- Email: [email protected]
A diode laser spectrometer for state-resolved experiments on the methane-surface system
CHEMICAL
9 February 1996
PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 249 (1996) 423-432
A diode laser spectrometer for state-resolved experiments on the methane-surface system D.K. Bronnikov a, P.V. Zyrianov a,~, D.V. Kalinin a, Yu.G. Filimonov a, A.W. Kleyn b, J.C. Hilico c,. a Russian Scientific Center 'Kurchatov Institute'. 123182 Moscow, Russian Federation b FOM-lnstituteJbr Atomic" and Molecular Physics. Kruislaan 407, 1098 SJ Amsterdam, 7"he Netherlands c Laboratoire de Physique de rUniversit£ de Bourgogne, BP 138. 21004 Dijon Cedex, France
Received 25 September 1995; in final form 17 November 1995
Abstract A diode laser spectrometer for studying the state-resolved scattering of a molecular beam of methane in a molecule-surface system is described. Preliminary estimation of the sensitivity of the spectrometer for future scattering experiments is done. The advantages of data obtained in the 3.3 and 7.7 ~m spectral regions are analyzed. A double pulse recording scheme for the elimination of low-frequency noise in the absorption spectra of the molecular beam is proposed and tested under static conditions. Measurement of the detailed rotational vibrational distribution in a jet of methane is done to obtain the main parameters of the direct beam in scattering experiments. The rotational distribution within each vibrational polyad is found to be of Boltzmann type. A method of calculating the population for a defined vibrational state or polyad is developed to analyze the evolution of the detailed distribution during the energy relaxation under non-equilibrium conditions of the molecular jet or molecule-surface system.
1. I n t r o d u c t i o n The dissociative chemisorption of methane on metals is one of the main steps of catalytic conversion of methane to higher hydrocarbons. Many studies have been devoted to the main factors that activate the C - H bond cleavage. Molecular beam experiments have probed the effects of the translational and vibrational energies of molecules, and the surface temperature on the dissociation. A strong depen-
dence of the CH 4 dissociation probability on the vibrational energy was observed [1-3]. The same dependence was tested in experiments with direct laser excitation of methane. Facilitation of the dissociative chemisorption was found to be negligible in this case. Many models have been suggested to account for both the results of these particular experiments and all variety of data [1-4]. State-resolved molecular beam experiments arc promising from the viewpoint of comprehending vibrational activation and as a test o f theoretical models. The structure of the energy levels of methane is
l Present address: Institute of General Physics, 38 Vavilov street, 117942 Moscow, Russian Federation. Corresponding author,
complicated and, consequently, the vibrational rotational distribution and energy relaxation in molecular beams need to be investigated. All previous state-re-
0009-2614/96/$12.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0009-261 4(95)0 l 413-6
D.K. Bronnikov et al. / Chemical Physies Letters 249 (1996) 423-432
424
solved beam experiments were mainly devoted to the behavior of vibrationally non-excited methane. Measurements of the rotational temperature and investigation of the nuclear spin relaxation of methane were carried out in a supersonic jet for the stagnation temperature 300 K [7,8]. Direct infrared absorption was used for measuring the state-to-state rotational energy transfer in crossed molecular beams for the Ar + C H 4 system [9]. The wide possibilities of diode laser spectroscopy were demonstrated in Ref. [10] where the observation of high vibrational and low rotational temperatures of methane in a supersonic jet for a stagnation temperature as high as 900 K was described. Diode laser spectroscopy is efficient for state-resolved experiments in polyatomic moleculesurface systems as well. This was demonstrated in experiments devoted to desorption of CO 2 molecules from a surface [11]. The interaction of a molecular beam of methane with a metal surface is planned for investigation by this method. For realization of this project, a diode laser spectrometer of high sensitivity with a multipass cell was developed and constructed to be compatible with a molecular beam apparatus. This apparatus was used for state-resolved experiments on the interaction of diatomic molecules with a surface by a resonance-enhanced multiphoton ionization method [12,13]. In this Letter, experimental data for estimation of the sensitivity of state-resolved measurements
for methane are presented. Diode lasers of this spectrometer have also been used for measurements of the rotational-vibrational distribution in a molecular jet of methane. This information about the detailed vibrational-rotational distribution in a direct beam is necessary for the proper interpretation of future results of scattering experiments and has not been obtained before. A method of calculating the population for a defined vibrational state or polyad has been developed to analyze the evolution of the detailed distribution during energy relaxation under non-equilibrium conditions, including the moleculesurface system.
2. Diode laser spectrometer
2.1. Optical apparatus The scheme of the proposed experiments is depicted in Fig. 1. The molecular beam apparatus is described in detail in Ref. [12]. A metal crystal is mounted on a manipulator and is placed in an ultrahigh vacuum (UHV) chamber. By turning the manipulator the crystal can be faced to different control systems of surface quality and the incident angle of the molecular beam can be changed as well. The optical system includes a basic channel for the measurement of spectra of the scattered molecular beam
Scattered
]
I
i/
alignment He+Ne laser
MB
I4
fl:s I
I j
t! Controlchan~ell-I---
,
gl'
m,..~.
~
,
2__
Basic channel
.
.~+-
,~1
.
I +
. ,,.. ,
x s ," irect MB .
F i g . 1. D i o d e l a s e r s p e c t r o m e t e r ;
.
.
.
-it
.
.
j+ . ,,
vcmtec~a
. •
crystal
U. H. V. .c h. a m ber . . .
I - IR detector, 2 - removable Fabry-P6rot
.
.
.
.
I
etalon, 3 - reference cell.
425
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
and a control channel to check and improve the laser radiation quality over the long accumulation time of the spectra. Two different outputs of the diode laser radiation are used for these c h a n n e l s . Diode lasers were obtained from the Ioffe Physical-Technical Institute, St. Petersburg for the 3.3 Ixm region and from the Lebedev Physical Institute, MOSCOW for the 7.7 g m region. A diode laser (DL) is mounted in a cryogenic refrigerator for cooling and thermostabilisation in the range 78-300 K. The optical baseplate also contains collimating optics, four rotatable cells for reference gases, a Fabry-P6rot etalon for calibration of the wavelength scale and two infrared detectors in liquid nitrogen cryogenic refrigerators with preamplifiers. To reach highest sensitivity, a multipass White cell with a base length of 130 mm is constructed to get passes of the laser beam in a small volume close to the crystal. The dimensions of the probing zone for the molecular beam are 20 mm in the direction of scattering and 5 mm across the beam. These sizes are defined by the geometry of laser beams in the probing volume. The third dimension depends on the diameter of the molecular beam spot at the crystal and the angle of divergence of the scattered beam out of the scattering plane. The axis of the White cell may be aligned 10 mm far from the surface of the crystal in the direction of scattering. There is a possibility of detecting the scattered beam under different angles (from 0 to 90 °) with respect to the direct beam due to the ability to change the position of the symmetry plane of the White cell. The number of passes of the laser beam can be adjusted up to 50, so that the total absorption path length in the scattered beam can be about 50 cm for a crystal with a diameter of 10 ram.
