Temperature dependence of the dissociative ionization of CO2

237 Internatiomi Q Elsevier

Journal of Mass

TEMPERATURE OF C02*

W.

M. JACKSON**,

Department

Spectrometry

and Ion Physics,

13 (1974)

237-250

Scientific Publishing Company, Amsterdam - Printed in The Netherlands

DEPENDENCE

OF THE DISSOCIATIVE

R. T. BRACKMANN***

of Physics,

University

AND

of Pittsburgh,

W.

IONIZATION

L. FIT%

Pittsburgh,

Pa. 15260

(U.S.A.)

(Received 30 August 1973)

ABSTRACT

The electron impact ionization

of CO,

as a function of temperattlre

of the

CO2 up to 1500 K has been studied using modulated beam mass spectrometry. It is found that in this temperature range the cross section for forming the primary ion C02+ is temperature-independent, as is the cross section for forming Ci. Formation of the fragment ions 0’ and CO+ depends on temperature, however, with the former decreasing and the latter increasing with increasing temperature. The observations are understood in terms of the thermal population of certain vibrationally excited states of the CO2 molecule and the experiment yields ratios of cross sections of the excited states to the ground state, for the production of the fragments.

INTRODUCTION

The temperature cxbons

dependence

of the dissociative

has been used to test the predictions

ionization

of large hydro-

of the quasi equilibrium

theory of

mass spectroscopy [l]. Very little work has been reported on smaller mo!ecules since it was known that this theory was not applicable in these cases. No predictions have been made since each case will depend on the details of the potential

energy surfaces of the ground and excited states of the molecule. One can say, * Data analysis was performed at Go.idard Space Flight Center. Greenbelt, Maryhxl_ This researchwas supported by the Advanced Research Projects Agency of the Department of Defense and was monitoredby U.S. Army Research Office-Durham under Contract No. DA-31-124ARO-D-440. ** Presentaddress: Goddard Space Flight Center (Code 691) Greenbelt, Maryland. *** Present address: Extranuclear Laboratories, Inc. Pittsburgh, Pa. 15238.

238 however, that the cross section for the particular process will depend on both the electronic transition moment and the Franck-Condon factor between the two levels. There are two triatomic systems (CQz and CS2) for which some energy levels are available for both the ion and the neutral molecule. This facilitates the theoretical calculations necessary to gain a complete understanding of any experimental results that can be obtained. Of the two available systems, COz was chosen because of its great abundance in the atmospheres of Mars and Venus and because CO, is currently being used in one of the more successful high-power continuous gas lasers [2]. The experimental results on the temperature dependence of dissociative ionization may be relevant in calculating the loss processes in CO, lasers and in the atmospheres of planets.

EXPERIMENTAL

The conventional approach for the study of dissociative ionization as a function of gas temperature uses a mass spectrometer where the gas is admitted to an ionization chamber and where the temperature of the.gas is controlled by the temperature of the ionization chamber walls. A number of limitations attend this approach, foremost of which is the limitation of temperature range imposed by the materials used to construct the ionization chamber. Other possible problems with this approach include changes of ion optics with deformations due to thermal expansion [3], the question of achievin g complete thermal equilibrium between the gas and the walls and possible changes of contact potentials on heating which can in turn affect ion extraction and lead to ion discrimination effects. These problems can be avoided by thermally decoupling the source of hot gas from the ionizing electron beam. A method of accomplishing this is to present the gas to the mass spectrometer as a molecular beam from a heated neutral beam source and to let the beam pass cleanly through an ionizer in which an electron beam crosses the molecular beam. By modulating (chopping) the molecular beam it is straightforward to distinguish signals arising from the interaction of the two beams as opposed to signals from ionizing residual gas in the mass spectrometer, since the former signals will be alternating at the modulation frequency and in specified phase, while the latter will appear as dc signals. In the present experiments, the Extranuclear Laboratories Modulated Beam Analytical Mass Spectrometer (EMBA II), which is shown schematically in Fig. 1, was used. The gas source was a tubular iridium furnace which could operate to temperatures up to 2200 K. The furnace was 6 mm in .diameter, 4 cm long and gas issued through an aperture approximately 1 mm in diameter. The furnace was heated by passing currents of up to 300 amperes along its length. The voltage across the furnace was used to determine the temperature in the experiments,

