and ArF, as indicated in Setser’s work [2-4] In the other ArX and KrX molecuies (particularly the latter), the C state probably hes srgnificantly higher than B. We are presently extendmg our measurements to some of these other molecules.
15 May 1980
References [l]
D. KhgJer, H.H. Nakano. D-L. Hue&. W-K. Bixhel. R.hf. HtU and C.K. Rhodes, Appl. Phys. Letters 33 (1978) 39. [2] 1-H. Kolts and D.W. Se&x. J. Phys. Chem. 82 (1978) 1776. 131 H.C. Brashears and D.W. Setser, Appl. Phys. Letters 33 (1978) 821. [4] H.C. Brashears and D.W. Setser. 1. Phys. Chem., submitted for publicatton. (5 1 P S Jultcnne and hf. Krauss. Appi. Phys. Letters 35 (1979) 55. [6] W.J. Stevens and hf. Krauss, to be pubhshed. [7] J. Telhnghuisen. A.K. Hays, J.ht. Hoffman and CC. Trsone, J. Chem Phys. 65 (1976) 4473. [8] T-H. Dunnmg Jr. and PJ. Hay. J. Chem. Phys. 69 (1978) 134. [9 ] P 1 Hay and T-H. Dunning Jr., 1. Chem. Phys. 69 (1978) 2209. [lOI R-W. Waynant and J.G. Eden, IEEE J. Quantum Electron. 15 (1979) 61. [I 11 J-C. Hsta. 1 A. Mangano, J-H. Jacob and M. Rokni. Appl Phys. Letters 34 (1979) 208. (121 W.E Ernst, C Pollock and F.K. fittel, to be pubfished. [ 131 hl P. Casassa, hl F. Golde and A. Kvaran. Chem. Phys.
Letters 59 (1978) 5 1. Acknowledgement Thus work was supported by the Defense Advanced Projects Agency (DARPA/ONR Contract No. K00014-76-C-0450) and the Vanderbilt Utuversrty Research Council.
Research
A-K. Hur, h1.R. McKeever and J. Telhnghunen. J. Quant. Spectry. Raduttve Transfer 21(1979) 387. r151 hf.R. hlcKeever, A Sur. A.K. HUI and 1. Tellinghuisen, Rev. SCI. Instr. 50 (1979) 1136. it61 DC. Lorents, D-L. Huesta. h1.V. XfcCusker. H.H. Nakano and RX. HtU, J. Chem. Phys. 68 (1978) 4657. 1171 hf.R. hIcKeever. h1.B. Moeller and J. Tellinghuisen. to be pubhshed. 1181 A Sur, A K. HUI and J. Tclhnghmsen, J. Mol. Spectty. 74 (1979) 465. (141
99
CHEMICAL
I
ENERGY OZDERiNG FROM TEMPERATURE Joel TELLINGHUISEN
PHYSICS
OF THE b AND C STATES IN XeCI, XeBr, AND KrCI, DEPENDENCE
CF EMISSIGN SPECT%
and Mark R. McKEEVER
*
Department of Chemistry.
Zlnderbrlt Umrersrty, Nashzvlle. Tennessee 37235.