2.2. Control, data acquisition LaserSpectrum's high speed data acquisition and laser control system was modified to be used for our specific task. This system was described in Ref. [14]. It supports basic diode laser control functions, signal recording, data accumulation and handling. All functional units of the electronic system, laser temperature controller, - laser current source, - data acquisition subsystem, -
[
][j
Mi. . . . . . troller
~
~t ~
a
~
~6"~p ie
~loeldand
j! -d ~!
L. . . . . . . .
[!lllllll ~ 1 [
Host
comp....
analog from ----< signals ~ preamplifiers
flash20Msp/s 8-bitADC ~'~, I ~ 12-bit .... p ~ <
jj
[- - ~
Diode laser
s..... ~ L
Temperature
~
Cryostat
condoner
Fig. 2. Blockdiagram of the electronicsystem.
are controlled by the high speed microcontroller SAB 80C166. A block diagram of the system is shown in Fig. 2. The current source implements the laser frequency tuning by periodically repeating laser current pulses of rectangular, triangular or more complex form. The mean current noise was tested to be less than 50 mA while the total current was 500 mA. The temperature of the diode laser is set by a 12-bit DAC and is stabilised within 3 × 10 -3 K. The system performs the analog data acquisition by a flash 8-bit ADC from one of three input channels. The highest sampling rate of the ADC is 20 Msp/s. The offset for the registration of each photosignal pulse can be changed by a 12-bit DAC. This allows one to increase the amplitude resolution (up to 12-bit) and, consequently, the signal-to-noise ratio ( S / N ratio) owing to signal accumulation over several pulses and simultaneous variation of the ADC offset. All ADC and DAC are calibrated in correspondence with physical values. The spectrum of diode laser radiation is stabilized by the control channel on the absorption spectrum of a reference gas. This feedback of frequency is implemented by a four-line sample and hold amplifier. The system is able to measure the amplitude of the photosignal at four points around any absorption line for each pulse and to produce a calibrated variation of the diode laser current parameters for keeping the absorption line in a definite position. The electronic system may be synchronized with another system and can produce a defined number of pulses for a one synchronization pulse. Each appropriate photo-
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
426
signal can be accumulated in a separate storage of the microcontroller. Primary data processing with high speed of manipulation such as accumulation and control of line position for stabilization, is bandled by the microcontroller, while more complex data processing and a user interface are supported by an IBM PC.
3. Experimental results
3.1. Sensitivity of the spectrometer
tuned by heating the crystal by the current pulse. The tuning rate lies in a range of 103-104 c m - ~ / s . Therefore, an absorbance spectrum of 1 cm-1 can be measured during one pulse of the molecular beam with a typical duration of 300 Vs. To determine the absorbance spectrum of a gas pulses of laser intensity l(t) and lo(t) are recorded with and without the gas in the cell. These values l(t) and lo(t) depend on the frequency because of tuning of the laser frequency during the current pulse. The absorbance spectrum A(v) is
A( v ) = In( l°( v ) ]
To carry out measurements of the methane spectra and to estimate the sensitivity, the multipass White cell was installed in a vacuum chamber, characterized by a base pressure 10 -4 Pa. The chamber was filled by pure methane or by a mixture CH 4 : Ar = 1:100 under different pressures. Mixtures were used to decrease the concentration of methane to the lowest controlled limit. The White cell was adjusted for 34 passes of the laser beam. To obtain radiation the diode laser is pumped by current pulses of rectangular or triangular form. The usual duration of the pulses in these experiments ranged from 300 to 1000 Ixs. The laser frequency is
~ I(v) ]' where lo(v) is the incident laser intensity and l(v) is the transmitted intensity. All measurements devoted to the sensitivity were done without frequency calibration. The spectra were measured for two regions around 3008 and 3012 c m - 1. The spectrum around 3008 c m - ~ was recorded with a methane pressure of 0.27 Pa. The value of the absorbance was found to be proportional to the pressure. A signal-to-noise ratio of 200 was obtained for the lowest concentration of 7 × 1 0 t3 molecules/ cm 3 used in the experiments. The peak-to-peak noise of the original spectra was decreased by filtering the
a
0.020
0.015
o.olo ..Q <
0.005
0.000 -
c
i
i
400
600
Frequency, arb. units Fig. 3. Spectra o f mixture C H 4 : A r = 1 : 100 in the spectral region o f 3 0 1 2 c m - l u n d e r different partial pressures o f methane, (a) - 0.13 Pa and (b) - 1.3 × 10 - 2 Pa. (c) Spectrum o f laser radiation measured in the double-pulse scheme. N u m b e r o f passes o f the laser beam is 34.
D.K. Bronnikov et a l./Chemical Physics Letters 249 (1996) 423-432
high-frequency noise. The same measurements were done in the region of 3012 cm -I for the mixture C H 4 : Ar = 1 : 100 for total pressures 13 and 1.3 Pa. These spectra are depicted in Fig. 3. A small modulation of the laser intensity l ( u ) of the order of magnitude 10 -3 l ( u ) w a s observed because of interference of the direct and scattered laser beams in the White cell. In the case of the equal interference for 1(~,) and lo(v) signals the modulation would be absent in the absorbance spectrum A(v). In our case the low frequency noise as a consequence of this modulation is present in the absorbance spectrum of Fig. 3a and 3b because the interference is different for l ( u ) and 10(~,) due to long-term instabilities of the optical apparatus. A new scheme was proposed and tested to measure the absorbance spectrum with the pulse-periodic molecular beam. The duration of one pulse of molecular beam and repetition rate of pulses are supposed to be around 500 Ixs and 10-100 Hz. In the beam experiments the data acquisition system allows one to record l ( u ) a n d /0(i,)with a short time interval of around 500 IXS. Due to this small delay between two measurements, the long term optical instabilities cannot produce a significant difference between lo(u) and l ( v ) signals. This method was tested without the molecular beam and l(u) and 10(~,) were accumulated in two different storages of the microcontroller with a time delay of 500 p~s for each pair of pulses. The resulting absorbance spectrum A(u) is presented in Fig. 3c where the low-frequency noise is absent. Therefore, for beam experiments the double-pulse scheme will give the possibility of eliminating the low-frequency noise and the parasitic interference. Taking into account the level of noise of the double-pulse scheme and the absorbance of Fig. 3b, a S / N ratio of about 20 can be obtained in beam experiments for a concentration of 3.5 × 10 ~2 molecules/cm 3. The most intense lines in the observed regions of 3008 and 3012 c m - t have rotational numbers 15-17 and 10-12 with line strengths 10-~ and 9 × 10-~ cm -2 atm -~ at 300 K, respectively. The intensities of lines in the spectral region 3018 cm-~ (beginning of the Q-branch) are 4 - 5 times higher with respect to those observed in the 3012 cm ~ range [15]. For these measurements the optical length of a single pass of a laser beam was equal to 130 mm. This means that for experiments on the interaction of
427
the molecular beam with the crystal the sensitivity will be 13 times less with respect to the present one because the optical length of the single pass in the scattered beam will be about 10 mm. Therefore, the detection limit with S / N ratio = 1 can be obtained in the spectral regions 3008, 3012 and 3018 c m - [ for concentrations 5 × 1012, 3 × 1012 and 5 × l 0 I1 molecules/cm 3 in the scattered molecular beam, respectively.