LIGHT

8 P~IOTOCELL

MODULATOR

PUMP PHASE REFERENCE ~

SIGNAL

1 -

PUMP

2

~X&ATED

PHASE SENSITIVE DETECTOR

BEAM 0 1

t

1 INTEGRATOR

BACKGROUND SIGNAL

I =

Fig. 1. Simplifiedschematicof EMBA II.

calibration of the voltage-temperature curve being determined separately using an in the optical pyrometer sightin, = on the aperture in the furnace. Uncertainties temperature measurements are believed to be &25 K. Molecules effuse from the aperture of the furnace? which is located in the first of two differentially pumped chambers. A fraction of these molecules are collimated into a molecular beam in passing through an aperture in the wall separating the two differentially pumped chambers. After entry into the second chamber rhe collimated molecular beam is square-wave modulated (chopped) by a rotating toothed wheel. The modulated beam travels a distance, L, and is then ionized by a crossed electron beam in the ionizer. The extraction region in the ionizer is determined by the focusing properties of a 3-element lens and the size of the molecular beam. The lens is focused for optimum peak shape consistent with the relatively high sensitivity. There are no inagnetic fields in the ionizer to cause discrimination effects in the ionizer. The ions are separated in a quadrupole mass spectrometer and then detected by an off-axis electron multiplierThe signal is then processed by a-Princeton Applied Research Model HR-8 Lock-in Amplifier, which measures both the amplitude and the phase of the ion signal. The signal phases can be used to determine the mass of the neutral parent of an observed ion or group of ions. If the beam is square-wave modulated at a frequency f (angular frequency o = 27rf), the fundamental Fourier component of the neutral beam density can be described by M(t) A detected si(t)

= A sin ot.

(1)

ion signal will lag the modulation 0Z sin(ot-4)

phase and be described

= sin (OZ-+i-+n)

where C$is a phase lag introduced

by two time lapses.

by (2)

240

One of these time lapses occurs because of the time required for an ion to traverse the length of the mass fiIter. This contribution to the phase lag is given hy

where Li is the length of the mass filter and t)i is the velocity of the ion, which in turn is related to the ion mass, Mi, and the energy given the ion, Ei, after its formation. The second time lapse is that for the neutral molecule to travel the distance L between the beam modulator and the ionizer. To a crude approximation (which ‘is valid for very low frequencies and/or short distances, L), 4, can be described by an expression similar to eqn. (3), i.e.,

where i&,is a mean velocity of the neutral molecules which is related to the neutral mass, M,, and the temperature, T (K) of the beam source. Because of the Maxwellian distribution of velocities, the expression for #, is considerably more complicated than given in eqn. (4), and in the present experiments the values for $, calculated by Harrison, Hummer and Fite [4] were used. The total phase lag is given by

and it is clear that for several ions originating from the same neutral parent, the signal phases should increase as (Mi)“. Figure 2 shows this to occur with the ions from Nt . This phase plot also shows the decrease of phase lag with increasing temperature for any given ion, as is implied qualitatively in eqn. (4). Most important it shows that at ail temperatures, the signal phases are proportional to (Mi)’ which implies that at ail temperatures all ions come from Nz, i.e., that there is no thermal dissociation. This can be contrasted with Fig. 3, which shows the phase plot for CO,. At the three lower temperatures it is seen that the situation is comparable with that for N,. However, at the highest temperature shown, the phases for the Oi and CO* lie above the line which indicates that some of these ions are coming from neutral parents lighter than COz, i.e., that thermal dissociation of the CO2 is occurring in the furnace beam source. In the present experiments, in order to ensure that all ions originated from internally excited CO, rather than from dissociation fragments, the temperature was kept below that at which dissociation was indicated by the.phase information.