Recervcd 31 January
m final form 29 February
1980,
15 May 1980
LETTERS
USA
1980
Inert-gas hahde emtssron spectra from a Tesla drscharge are studred as a functron of pressure and temperature From the temperature dependence of the mtimte pressure ratro of broad-band (C - A and B - A) emrssion to B - X emisston, the energy separattons, TeC - T eB, are found to be -130 cm-t (XeCI), -80 cm-’ (XeBr) and 375 cm-’ (KrCI). Estrmates of the (C - A)/(B - X) spontaneous emrssron branchmg rattos agree well with thcoretrcal predtctrons
1. Introduction The discovery and development of the Inert-gas halide lasers over the last five years has inspired much basic research on the spectroscopy and kmetrcs of these systems. One question of recent Interest IS the energy ordenng of the two lowest ron-parr exerted states m the IgX molecules [l-6 j _These states are commonly labeled 3 and C by experimentahsts [7] and have Hund’s case (c) designahons S2 = l/2 and z2 = 3/2, respectively Detarled theoretical calculattons [6,8,9] predict these states to have practrcally the same electromc energies (TeB and T<), with C lying slightly higher than B. However experimental compansons of total spontaneous emissron in the broad C + 4(3/2) band with that in the sharply peaked B + X system indrcate that C hes about 600 cm-* below 9 m XeF [l-3,10] Thus result is supported by studies of XeF laser performance as a function of temperature, which show that the B + X laser unproves as the temperature IS increased to ==SOOK, whrle the C + A laser operates better at lower temperatures [ 11,121. Relative mtensrty measurements for other IgX species [2,4] suggest that the reversed ordermg may be a general feature of these molecules, although the Indicated separations for the other igF l
Present address: Photo Products Department, E I du Pont de Nemours. Inc. Towanda, Pennsylvama 18848, USA
94
and IgCl specres are less than the 600 cm-t value obtamed for XeF. With the exceptlon of the temperature-dependent studtes of XeF laser performance, all the experunental evrdence for the reversed ordermg of the R and C states comes from relative intensity data at a single temperature (300 K), interpreted with the aid of the theoretical estunates [8,9] of the (C + A)/(C + X) spontaneous emission branching ratio. While the evidence is overwhelmmgly in support of the near degeneracy of the B and C states, the splittings, & = Te TeB, and indeed the ordenngs deduced in these studies could be in error rf the theoretrcal branching ratios are not correct. Also, the theoretical calculations Suggest that the B + A( l/2) transition has appreciable mtensrty m the non-Iluonde IgX molecules, and this transttion has been clearly identtfled ln some IgGr and IgI molecules [ 131. In the IgCl molecules the B + A and C + A transitions overlap so badly in the h&-pressure spectra as to be unresolvable (see below). Stdl the B -+ A contnbutlon to the broad-band emlsslon must be somehow taken mto account to avoid systematrc error in the resultant AE values. To address the above mentioned deficiencies, we have investrgated the temperature dependence of the relatrve intensities for broad-band (B + A and C + A) emission and B + X emrssron m XeCl, XeBr, and KrCI. The expenments utilize our thermally controlled Tesla discharge [14,15], operated near 360 K and
800 K at pressures in the 100-750 Torr regrme. In the data analysrs the C + A transitron is taken into account. and experimental estimates are obtamed for both the energy separation & and the spontaneous emission branching ratio, A, = AC _ A/‘1 B _. X_ The results for AE bear out the earlier indications of reversed B/C ordenng m XeCl and XeBr, but yield a “correct” ordenng m KrCl.
2. Theory
kc-(+kQc
WIB)_
= k&kCB
= Keg = exp (-Ae/kT),
(4)
where Kq is the equihbrium constant for the process, lg( M) + IgX( B) * Ig( hl) f &X(C), and the second approximation is obtained by neglecting any differences m the rotational and vrbrational partition functions for the B and C states. The Infinite-pressure ratio of spontaneous emission intensities (quanta/s) in the C + A and B * X transitrons is 1, = [I(C + A)/I( G * X)],
We revrew bnefly the steady-state kinetrcs scheme whrch is pertinent to the data analysrs [ 1,2] _Stnctly speakmg the Tesla drscharge is not a steady-state source [ 151. However one can readdy show that the relative mtensrties obtamed from a transient source wrll equal those obtamed m steady state in the hrghpressure hmit. For the decay of the exerted states we mclude spontaneous emrssron, colhsional quenchmg, and collisronal couphng via the buffer gas. Representmg the B- and C-state concentratrons and the buffer gas concentration by B. C, and Al, respectively, we have in steady state,
kg-($
15 hfay 1980
CHEhlICAL PHYSICS LEI-I’ERS
Volume 72, number 1
+kQs bf + k,&f)B
+ k&fC
= 0,
(1)
III + k&f)C
+ k&fB
= 0,
(2)
in which the quenchmg constants are denoted kQB are kcB (for C -, R) and kqc, the couphng constants and kg=, the total radrative decay rates are 7;’ and 7:‘, and the productron rates are k, and kc_ (The production mechanism in our drscharge IS not understood m detarl, but both the broad-band and B + X intensities depend only weakly on total buffer gas pressure for the discharge mrxtures investigated here; hence the production rates are approxrmated as independent of hf_) Solving for the concentration ratio, we obtun
A body of accumulated data indicates that for hl = He, Ne, and Ar, kQB = kw
=(AC_.A/A~__X)(~/&,,
=+exp(-Wk’l?.
(5)
Thus If I, IS known at two temperatures, one can determine AE and the branching ratio A, from AE = kT1 T2(T2 - T,)-’ In Ar = (T2 - TI)-‘(T2
In(lr2/lrl). Infrz - Tr hfrl).