3.2. Study of the distribution in jets The present diode lasers were tested in investigations of the vibrational rotational distribution in a methane planar jet. The molecular jet installation is described in Ref. [10]. Methane was heated up to 900 K before supercooling in the jet. The dimensions of the slit nozzle and the stagnation pressure were 0.3 × 300 mm and 2.5 bar, respectively. Measurements were done with the diode laser beam aligned perpendicular to the direction of the jet with an optical path length of 300 mm.
3,2.1. Spectroscopic background The vibrational structure of C H 4 is described in Ref. [10]. The interacting bending modes u4 and u 2 with corresponding energies 1311 and 1533 cm -~ are roughly onehalf of the stretching modes u~ (2916.5 c m - i ) a n d u 3 (3019 c m - I ) . Due to Coriolis and Fermi resonances, a polyad scheme is necessary to describe the vibration-rotational levels. The polyad N contains al kinds of harmonic combination bands such as /l b -t'- 2n s = N, where n b and n~ are the numbers of bending and stretching quanta, respectively. The labels given to the first polyads, with their vibrational compositions, are given in Table 1. Up to now, the energies for the ground vibrational state and the two first excited polyads, dyad [16] and pentad [15] are known with good accuracy (better than 10-2 c m - ~), sufficient for assignments in diode laser spectra. The study of the third excited polyad is in progress [17] and upper polyads are practically unknown. Concerning infrared intensities, models adapted to the polyad scheme have been developed and applied to the dyad (containing u4) [18], the pentad (containing ~'3) [15] and the associated hot band systems (pentad*--dyad) [19] and (octad dyad) [17]. Then, transition moments for the ~'4
D.K.Bronnikovet al./ ChemicalPhysicsLetters249 (1996)423-432
428
(P, *-- P,_ ~) or v 3 (P,, *-- P,_ 2) cascades can be estimated with confidence,
population of rovibrational levels was obtained from a comparison of measured absorbances with corresponding predicted values, as explained below (Section 3.2.3). This method was applied previously to measurements [10,20] which were done in the 7.7 Ixm region for a few spectral regions, each of them being measured with one laser scan. All the results obtained in the 7.7 i~m region are gathered together in Fig. 5 where it is clear that a partial equilibrium distribution of the population for the energy levels within each polyad are observed and can be characterized by rotational temperatures, which are also reported in Fig. 5. The same information about the rotational distribution for ground and dyad states and the vibrational temperature was also extracted from the experimental spectrum shown in Fig. 4b. The rotational temperatures for the ground and dyad states were found to be coincident with the values appearing in Fig. 5 to within 10%.
3.2.2. Results An example of experimental and appropriate calculated spectra are presented in Fig. 4, where calibration of the frequency scale of the experimental spectrum is done in accordance with the positions of well-known absorption lines. Good correspondence of the calculated and experimental spectra is obtained for the given spectral region. The calculated spectrum includes transitions of u 3, of hot bands P3 "Jr-//4 124 and v 2 + v 3 - v 2 and even some weak lines probably from u 3 + 2 v4 - 2 u4. It also contains v 3 lines of ~3CH4 (in natural abundance). For the simulation, a resolution of 4 x 10 -3 cm-~ and a Gaussian apparatus lineshape was assumed and convoluted with the usual Voigt profile. The pl (equivalent gas density) was 330 Pa X 30 cm. The simulation of absorbance itself is made with a vibrational temperature of 900 K and rotational temperatures for different polyads as they were obtained from a detailed energy distribution of methane in the supersonic jet. The Doppler temperature is supposed to be 150 K in this simulation. This distribution of the -
-
3.2.3. Estimation ofpolyad populations To understand the relative population of the polyads for comparison with the initial one before supercooling, calculations of the total polyad population are also needed. In absorption, the line intensity
1.8 1.6 1.4
.
u
1.o-
g
~
!
-
< 0 0.20.4. 6 - ."
o.o3007.4
]~~
a
]/// l!, ~ ]l ~ [ ~ ~ l ~ ] l i ~' ~ l i @ l
b I
I
I
I
I
I
3007.6
3007.8
3008.0
3008.2
3008.4
3008.6
Frequency, cm4 Fig. 4. (a) Calculated and (b) experimental absorbance spectra of CH 4 molecules under conditions of a molecular jet. The spectrum consists of lines of four bands: (D) v3 *-- 0, (*) v~ *- 0 of 13CH4, ( ' ) lJ2 + ~'3 +- 1)2 and v3 + v4 ,- v4.
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
429
O"l-g=210K
Tdyacl=21OK
-
c 4
-4
~
-6-
\
Tpentad=205K
Z -8,
-10 0
10;0
20;0 3000 Energy, cm -1
40'00
50'00
Fig. 5. Vibrational rotational distribution of methane under conditions of a molecular jet with stagnation temperature 900 K. The population data are obtained from spectra of the 7.7 t~m region.
integrated over a lineshape expressed in wavenumbets and normalized to unit pressure is ~ 8"rr3 Ni /"if
1 --
Sif- 3h~ p c
diN r
df | - - R i f l a.
The integrated absorbance of the line is (in cm-~), so that aif
8333
t"if
(1)
dfNi ] di Air=plS~r
1 - - diNr ] -dr -Rill a.