241

L = 12.5 cm

N2

f = 2000

40

”

60

-

80

-

120

-

140

-

160

-

180

-

2000

0

I

2

3

HI

4

5

6

Fig. 2. Phase plots of the parent and fragment ions of N2.

L=20cm f = 2000Hr

Fig. 3. Phase plots of the parent and fragment ions of CO2 .

242 RJzsuJLTs The relative ratios of fragment ion signal amplitudes as functions of source temperature are plotted in Fig. 4. In this figure all curves have been renormalized for the source at room temperature. The actual observed room temperature ratios wereapproximately 10% for O+/COzf, 7% for COf/C02i,and3%forC*/C02’. Both the O+ fragment and the CO+ fragment change markedly with beam temperature while the Cc fragment remains relatively constant. This type of behavior was found to be independent of the experimental parameters such as focusing conditions in the ionizer, chopping frequency, pressure in the source, etc. The same behavior was observed for nominal electron energies of 30, 50 and 100 volts. However, at 30 eV no C’ ions Were observed within the det-zction limit of the experiment_ This is in reasonable agreement with a threshold of 28.1 volts for the production of C+ and two oxygen atoms from COz [5]. 32 c

I

500

I

I

900

I

I

1300

1

I

1700

I

1

210

T t-K)

Fig. 4. Amplitude ratios of the fragment ions of CO, versus temperature. The curves for both the CO’ and O+ fragments in Fig. 4 rise rapidly as the furnace temperature is raised above 1500 IL The increase in this ratio at the high temperatures is due to thermal decomposition of the CO2 molecule. The evidence for this is that the mass 28 and 16 peaks deviate from the phase curves at high temperature. (See Fig. 3. ) The consistency of these results implies that the effective cross sections for the production of the parent ion (CO,+) and/or the fragment ions are dependent on the temperature and therefore the internal energy of the molecule. That the cross section for production of the parent ion is not strongly temperature dependent, if at all, is demonstrated by a comparison with the ionization of argon. In particular, in a beam experiment where the beam carries a constant mass flow, controlled by the rate of admission of gas into the beam source, and where

243

the ionization cross section is known not to be temperature-dependent, such as argon, the ion production should decrease inversely as the velocity ofthe particle and therefore inversely as the square root of the absolute temperature. The ion signals in general do not quite folfow this temperature dependence because the initial velocity

of the ion immediately

following

ionization,

i.e., the velocity

of

the neutral before ionization,

affects the collection efficiency of the ions 15J. Nonetheless, the Ar+ signal as a function of beam source temperature can be compared with the C02+ signal in order to determine whether the cross section for forming COz+ is temperature-dependent. Figure 5 shows that as a function of temperature the Ar+ and CO2 i signals are similar up to temperatures at which dissociation of the CO2 occurs. It can thus be concluded that it is the effective cross sections for producing the fragment ions that are temperature-dependent.

DATA ANALYSIS

The dependence of the effective cross section for producing a given fragment ion on electron impact ionization of CO, upon the temperature of the CO2 suggests that different internal energy states have different cross sections for producing a given fragment ion and that the temperature dependence of the effective cross section arises through the temperature dependence of the internal energy state population distribution_ It becomes of interest to attempt to identify the particular states of the CO2 which preferentially produce the observed fragment ions and to estimate the relative cross sections. The signal for a given fragment ion, S,, can be written as

(6)

0.4

e

(A+),

A

(co&

/

(A+)300.r

/ (co2+)soo*K

-

A A 0.2 0.0

I 500

I

1 900

I

I 1300

I

I IT00

i

I 2100

T tgK)

Fig. 5. Comparison between argon and CO2 parent ion amplitude ratios as a function of furnace temperature.

244

where A(T) is the normalized amplitude for a square-chopped Maxwellian beam, calculated by Harrison et al. [4], for a beam of CO, molecules with the modulation frequency and flight time used, crfi is the cross section for producing the f-th fragment ion if the CO, molecules in this i-th state, Fi is the fraction of CO, molecules in this i-th state, and &-contains all other temperature-independent physicai and instrumental parameters. The signal, S, of the parent ion (CO,+)

sp =

BpA(T)CGpiFi

is given by

*

(7)

temperature-independent, which in turn implies that CGpi~i = bP = constant

(8)

and thus S, = &,A(T)Q.