(6) (7)
In the experiments we measure the total broad-band emasion, which includes a contribution from the C + A transition. Hence the desired I, values are obtained by subtractmg the B j A contribution, I, = [f(broad-band)/f(B
+ X)],
- A,_,/A,_x
For XeBr we are able to obtain an experimental estimate of the branching ratio B, in eq. (8) from an approxunate resolution of the broad-band emission into the two components. However for XeCl and KrQ we must fall back on the theoretrcal estimates of this raho. In all cases the uncertainty in B, represents a srgnificant source of error in our determination_
3. Experimental
spectra
For our spectroscopic source we used the Tes!a discharge described m detll elsewhere [15]. Spectra were recorded at two temperatures - “room-T” and 500°C - giving estimated heavy-body discharge temperatures of 360 K and 800 K, respectively [ 14]_ The emission was dispersed through a McPherson model 218 0.3 m monochromator and detected with a Hammamatsu R456 photomultiplier. The average dc current was measured with a Keithfey picoammeter and
Volume
72. number
1
CHEhllCAL
recorded on a chart recorder. The spectrometer was intensity calibrated from 2000 to 3700 X wnh a D, standard lamp from Optronic Laboratories, and from 3300 to 6000 W with a tungsten stnp filament lamp. The calibration ytelded a response functton whrch was flat wnhm 2% from 2800 to 3600 A, so no mtensny correctrons were needed for the XeCl and XeBr spectra. However the response functron dropped appreciably at shorter wavelengths, necessitating a 20% reductron m the raw I&l,, ratios for KrCl. Spectra were recorded as a function of total pressure m the range 100-750 Torr. The discharge mixtures typically contained less than 1 .O Torr of halogen, about 20 Torr oi Xe or Kr, and Ar as buffer gas In the KrCl experunents we checked for possible dependence on the halogen-beanng reagent and buffer by using PC!, and Ccl, as alternative Cl sources. and Kr as a buffer. These expenments gave intensity ratwos which were consistent with those obtained with Cl,/Kr/Ar mixtures However we did observe a shght Increase (==lOZ) in the f&1,X ratio m the room-?. experiments when the drscharge was operated m open arr Instead of mstde the oven. We tentatrvcly attnbute thus effect to a higher discharge temperature m the open-an discharge, which was more vrgorous, as mdrcated by a five-fold stronger emission signal. Wth the oven in place the radiant output was comparable to *hat observed u-t our OH temperature determmatron [l-l], so we believe our stated temperatures of 360 K and 800 K are reliable within 20 K. Typical spectra are shown for XeCl at two pressures in fig 1, and for XeBr and KrCl at two temperatures m figs. 2 and 3. For each molecule both the B - X band and the broad band are broader at low
PHYSICS
15 May 1980
LETTERS
-B-X
BilA
C-A
3000
3500
x(A)
FIN 1. XeCl spectra recorded for a Tesla discharge of mwtures contammg 0 06 Torr CL2, 18 7 Torr Xe, and Ar to the lrdlcated total pressures Esumated dlschargc temperature was 360 K.
cXeBr
B-X
rBr2
O-A
P and HughT, where excited vlbratlonal levels make greater relative contrtbuttons to the total emtsston. In the KrCl and XeBr spectra, the broad-band emrssron IS overlapped by a halogen system. The halogen concentratrons m the discharge were kept below 0 5 Torr to muumize the relative mtensrty of the halogen band (and m the case of KrC!, the Ar,Cl emission [ 161, which was easily observed m Ar/Cl, discharges). The broad-band spectra were corrected for the spectrometer response function (in the case of KrCl) and, with the aid of quantum spectral simulations [ 171, were extrapolated to long and short wavelengths, through the regions of overlap with the halogen bands and the B + X band. These resolved spectra and the 96
Fig. 2. XeBr spectra recorded for discharge mtxtures of 0 55 Torr Brz, 18.7 Torr Xe, and 683 Torr Ar at 360 );; and 1.13 Torr Br2.19.9 Torr Xe, and 629 Torr Ar at 800 li
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15 May L980
LETTERS
narrow B --f X bands were then integrated to obtain the intensity ratios shown as a function of I/P in fig. 4. Least-squares fits were used to obtain the desired infinite-P intercepts from these data. For XeQ and XeUr the high-T intercepts were smaller than the low-T values, indicating that the C state lies lower than the B state in these molecules_ The opposite dependency was observed for KrCl. These results are analyzed in more detail below.