--7- = 3h---TNi-7" In Eqs. (1) and (2),
dtN i ] d i u/c is the wavenumber
(2)
of the
transition i --+ f, N i (N r) is the population of the initial (final) energy level and d i and df are the degeneracies of these levels. In the case of methane, d = go(2 J "f- 1) with gc corresponding to the nuclear spin and symmetry degeneracy (go = 5' 2' 3 f°r C = A, E, F). l~, is the isotopic abundance (0.988 for 12CH4 in natural methane). Finally, Rif is the 'weighted transition moment squared' as defined, for example, by Gamache and Rothman [21]. In the experiment, A~r, l and v / c are measured; R~f can be calculated from the known dipole moment parameters; from Fig. 5, it seems reasonable to estimate the
fact°r l-d~Nf/dfN~ bY l-exp(-hcu/kTs) where T~ is the stagnation temperature; finally, the population N i of the initial state of the transition can be
extracted from Eq. (2). At this step, one can explain how the structure of the population of states is first obtained. In Eq. (1), one can also replace N i by e x p ( - E i / k T ~ ) / Z ( T e) w h e r e T~ is some chosen total equilibrium temperature and Z(T~) the associated partition function and one obtains Sir which is exactly the line strength in c m - 2 / a t m at T~. Then, the quantity Aif exp(-Ei/kT~)/Sir is proportional to N i and its logarithm gives, in arbitrary units, the distribution of populations as shown, for example, in Fig. 5. In this case, the populations of energy levels in a given polyad is of Boltzman type. This implies the following relation between the population Ni of an individual energy level from this polyad and the population Np of the complete polyad:
Npdi(E_~Tp) N~ =
Zp exp -
,
(3)
where Tp is the 'polyad temperature' which can be determined experimentally from the slope of the distribution of populations in this polyad (see Fig. 5) and where Zp is a 'polyad partition function' given by
(
E, )
Zp = ~ d~ exp . i cp ~Tp
(4)
430
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 4 2 3 - 4 3 2
Table I Composition o f the first vibrational polyads o f methane N
Label
0 1
ground dyad
2 3 4
pentad octad tetradecad
Number of levels
Number of sublevels
1 2
I 2
5 8 14
9 24 60
Composition (increasing energy order) g r o u n d state v4, u~ 2 u 4, v 2 + v4, v I, v 3, 2 v 2 3v4, u2 + 2~'4, uL + u4, I)3 -~- P4, 2v2 + v4, /'Jl ~- /72, v2 q- /~3, 3u2 4u 4, .02 + 3 u 4, u I + 2u4, .v3 + 2u4, 2 u 2 + 2u4, u~ + u 2 + u4, 2Ul, u 2 + u 3 + u4, u I + u s, 3u_~ + /74, Pl + 2 u 2 , 2 u 3 , 2r'2 + u3, 4u2
This polyad partition function can be calculated from the known energy levels of this polyad (truncated to a reasonable J value), so that Np can be calculated from one (or more)Ni. Thus the concentrations of CH 4 in ground, dyad and pentad states for the experimental conditions of Fig. 5 were found to be equal 1.7 x 1 0 ~6, 8.3 × 10 ts, and 2.8 x 10 ~5 molecules/cm 3, respectively,
4. Discussion The data presented on the sensitivity of the diode laser spectrometer and on the spectroscopy of vibrationally excited methane under conditions of the supersonic jet allow one to compare the advantages of the 3.3 and 7.7 Ixm spectral regions for state-resolved experiments for the molecular beam-surface interaction. The 7.7 txm region provides more rich information because in this case 'hot' transitions are investigated with the smallest step v4 and the population of states up to the pentad levels (Table 1) can be probed. The upper levels of the transitions for this case are well known. For 'hot' transitions from the pentad levels in the 3.3 Ixm region the energies of upper levels can only be predicted with poor accuracy, so that only ground and dyad states can be probed with these lasers. On the other hand, measurements in the 3.3 ixm region are more sensitive because the intensities of lines are more than two times higher and because the higher power of the lasers [22] and lower noise of InSb photodiodes allow the recording of spectra with a better value of the S / N ratio, The observed vibrational-rotational distribution
of methane shows strong rotational relaxation of molecules in different vibrational states (Fig. 5). The rotational temperature was found to be the same ( 2 1 0 + 5 K) for each observed vibrational polyad and this result is independent of the wavelength (3 Ixm or 7.7 lxm) used to study the populations. The ratio of the populations of the ground, dyad and pentad states with respect to the total one for the experimental conditions of Fig. 5 were found to be equal to 0.58, 0.28 and 0.095, respectively. The same ratios for the initial conditions of the stagnation temperature 900 K are 0.55, 0.30 and 0.11. This means that within experimental accuracy relaxation of the vibrational energy was not found. The observed type of the distribution with the small rotational temperature within each polyad and the high vibrational total temperature was not taken into account in analysis of the effect of the vibrational energy on the dissociative chemisorption in experiments [2,3] for the methane beam-surface systern. In these papers the relative populations both between and within polyads were supposed to be unchanged during expansion of the beam and corresponded to the temperature of a nozzle. The present results point out the strong redistribution of the population between vibrational levels of the polyads due to supercooling in the molecular jet. For exampie, for the discussed case of the stagnation and dyad temperatures 900 and 210 K the populations of the P4 and u 2 vibrational states become 1.3 times higher and 2.2 times lower with respect to the appropriate populations before supercooling. For the molecules in dyad states cooled up to the temperature Tr0 equal to 100 K the corresponding coefficients for the depopulation of u 2 and overpopulation of u4 will be
D.K. Bronnikov et a l . / Chemical Physics Letters 249 (1996) 423-432
431
12 and 1,4, respectively. These estimations were done in supposition of the unchanged integral population of polyads during relaxation in the jet. Therefore, in discussing the observed increase in the sticking probability of methane [ 1 - 3 ] by the vibrational excitation of the molecular beam it is worth paying attention to the drastic increase in
distribution during energy relaxation under non-equilibrium conditions of the molecular jet or m o l e c u l e surface system. In the case of a molecular jet, no relaxation of vibrational energy between polyads was observed.
population of the u4 vibrational states and the strong depopulation of the other states in the polyads due to supercooling. The states of mode u4 are the lowest and, consequently, most populated in each polyad. In experiments [1-3] axisymmetric types of continuous molecular beam with stagnation temperatures around l000 K were used. Another experimental condition of jet expansion in our case does not allow the
Acknowledgement
prediction of the rovibrational distribution in these molecular beams from our data with high accuracy. Measurements of the vibrational distribution of molecules before and after interaction with a surface will give the most correct account of the role of vibrational energy in p r o m o t i n g d i s s o c i a t i v e chemisorption in beam experiments.
This work was partially supported by N A T O International Scientific Exchange Programs under Linkage Grant 921120 and in part by the International Science Foundation under Grant N M3T000. DKB and Y u G F thank the F O M Institute for Atomic and Molecular Physics, where the data of Section 3. I were taken, for its support and hospitality during several visits.
References
5, C o n c l u s i o n
[I] C.T. Rettner, H.E. Pfnur and DJ. Auerbach, Phys. Letters 54 (1985) 2716. [21 M.B. Lee, Q.Y. Yang and S.T. Ccyer, J. Chem. Phys. 87 (1987) 2724. [3] G.R. Schoofs, C.R. Arumainayagam, M C . McMaster and
A diode laser spectrometer is constructed for investigations of the state-to-state resolved interaction of a molecular beam of methane with a metal surface. The sensitivity of the diode laser spectrometer
R.J. Madix, Surface Sci. 215 (1989) 1. [4] A.C. Luntz and J. Harris, Surfacc Sci. 258 (1991) 397. [5] S.G. Brass, D.A. Reed and G. Ehrlich, J. Chem. Phys. 87 (1987) 4285.
was checked with a static gas under room temperature conditions. It was estimated for future experimerits that in the scattered molecular beam the detection limit can be reached for concentrations of t0125 × 10 J~ m o l e c u l e s / c m 3 for the rotational temperature 300 K. The double-pulse registration scheme
[6] J.T. Yates Jr., J.J. Zinck, S. Sheard and W.H. Weinberg, J. Chcm. Phys. 70 (1979)2266.