(9)

The fraction of molecules in the i-th state is given, under equilibrium conditions, bY F_

=

Bi

1

exP(-4kT)

Q(T)

where gi is the weight of the i-th state, Ei is the energy of the i-th state and Q(_1-)is the partition function. Combining the above equations, the ratio of signals of a fragment ion to the parent ion is given by

This ratio, referred to the same ratio at a reference temperature, T,,, (300 K) is given by r,(T) = ~-K(T) =

Rf(T* )

CGfiFiCT) CGfiFiCTO)

a

w

A non-linear least squares procedure could be used in principle in order to determine all the cross sections bfi. However, for present purposes, determining the relative-magnitudes of these cross sections is sufficient and the problem is simplified. In particular, noting that the sum term in the denominator of eqn. (12) is independent of temperature, we can write r,(T) =

Fy

F:(T) =

CBfiF,(T) i

where

(13)

245 y = cB,;F-,(T,)

= constant

(14)

and Bfi

=

“fi/Y*

(151

It is convenient to further define &T)

=

e(T,> Q(T)

(16)

where the subscript zero indicates the groundstate of CO, _ The problem becomes one of calculating the functions F;(T) and then performing a linear least squares fit of the coefficients B,i to yield the values of r,(T) determined in the experiment. In the present study it was assumed that rotational contributions could be neglected and only thermally populated vibrational and electronic states were considered. Equation (13) has the form of a multiparameter equation [7] for which a iinear least squares program can be used to determine the unknown coefficients B,i. Performing this calculation for all of the known levels of CO, is extremely dificult and the accuracy of a least squares caiculaiion decreases as the number of parameters increase_ To circumvent this, the calculation was performed by starting with a single excited level and adding others until there was reasonable agreement between the theoretical curve and the experimental points, and the addition of more excited states afforded no further apparent improvement. The B,i values were used to calculate values of Ccri= (Bfi/Br,) = (Ori/~fo), i.e., the ratio of the cross section for producing a given fragment ion from the i-th state of COz as compared to the groundstate. In performing the analysis the value of r,(T,,) was always taken as unity, although in the course of a run the actual signals showed some experimental scatter (as high as 4 oAdeviation between the beginning and the end of a day’s running). The function x-,(T), which decreases with increasing temperature, is a direct measure of the population of the ground vibrational state (the 000 level) of COz. Since the Oi ratio, r,, (T) decreases with temperature it can be anticipated that the higher order terms in this equation add very little to the overall function. This is verified in Fig. 6 where the results of a least squares fitting procedure using only the 010 excited vibrationa level of CO2 are plotted along with the function x0(T). The curve through the points is the derived curve and the root mean square (RMS) deviation from this curve is 0.032. Since only one excited level is used, there is only one unknown in eqn. (13) and an exact solution can be obtained for each of the experimental points. The averaged talc-ulated value of ~~~~~~~is 1.17 which agrees well with the least squares value of :.12. The cross section for the dissociative ionization of CO2 to give O+ from this excited level is therefore only slightly larger than the cross section from the ground

246

lOLo= 667.3

t20,0=l_12

cm’-’

RMS = 0.032

I.6

1

iI 1.2 c +

0

0.8

0.4

0

300

500

700

900

I100

1300

T (OKI

Fig. 6. Least squares fit of the 0+ temperature data and the change in population of the 000 ground vibrational level of CO, with increasing temperature.