4. Discussion 4.1. XeCl
2200
2500
AlAl
Fig 3 KrCl spectra recorded for drscharge mrxtures of 0.23 Torr Cls, 19 2 Torr Kr. and 624 Torr Ar at 360 K; and 0.14 Torr Cla. 21.1 Torr Kr. and 718 Torr Ar at 800 K. (These spectra not corrected for spectrometer response )
048 XeBr
t
016
The intercepts and their standard errors from the least-squares fits of the XeCl data were 0.2 10 + OIlO7 at 360 K and 0.174 f 0.006 at 800 K. Using eqs. (6 j (8) we calculated AE and A, for a range of assumed Br values. Results are shown in fig. 5. At the theoret~cal value, B, = 0.065 [9], we obtain AE = -128 C 35 cm-l and A, = 0.087 f 0.009. The latter value is in perfect agreement with the theoretical branching rauo [9]. Our AE value is considerably smaller in magetude than the estimate of -230 t 30 cm-1 given by Brashears and Setser [4] _ However the latter authors based their determmation on an assignment of all broad-band emission to the C + A transition alone. On reprocessing theu data with allowance for the B + A contrrbution, we obtain Ae = -165 cm-l,
1
OD8 -
. .
.
.-
. I
I
I
0
I
I
10
P-‘(lo-3 tort+ Frg 4. Ratros of broad-band to B - X mtensrty for XeBr, XeCI, and KrCl at 360 K (sohd potnts and hnes) and 800 K (open pomts and broken lures). The hnes represent leastsquares fits of the data - quadratrc for XeCl at 360 K. lmear m all other cases
I 0
I
I
I
I
I
I
a10
Fig. 5. Calculated A, and de values for XeCl as functions of El,.'The dashed lines indicates the errors (10)). and tie dotted hnes mark the theoretical branching ratios from ref. [9] _
97
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which agrees reasonably
well with our value. Of course
both values depend strongly on the assumed value of B,. With allowance for a possible 20% error m the theoretIca estimate of this quantity, the error in & increases to 50 cm-l _ The curvature m our 360 K data (fig. 4) resembles that observed by Rrashears and Setser at 300 K but 1s not as pronounced_ These authors explained the curvature in terms of a vibrational dependence of the Crj conversion rates, with lower rates for the low u’ levels which dominate m the near-Boltzmann vlbrational distnbutions achieved at high P. Our weaker curvature at 360 K and evident lack of curvature at 800 K can be taken as consistent with thus explanation, since the vIbratIonal dlstnbutlons shift toward higher u’ at these temperatures_ Of course there is no guarantee that the initially prepared vibrational and electronic distnbutlons are the same m our expenment as in that of Brashears and Setser, so no reason to expect perfect agreement m the pressure dependence. 4.2. XcBr The XeBr ratios showed a slight mcrease with mcreasing P at 360 K but no obvious curvature_ At 800 K there was virtually no P dependence m the ratios. Linear fits were used for both data sets, yieldmg infbnte-P ratios of 0.438 f 0 01 1 at 360 K and 0.413 2 0.008 at 800 K. In the XeBr spectrum the broad band IS asymmetncal and can be resolved mto two peaks, as shown in fig. 2. From theoretical considerations the B + A peak 1s almost surely the one at longer wavelength. Our resolution of the 360 K spectrum indicates that 65 + 7% of the broad-band emission is B --f A, from which we calculate B, = 0.285 f 0.030. Using this value m eqs (6)-(8) we obtain & = -80 -C40 cm-l and A r = 0.112 + 0.025. Here again a maJor source of uncertainty (particularly for _-Ir) IS the residual uncertainty m B,. Our estimates of A, and B, are 9Pr, and 17% greater, respectively, than the theoretical values [9] _ 4.3. KrCI Both data sets for KrCl show a slight decrease in IB~/I~x with increasing P. The infinite-P ratios of 0.057 f 0.003 at 360 K and 0.122 + 0.004 at 800 K 98
15 May 1980
CHEMICAL PHYSICS LETTERS 1000 -
I
1
I
I
/L
i’0 /_
500AC
-loo-
----_-I
--_-__-_-_ 1 1
I
01
FIN 6. A, and & for &Cl, as functions of f3,. Note loganthmlc ordmate scales.