[71 A. Amrein, M, Quack and U. Schmitt. J. Phys. Chem. 92 (1988) 5455. [8] M. Hepp, G. Winnewisser and K. Yamada, J. Mol. Spectry. 146 (1991) 18 I; 164 (1994) 311.
[9] D.J. Nesbitt, J.W. Nibler, A. Schiffmann and W.B. Chapman, J. Chem. Phys. 98 (1993) 9513.
proposed for experiments with the molecular beam will provide the probability of eliminating the lowfrequency noise in absorption spectra of the scattered beam. The diode lasers of the spectrometer were used for measurements of the energy distribution in internal states in supersonic jets of methane. The rotational distribution of molecules within each vibrational polyad including the ground s t a t e w a s found to be Boltzmann-like with the same temperature. Calculations of population for a defined vibrational state or polyad were done for an observed type of distribution to analyze the evolution of the detailed
[10] J.C. Hilico, G.S. Baronov, D.K. Bronnikov, S.A. Gavrikov, 1.I. Nikolacv, V.D. Rusanov and Yu.G. Filimonov, J. Mol. Spectry. 161 (1993) 435. [11] G.S. Barnov, D.K. Bronnikov and S.A. Gavrikov, Soviet Phys. JETP 73 (1991)911. [12] M.E.M. Spruit, E.W. Kuipers, M.G. Tenner, J. Kimman and A W. Klcyn, J. Vacuum Sci. Technol. A 5 (1987) 496. [13] F.H. Gcuzcbrock, A.E. Wiskerke, M.G. Tcnner, A.W. Kleyn, s Stolte, A. Namiki, J. Phys. Chem., 95 (1991) 8409; A.E. Wiskerke, C.A. Taatjes, A.W. Klcyn, R.J.W.E. Lahaye, S. StoRe, D.K. Bronnikov and B.E. Hayden, J. Chem. Phys. 1(12 (1995) 3835. [14] A.I. Kuznetsov, D.M. Loukianov and H. Martin, Tunable diode laser applications, SPIE 1724 (1992) 128.
432
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
[15] J.C. Hilico, J.P. Champion, S. Toumi, VI.G. Tyuterev and S.A. Tashkun, J. Mol. Spectry. 168 (1994) 455. [16] J.P. Champion, J.C. Hilico, C. Wenger and L.R. Brown, J. Mol. Spectry. 133 (1989) 256-272. Il7] J.C. Hilico, S. Toumi and L.R. Brown, in: Laboratory and astronomical high resolution spectra, ASP Conf. Ser. 81 (1995) pp. 322-324. [18] L.R. Brown, M. Loete and J.C. Hilico, J. Mol. Spectry. 133 (1989) 273.
[19] O. Ouardi, Thesis. Universite de Bourgogne, Dijon (1988). [20] J.C. Hilico, D.K. Bronnikov, D.V. Kalinin, V.D. Rusanov and Yu.G. Selivanov, in preparation. [21] R.R. Gamache and L.S. Rothman, J. Quantum Spectry. Radiative Transfer 48 (1992)519-525. [22] T.N. Danilova, O.G. Ershov, A.N. Imenkov, 1.N. lvchenko, V.V. Sherstnev and Yu.P. Yakovlev, Tech. Phys. Letters 20 (1994) 172.
9 February 1996
PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 249 (1996) 423-432
A diode laser spectrometer for state-resolved experiments on the methane-surface system D.K. Bronnikov a, P.V. Zyrianov a,~, D.V. Kalinin a, Yu.G. Filimonov a, A.W. Kleyn b, J.C. Hilico c,. a Russian Scientific Center 'Kurchatov Institute'. 123182 Moscow, Russian Federation b FOM-lnstituteJbr Atomic" and Molecular Physics. Kruislaan 407, 1098 SJ Amsterdam, 7"he Netherlands c Laboratoire de Physique de rUniversit£ de Bourgogne, BP 138. 21004 Dijon Cedex, France
Received 25 September 1995; in final form 17 November 1995
Abstract A diode laser spectrometer for studying the state-resolved scattering of a molecular beam of methane in a molecule-surface system is described. Preliminary estimation of the sensitivity of the spectrometer for future scattering experiments is done. The advantages of data obtained in the 3.3 and 7.7 ~m spectral regions are analyzed. A double pulse recording scheme for the elimination of low-frequency noise in the absorption spectra of the molecular beam is proposed and tested under static conditions. Measurement of the detailed rotational vibrational distribution in a jet of methane is done to obtain the main parameters of the direct beam in scattering experiments. The rotational distribution within each vibrational polyad is found to be of Boltzmann type. A method of calculating the population for a defined vibrational state or polyad is developed to analyze the evolution of the detailed distribution during the energy relaxation under non-equilibrium conditions of the molecular jet or molecule-surface system.
1. I n t r o d u c t i o n The dissociative chemisorption of methane on metals is one of the main steps of catalytic conversion of methane to higher hydrocarbons. Many studies have been devoted to the main factors that activate the C - H bond cleavage. Molecular beam experiments have probed the effects of the translational and vibrational energies of molecules, and the surface temperature on the dissociation. A strong depen-
dence of the CH 4 dissociation probability on the vibrational energy was observed [1-3]. The same dependence was tested in experiments with direct laser excitation of methane. Facilitation of the dissociative chemisorption was found to be negligible in this case. Many models have been suggested to account for both the results of these particular experiments and all variety of data [1-4]. State-resolved molecular beam experiments arc promising from the viewpoint of comprehending vibrational activation and as a test o f theoretical models. The structure of the energy levels of methane is
l Present address: Institute of General Physics, 38 Vavilov street, 117942 Moscow, Russian Federation. Corresponding author,
complicated and, consequently, the vibrational rotational distribution and energy relaxation in molecular beams need to be investigated. All previous state-re-
0009-2614/96/$12.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0009-261 4(95)0 l 413-6
D.K. Bronnikov et al. / Chemical Physies Letters 249 (1996) 423-432
424
solved beam experiments were mainly devoted to the behavior of vibrationally non-excited methane. Measurements of the rotational temperature and investigation of the nuclear spin relaxation of methane were carried out in a supersonic jet for the stagnation temperature 300 K [7,8]. Direct infrared absorption was used for measuring the state-to-state rotational energy transfer in crossed molecular beams for the Ar + C H 4 system [9]. The wide possibilities of diode laser spectroscopy were demonstrated in Ref. [10] where the observation of high vibrational and low rotational temperatures of methane in a supersonic jet for a stagnation temperature as high as 900 K was described. Diode laser spectroscopy is efficient for state-resolved experiments in polyatomic moleculesurface systems as well. This was demonstrated in experiments devoted to desorption of CO 2 molecules from a surface [11]. The interaction of a molecular beam of methane with a metal surface is planned for investigation by this method. For realization of this project, a diode laser spectrometer of high sensitivity with a multipass cell was developed and constructed to be compatible with a molecular beam apparatus. This apparatus was used for state-resolved experiments on the interaction of diatomic molecules with a surface by a resonance-enhanced multiphoton ionization method [12,13]. In this Letter, experimental data for estimation of the sensitivity of state-resolved measurements
for methane are presented. Diode lasers of this spectrometer have also been used for measurements of the rotational-vibrational distribution in a molecular jet of methane. This information about the detailed vibrational-rotational distribution in a direct beam is necessary for the proper interpretation of future results of scattering experiments and has not been obtained before. A method of calculating the population for a defined vibrational state or polyad has been developed to analyze the evolution of the detailed distribution during energy relaxation under non-equilibrium conditions, including the moleculesurface system.