vibrational level of C02. The addition of more states than only the 000 and 010 state in eqn. (13) does not improve the least squares fitting to the data. Unquestionably this is due to the experimental data scatter, but it seems evident that if other states contribute at all to the formation of the 0’ fragment their cross sections cannot be larger than the groundstate cross section and may possibly be comparable or smaller. The situation with CO+ is quite different_ The CO+ curve in Fig. 4 markedly increases with increasing temperature, even at low temperatures, where the population of the vibrationally excited state is small. This implies that the cross section for production of CO+ must be markedly larger for at least one vibrationally excited state of CO,, than it is for the groundstate of CO,. The question to which the least squares analysis was addressed to was the identification of any such states and the estimation of their cross sections. In attempting to fit eqn. (14) to the data, using only the ground state and a single excited state chosen from the first six excited states, it was found that no fit could be obtained that was suitable over the entire temperature range. The standard deviation in the experimental points was calculated by first averaging the observed data at one temperature and calculating the deviation of each of these measurements from the average. The square root of the sum of the squares of

247 TABLE I TWO

LEVEL MODEL

&cl

FOR co+

&i

0.35 0.91 0.96 1.2 1.2 1.3

5.6 9.6 33 17 41 113

TABLE

2

THREE LEVEL MODEL

&J

1.3 1.2 1.0 1.0 0.94 1.1 1.1

&I

-3.3 -2.1 0.81 1.2 1.8 -28 2.4

1.1

3.5

1.1 1.1 1.1 1.1 1.1 1.1 1.1

4.7 9.9 14 18 35 23 87

FRAGMENT

RMS

a

&(cm-*)

Leoel

0.39 0.17 0.13 0.082 0.10 0.15

16.1 10.6 35.0 14.7 34 90

667.3 1285.5 1388-O 1932.5 2076.5 2349.3

010 020 100 030 110 001

FOR CO+

&2

14.3 44 15 34 88 130 13 27

61 12 24 54 -45 -43 - 130

FRAG_MENT

RMS 0.100 0.092 0.060 0.0555 0.0529 0.079 0.065

aW -2.5 -1.7 0.79 1.22 1.90 -25.1 2.2

0.062

3.2

0.057 0.066 0.064 0.059 0.072 0.074

4.4 9.0 12.8 16.9 32.1 20.8

0.078

77.1

at.3

B(Z) (cm-‘)

E(2) (cm-‘)

11.1 35.7 14.9 34.7 94.0 116 11.9

667.3 667.3 667.3 667.3 667.3 1285.5 1285.5

1285.5 1388.0 1932.5 2076.5 2349.0 8388.0 2932.5

24.8

1285.5

2076.5

1295.5 1388.0 1388.0 1388 1932.5 1932.5

2349.3 1932.5 2076.5 2349.3 2076.5 2349.3

2076.5

2349.3

57.3 11.1 22.3 49.9 -40.3 -37.9

-115.3

these deviations divided by the number of observations minus 1 was used to cal-

culate the experimental standard deviation of 0.042. From Table 1 it is seen that no one excited level gives a RMS value of less than twice the experimental standard deviation. Clearly a single excited level is not adequate to explain the observations. It was found that upon using two excited levels, the data could be fitted to within the experimental accuracy over the entire temperature range. Table 2 presents best fits for the two excited level calculations, for daerent pairs of known excited vibrational levels of COz , The lowest RMS deviation occurs for the case of the lower of the two levels being the 010 bending mode level and the upper level being either the 110 level (symmetric stretching plus bending mode) or the 001 (asymmetric stretching mode). Figures 7 and 8 show the data points superposed on the least squares fit curve. It is clear that the experiment is not sufficiently precise to prefer one or the other of the above indicated levels as the upper level in a three state model.

1.6

F +

0

k!?

0-i

ao,o’l.2

Ql10

t

RMS

=34.7

667.3

CII?

6010

=

E,,~

= 2076.5cm-’

aOIOf

1.90

eOiO

QOO, = 94.0

= 0.0555

RMS

=

667.3

Cm-’

EOO, = 2349.3cm-’

- 0.0529

o-4

t

I

0300

500

700

900

1100

1300

T IoK) Fig. 7. Two level Ieast squares fit of the CO+ data using as the two excitedvibrational levels the 010 and 110 levels of COz -

I 500

I

I 700

I

I 900

I

I II00

I

I i3OC

T (OK) Fig. 8. Two level least squares fit of the CO’ data using as the two excited vibrational levels the 010 and 001 level of COz .