mdlcate clearly that C lies above B in KrCl. The calculated & and A, values are shown as functions of B, m fig. 6. Note that AE IS particularly sensitive to B, in tlus case, but that A, is not. Thus situation 1s the reverse of that for XeC1 and XeCr, where the C state was found to lie beiow B. We could locate no pubhshed estunates of the branching ratios for KrCI. However from the trends evident m the theoretical calculations on the IgF and XeX molecules, we expect these ratios to be simdar to those for XeCI. Takmg B, = 0.06, we obtain & = 375 + 70 cm-t and ii, = 0.12 2 0.02. Our value for &z disagrees with the prehmmary indlcatlon of -100 cm-t by Brashears and Setser [4]. The neglect of the B + A emission m the latter work cannot account for such a large discrepancy, so we can offer no explanation for it
5. Conclusion From a study of the temperature dependence of relative emission intensities in a Tesla discharge, we have determined the energy separations of the B and C states m XeCl, XeBr, and KrCI. The results venfy earlier indications of a reversed ordering of these states m the XeX molecules, but an alphabetic ordenng is found for KrCI. Our experimental estimates of the spontaneous emission ratios are m good agreement wth theoretlcal predlctlons. Our treatment has neglected any differences III the
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rotatronal and vrbrational partitron functions for the B and C states, as was noted in conjunction with eq. (4). Because we use temperature dependence, this neglect has no effect on the & determmation, but it could lead to errors in the branchmg ratro A,. Taking XeCI as an example, If the C-state internuclear distance Rd is smaller than R,, by 0.1 A, as seems reasonable from the observed [ 181 0.09 A drfference between ReD and R,,, the true A, would be larger than the value we obtain by a factor (R,B/ReC)2, which 111 this case IS 1.07. In vrew of the lack of detailed spectroscop~c mformation about the C states, such corrections do not appear to be warranted at thus time. From the trends evident m the C/B separations for XeF, XeCI, XeBr, and ICrCl, rt seems hkely that the C state lies withm a200 cm-l of the B state in XeI, KrF, and ArF, as indicated in Setser’s work [2-4] In the other ArX and KrX molecuies (particularly the latter), the C state probably hes srgnificantly higher than B. We are presently extendmg our measurements to some of these other molecules.
15 May 1980
References [l]
D. KhgJer, H.H. Nakano. D-L. Hue&. W-K. Bixhel. R.hf. HtU and C.K. Rhodes, Appl. Phys. Letters 33 (1978) 39. [2] 1-H. Kolts and D.W. Se&x. J. Phys. Chem. 82 (1978) 1776. 131 H.C. Brashears and D.W. Setser, Appl. Phys. Letters 33 (1978) 821. [4] H.C. Brashears and D.W. Setser. 1. Phys. Chem., submitted for publicatton. (5 1 P S Jultcnne and hf. Krauss. Appi. Phys. Letters 35 (1979) 55. [6] W.J. Stevens and hf. Krauss, to be pubhshed. [7] J. Telhnghuisen. A.K. Hays, J.ht. Hoffman and CC. Trsone, J. Chem Phys. 65 (1976) 4473. [8] T-H. Dunnmg Jr. and PJ. Hay. J. Chem. Phys. 69 (1978) 134. [9 ] P 1 Hay and T-H. Dunning Jr., 1. Chem. Phys. 69 (1978) 2209. [lOI R-W. Waynant and J.G. Eden, IEEE J. Quantum Electron. 15 (1979) 61. [I 11 J-C. Hsta. 1 A. Mangano, J-H. Jacob and M. Rokni. Appl Phys. Letters 34 (1979) 208. (121 W.E Ernst, C Pollock and F.K. fittel, to be pubfished. [ 131 hl P. Casassa, hl F. Golde and A. Kvaran. Chem. Phys.
Letters 59 (1978) 5 1. Acknowledgement Thus work was supported by the Defense Advanced Projects Agency (DARPA/ONR Contract No. K00014-76-C-0450) and the Vanderbilt Utuversrty Research Council.
Research
A-K. Hur, h1.R. McKeever and J. Telhnghunen. J. Quant. Spectry. Raduttve Transfer 21(1979) 387. r151 hf.R. hlcKeever, A Sur. A.K. HUI and 1. Tellinghuisen, Rev. SCI. Instr. 50 (1979) 1136. it61 DC. Lorents, D-L. Huesta. h1.V. XfcCusker. H.H. Nakano and RX. HtU, J. Chem. Phys. 68 (1978) 4657. 1171 hf.R. hIcKeever. h1.B. Moeller and J. Tellinghuisen. to be pubhshed. 1181 A Sur, A K. HUI and J. Tclhnghmsen, J. Mol. Spectty. 74 (1979) 465. (141
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