2. Diode laser spectrometer
2.1. Optical apparatus The scheme of the proposed experiments is depicted in Fig. 1. The molecular beam apparatus is described in detail in Ref. [12]. A metal crystal is mounted on a manipulator and is placed in an ultrahigh vacuum (UHV) chamber. By turning the manipulator the crystal can be faced to different control systems of surface quality and the incident angle of the molecular beam can be changed as well. The optical system includes a basic channel for the measurement of spectra of the scattered molecular beam
Scattered
]
I
i/
alignment He+Ne laser
MB
I4
fl:s I
I j
t! Controlchan~ell-I---
,
gl'
m,..~.
~
,
2__
Basic channel
.
.~+-
,~1
.
I +
. ,,.. ,
x s ," irect MB .
F i g . 1. D i o d e l a s e r s p e c t r o m e t e r ;
.
.
.
-it
.
.
j+ . ,,
vcmtec~a
. •
crystal
U. H. V. .c h. a m ber . . .
I - IR detector, 2 - removable Fabry-P6rot
.
.
.
.
I
etalon, 3 - reference cell.
425
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
and a control channel to check and improve the laser radiation quality over the long accumulation time of the spectra. Two different outputs of the diode laser radiation are used for these c h a n n e l s . Diode lasers were obtained from the Ioffe Physical-Technical Institute, St. Petersburg for the 3.3 Ixm region and from the Lebedev Physical Institute, MOSCOW for the 7.7 g m region. A diode laser (DL) is mounted in a cryogenic refrigerator for cooling and thermostabilisation in the range 78-300 K. The optical baseplate also contains collimating optics, four rotatable cells for reference gases, a Fabry-P6rot etalon for calibration of the wavelength scale and two infrared detectors in liquid nitrogen cryogenic refrigerators with preamplifiers. To reach highest sensitivity, a multipass White cell with a base length of 130 mm is constructed to get passes of the laser beam in a small volume close to the crystal. The dimensions of the probing zone for the molecular beam are 20 mm in the direction of scattering and 5 mm across the beam. These sizes are defined by the geometry of laser beams in the probing volume. The third dimension depends on the diameter of the molecular beam spot at the crystal and the angle of divergence of the scattered beam out of the scattering plane. The axis of the White cell may be aligned 10 mm far from the surface of the crystal in the direction of scattering. There is a possibility of detecting the scattered beam under different angles (from 0 to 90 °) with respect to the direct beam due to the ability to change the position of the symmetry plane of the White cell. The number of passes of the laser beam can be adjusted up to 50, so that the total absorption path length in the scattered beam can be about 50 cm for a crystal with a diameter of 10 ram.
2.2. Control, data acquisition LaserSpectrum's high speed data acquisition and laser control system was modified to be used for our specific task. This system was described in Ref. [14]. It supports basic diode laser control functions, signal recording, data accumulation and handling. All functional units of the electronic system, laser temperature controller, - laser current source, - data acquisition subsystem, -
[
][j
Mi. . . . . . troller
~
~t ~
a
~
~6"~p ie
~loeldand
j! -d ~!
L. . . . . . . .
[!lllllll ~ 1 [
Host
comp....
analog from ----< signals ~ preamplifiers
flash20Msp/s 8-bitADC ~'~, I ~ 12-bit .... p ~ <
jj
[- - ~
Diode laser
s..... ~ L
Temperature
~
Cryostat
condoner
Fig. 2. Blockdiagram of the electronicsystem.
are controlled by the high speed microcontroller SAB 80C166. A block diagram of the system is shown in Fig. 2. The current source implements the laser frequency tuning by periodically repeating laser current pulses of rectangular, triangular or more complex form. The mean current noise was tested to be less than 50 mA while the total current was 500 mA. The temperature of the diode laser is set by a 12-bit DAC and is stabilised within 3 × 10 -3 K. The system performs the analog data acquisition by a flash 8-bit ADC from one of three input channels. The highest sampling rate of the ADC is 20 Msp/s. The offset for the registration of each photosignal pulse can be changed by a 12-bit DAC. This allows one to increase the amplitude resolution (up to 12-bit) and, consequently, the signal-to-noise ratio ( S / N ratio) owing to signal accumulation over several pulses and simultaneous variation of the ADC offset. All ADC and DAC are calibrated in correspondence with physical values. The spectrum of diode laser radiation is stabilized by the control channel on the absorption spectrum of a reference gas. This feedback of frequency is implemented by a four-line sample and hold amplifier. The system is able to measure the amplitude of the photosignal at four points around any absorption line for each pulse and to produce a calibrated variation of the diode laser current parameters for keeping the absorption line in a definite position. The electronic system may be synchronized with another system and can produce a defined number of pulses for a one synchronization pulse. Each appropriate photo-
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
426
signal can be accumulated in a separate storage of the microcontroller. Primary data processing with high speed of manipulation such as accumulation and control of line position for stabilization, is bandled by the microcontroller, while more complex data processing and a user interface are supported by an IBM PC.