Least square fittings using three excited states and six excited states were also carried out, but no improvement over the fit using only two excited states were obtained_ For the six-level calculations, some of the 3-s were negative which is physically unrealistic, since all cross sections are by definition positive.

DISCUSSION

The present results on the temperature dependence of dissociative ionization can be at feast partially understood using the model that electron impact ionization produces an excited COZi ion which then breaks up. The excited state can be either a high lying repulsive state or a one electron state which predissociates. High lying repulsive states do not generally show strong Franck-Condon effects since it would require a special case such as a very steep repulsive curve placed so that the vibrational overlap from the upper levels of the ground state is less than from the excited vibrational level. We thus turn to predissociating states as the possible cause of our observations.

249 Of particular interest is the C2Xl state of the ion. Eland [S] has shown in an extensive study of the photoelectron spectrum of CO, that the OOWvibrational level of this state is 100 y0 predissociated. Further the energy of this level is insufhcient to produce CO* and 0, so that the products of the dissociation must be 0’ and CO. Higher levels of this C state can dissociate to yield CO+ and 0, but according to Brundle and Turner [9] the Franck-Condon factor for exciting all the higher levels from groundstate CO2 is only about 10 oA compared to 90 ok for excitation of the 000 level of the C state. Thus one would expect that for dissociative ionization proceeding exclusively through the C state of the Cot’ ion, the ratio of CO+/O+ would be of the order of 0.11. The observed ratio of about 1 suggests that most of the dissociative ionization to CO+ proceeds through states other than one electron states. However, the temperature dependence observed in the present experiment may be qualitatively attributable to only those fragment ions that are formed by passage through the C state of the CO,” ion_ In particular although excitation of this state from ground state of CO2 preferentially populates the lowest vibrational levels of the ion state, where 0’ production would occur, it would. be expected that excitation from excited levels of CO, would populate the higher levels of the ion, thus reducing the O+ production and increasing the CO* production. Analysis of the data presented in the preceding section suggests that only the ground level and lowest excited level, the 010 state, of CO2 are responsible for producing the O+. Presumably the higher levels of CO, have small FranckCondon factors for going to the lower vibrational levels of the C state of the CO: ion. The population of the higher levels of this state of the ion, which dissociates to form CO’, would lead to the observed increase of this ion signal with temperature. Although this model of the process is qualitatively appealing, the very large apparent cross sections obtained from the data fitting does not seem consistent with considering only the C state of the ion, and only the Franck-Condon factors that are known at present. Possibly other states of CO,+ which were highly vibrationally excited would have to be included in a satisfactory quantitative picture.

REFERENCES

1 M. Vestal, in P. Ausloos (editor), Fundamental Processes in Radiation Chemistry, Interscience, New York, 1968, p_ 85. 2 N. N. Sobolev and V. V. Sokovikov, in L. Branscomb (editor), Invired Papers of Vth ICPEAC, University of Colorado Press, Z967. 3 A. Cassuto, in R. M. Elliott (editor), Advances in Mass Specfrometry, Vol. 2. Macmillan, New York, 1963, p. 296. 4 H. Harrison, W. L. Fite and D. G. Hummer, J. Chem. Phys.. 41 (1964) 2567.

250 5 H. Ehrhardt and A. Kresling, 2. Natwforsch-, 22a (1967) 2036. 6 G. Herzberg, Molecular Spectra and Molecular Structure, Vol. II, Van Nostrand Co., Inc., New York, 1945, p. 501. 7 E. Bright Wilson, Jr., An Introduction to Scientific Research, McGraw-Hill, New York, 1952, p. 220. 8 J. ‘-I. D. Eland, Int. 3. Ma& Spectrom. Ion Phys-, 9 (1972) 397. 9 C. R. Brundle and D. W. Turner, Inc. 3. Mass Spectrom. Ion Phys., 2 (1969) 195.