3. Experimental results
3.1. Sensitivity of the spectrometer
tuned by heating the crystal by the current pulse. The tuning rate lies in a range of 103-104 c m - ~ / s . Therefore, an absorbance spectrum of 1 cm-1 can be measured during one pulse of the molecular beam with a typical duration of 300 Vs. To determine the absorbance spectrum of a gas pulses of laser intensity l(t) and lo(t) are recorded with and without the gas in the cell. These values l(t) and lo(t) depend on the frequency because of tuning of the laser frequency during the current pulse. The absorbance spectrum A(v) is
A( v ) = In( l°( v ) ]
To carry out measurements of the methane spectra and to estimate the sensitivity, the multipass White cell was installed in a vacuum chamber, characterized by a base pressure 10 -4 Pa. The chamber was filled by pure methane or by a mixture CH 4 : Ar = 1:100 under different pressures. Mixtures were used to decrease the concentration of methane to the lowest controlled limit. The White cell was adjusted for 34 passes of the laser beam. To obtain radiation the diode laser is pumped by current pulses of rectangular or triangular form. The usual duration of the pulses in these experiments ranged from 300 to 1000 Ixs. The laser frequency is
~ I(v) ]' where lo(v) is the incident laser intensity and l(v) is the transmitted intensity. All measurements devoted to the sensitivity were done without frequency calibration. The spectra were measured for two regions around 3008 and 3012 c m - 1. The spectrum around 3008 c m - ~ was recorded with a methane pressure of 0.27 Pa. The value of the absorbance was found to be proportional to the pressure. A signal-to-noise ratio of 200 was obtained for the lowest concentration of 7 × 1 0 t3 molecules/ cm 3 used in the experiments. The peak-to-peak noise of the original spectra was decreased by filtering the
a
0.020
0.015
o.olo ..Q <
0.005
0.000 -
c
i
i
400
600
Frequency, arb. units Fig. 3. Spectra o f mixture C H 4 : A r = 1 : 100 in the spectral region o f 3 0 1 2 c m - l u n d e r different partial pressures o f methane, (a) - 0.13 Pa and (b) - 1.3 × 10 - 2 Pa. (c) Spectrum o f laser radiation measured in the double-pulse scheme. N u m b e r o f passes o f the laser beam is 34.
D.K. Bronnikov et a l./Chemical Physics Letters 249 (1996) 423-432
high-frequency noise. The same measurements were done in the region of 3012 cm -I for the mixture C H 4 : Ar = 1 : 100 for total pressures 13 and 1.3 Pa. These spectra are depicted in Fig. 3. A small modulation of the laser intensity l ( u ) of the order of magnitude 10 -3 l ( u ) w a s observed because of interference of the direct and scattered laser beams in the White cell. In the case of the equal interference for 1(~,) and lo(v) signals the modulation would be absent in the absorbance spectrum A(v). In our case the low frequency noise as a consequence of this modulation is present in the absorbance spectrum of Fig. 3a and 3b because the interference is different for l ( u ) and 10(~,) due to long-term instabilities of the optical apparatus. A new scheme was proposed and tested to measure the absorbance spectrum with the pulse-periodic molecular beam. The duration of one pulse of molecular beam and repetition rate of pulses are supposed to be around 500 Ixs and 10-100 Hz. In the beam experiments the data acquisition system allows one to record l ( u ) a n d /0(i,)with a short time interval of around 500 IXS. Due to this small delay between two measurements, the long term optical instabilities cannot produce a significant difference between lo(u) and l ( v ) signals. This method was tested without the molecular beam and l(u) and 10(~,) were accumulated in two different storages of the microcontroller with a time delay of 500 p~s for each pair of pulses. The resulting absorbance spectrum A(u) is presented in Fig. 3c where the low-frequency noise is absent. Therefore, for beam experiments the double-pulse scheme will give the possibility of eliminating the low-frequency noise and the parasitic interference. Taking into account the level of noise of the double-pulse scheme and the absorbance of Fig. 3b, a S / N ratio of about 20 can be obtained in beam experiments for a concentration of 3.5 × 10 ~2 molecules/cm 3. The most intense lines in the observed regions of 3008 and 3012 c m - t have rotational numbers 15-17 and 10-12 with line strengths 10-~ and 9 × 10-~ cm -2 atm -~ at 300 K, respectively. The intensities of lines in the spectral region 3018 cm-~ (beginning of the Q-branch) are 4 - 5 times higher with respect to those observed in the 3012 cm ~ range [15]. For these measurements the optical length of a single pass of a laser beam was equal to 130 mm. This means that for experiments on the interaction of
427
the molecular beam with the crystal the sensitivity will be 13 times less with respect to the present one because the optical length of the single pass in the scattered beam will be about 10 mm. Therefore, the detection limit with S / N ratio = 1 can be obtained in the spectral regions 3008, 3012 and 3018 c m - [ for concentrations 5 × 1012, 3 × 1012 and 5 × l 0 I1 molecules/cm 3 in the scattered molecular beam, respectively.
3.2. Study of the distribution in jets The present diode lasers were tested in investigations of the vibrational rotational distribution in a methane planar jet. The molecular jet installation is described in Ref. [10]. Methane was heated up to 900 K before supercooling in the jet. The dimensions of the slit nozzle and the stagnation pressure were 0.3 × 300 mm and 2.5 bar, respectively. Measurements were done with the diode laser beam aligned perpendicular to the direction of the jet with an optical path length of 300 mm.
3,2.1. Spectroscopic background The vibrational structure of C H 4 is described in Ref. [10]. The interacting bending modes u4 and u 2 with corresponding energies 1311 and 1533 cm -~ are roughly onehalf of the stretching modes u~ (2916.5 c m - i ) a n d u 3 (3019 c m - I ) . Due to Coriolis and Fermi resonances, a polyad scheme is necessary to describe the vibration-rotational levels. The polyad N contains al kinds of harmonic combination bands such as /l b -t'- 2n s = N, where n b and n~ are the numbers of bending and stretching quanta, respectively. The labels given to the first polyads, with their vibrational compositions, are given in Table 1. Up to now, the energies for the ground vibrational state and the two first excited polyads, dyad [16] and pentad [15] are known with good accuracy (better than 10-2 c m - ~), sufficient for assignments in diode laser spectra. The study of the third excited polyad is in progress [17] and upper polyads are practically unknown. Concerning infrared intensities, models adapted to the polyad scheme have been developed and applied to the dyad (containing u4) [18], the pentad (containing ~'3) [15] and the associated hot band systems (pentad*--dyad) [19] and (octad dyad) [17]. Then, transition moments for the ~'4
D.K.Bronnikovet al./ ChemicalPhysicsLetters249 (1996)423-432
428
(P, *-- P,_ ~) or v 3 (P,, *-- P,_ 2) cascades can be estimated with confidence,
population of rovibrational levels was obtained from a comparison of measured absorbances with corresponding predicted values, as explained below (Section 3.2.3). This method was applied previously to measurements [10,20] which were done in the 7.7 Ixm region for a few spectral regions, each of them being measured with one laser scan. All the results obtained in the 7.7 i~m region are gathered together in Fig. 5 where it is clear that a partial equilibrium distribution of the population for the energy levels within each polyad are observed and can be characterized by rotational temperatures, which are also reported in Fig. 5. The same information about the rotational distribution for ground and dyad states and the vibrational temperature was also extracted from the experimental spectrum shown in Fig. 4b. The rotational temperatures for the ground and dyad states were found to be coincident with the values appearing in Fig. 5 to within 10%.
3.2.2. Results An example of experimental and appropriate calculated spectra are presented in Fig. 4, where calibration of the frequency scale of the experimental spectrum is done in accordance with the positions of well-known absorption lines. Good correspondence of the calculated and experimental spectra is obtained for the given spectral region. The calculated spectrum includes transitions of u 3, of hot bands P3 "Jr-//4 124 and v 2 + v 3 - v 2 and even some weak lines probably from u 3 + 2 v4 - 2 u4. It also contains v 3 lines of ~3CH4 (in natural abundance). For the simulation, a resolution of 4 x 10 -3 cm-~ and a Gaussian apparatus lineshape was assumed and convoluted with the usual Voigt profile. The pl (equivalent gas density) was 330 Pa X 30 cm. The simulation of absorbance itself is made with a vibrational temperature of 900 K and rotational temperatures for different polyads as they were obtained from a detailed energy distribution of methane in the supersonic jet. The Doppler temperature is supposed to be 150 K in this simulation. This distribution of the -
-
3.2.3. Estimation ofpolyad populations To understand the relative population of the polyads for comparison with the initial one before supercooling, calculations of the total polyad population are also needed. In absorption, the line intensity
1.8 1.6 1.4
.
u
1.o-
g
~
!
-
< 0 0.20.4. 6 - ."
o.o3007.4
]~~
a
]/// l!, ~ ]l ~ [ ~ ~ l ~ ] l i ~' ~ l i @ l
b I
I
I
I
I
I
3007.6
3007.8
3008.0
3008.2
3008.4
3008.6
Frequency, cm4 Fig. 4. (a) Calculated and (b) experimental absorbance spectra of CH 4 molecules under conditions of a molecular jet. The spectrum consists of lines of four bands: (D) v3 *-- 0, (*) v~ *- 0 of 13CH4, ( ' ) lJ2 + ~'3 +- 1)2 and v3 + v4 ,- v4.
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
429
O"l-g=210K
Tdyacl=21OK
-
c 4
-4
~
-6-
\
Tpentad=205K
Z -8,
-10 0
10;0
20;0 3000 Energy, cm -1
40'00
50'00
Fig. 5. Vibrational rotational distribution of methane under conditions of a molecular jet with stagnation temperature 900 K. The population data are obtained from spectra of the 7.7 t~m region.
integrated over a lineshape expressed in wavenumbets and normalized to unit pressure is ~ 8"rr3 Ni /"if
1 --
Sif- 3h~ p c
diN r
df | - - R i f l a.
The integrated absorbance of the line is (in cm-~), so that aif
8333
t"if
(1)
dfNi ] di Air=plS~r
1 - - diNr ] -dr -Rill a.
--7- = 3h---TNi-7" In Eqs. (1) and (2),
dtN i ] d i u/c is the wavenumber
(2)
of the
transition i --+ f, N i (N r) is the population of the initial (final) energy level and d i and df are the degeneracies of these levels. In the case of methane, d = go(2 J "f- 1) with gc corresponding to the nuclear spin and symmetry degeneracy (go = 5' 2' 3 f°r C = A, E, F). l~, is the isotopic abundance (0.988 for 12CH4 in natural methane). Finally, Rif is the 'weighted transition moment squared' as defined, for example, by Gamache and Rothman [21]. In the experiment, A~r, l and v / c are measured; R~f can be calculated from the known dipole moment parameters; from Fig. 5, it seems reasonable to estimate the
fact°r l-d~Nf/dfN~ bY l-exp(-hcu/kTs) where T~ is the stagnation temperature; finally, the population N i of the initial state of the transition can be
extracted from Eq. (2). At this step, one can explain how the structure of the population of states is first obtained. In Eq. (1), one can also replace N i by e x p ( - E i / k T ~ ) / Z ( T e) w h e r e T~ is some chosen total equilibrium temperature and Z(T~) the associated partition function and one obtains Sir which is exactly the line strength in c m - 2 / a t m at T~. Then, the quantity Aif exp(-Ei/kT~)/Sir is proportional to N i and its logarithm gives, in arbitrary units, the distribution of populations as shown, for example, in Fig. 5. In this case, the populations of energy levels in a given polyad is of Boltzman type. This implies the following relation between the population Ni of an individual energy level from this polyad and the population Np of the complete polyad:
Npdi(E_~Tp) N~ =
Zp exp -
,
(3)
where Tp is the 'polyad temperature' which can be determined experimentally from the slope of the distribution of populations in this polyad (see Fig. 5) and where Zp is a 'polyad partition function' given by
(
E, )
Zp = ~ d~ exp . i cp ~Tp
(4)
430
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 4 2 3 - 4 3 2
Table I Composition o f the first vibrational polyads o f methane N
Label
0 1
ground dyad
2 3 4
pentad octad tetradecad
Number of levels
Number of sublevels
1 2
I 2
5 8 14
9 24 60
Composition (increasing energy order) g r o u n d state v4, u~ 2 u 4, v 2 + v4, v I, v 3, 2 v 2 3v4, u2 + 2~'4, uL + u4, I)3 -~- P4, 2v2 + v4, /'Jl ~- /72, v2 q- /~3, 3u2 4u 4, .02 + 3 u 4, u I + 2u4, .v3 + 2u4, 2 u 2 + 2u4, u~ + u 2 + u4, 2Ul, u 2 + u 3 + u4, u I + u s, 3u_~ + /74, Pl + 2 u 2 , 2 u 3 , 2r'2 + u3, 4u2
This polyad partition function can be calculated from the known energy levels of this polyad (truncated to a reasonable J value), so that Np can be calculated from one (or more)Ni. Thus the concentrations of CH 4 in ground, dyad and pentad states for the experimental conditions of Fig. 5 were found to be equal 1.7 x 1 0 ~6, 8.3 × 10 ts, and 2.8 x 10 ~5 molecules/cm 3, respectively,
4. Discussion The data presented on the sensitivity of the diode laser spectrometer and on the spectroscopy of vibrationally excited methane under conditions of the supersonic jet allow one to compare the advantages of the 3.3 and 7.7 Ixm spectral regions for state-resolved experiments for the molecular beam-surface interaction. The 7.7 txm region provides more rich information because in this case 'hot' transitions are investigated with the smallest step v4 and the population of states up to the pentad levels (Table 1) can be probed. The upper levels of the transitions for this case are well known. For 'hot' transitions from the pentad levels in the 3.3 Ixm region the energies of upper levels can only be predicted with poor accuracy, so that only ground and dyad states can be probed with these lasers. On the other hand, measurements in the 3.3 ixm region are more sensitive because the intensities of lines are more than two times higher and because the higher power of the lasers [22] and lower noise of InSb photodiodes allow the recording of spectra with a better value of the S / N ratio, The observed vibrational-rotational distribution
of methane shows strong rotational relaxation of molecules in different vibrational states (Fig. 5). The rotational temperature was found to be the same ( 2 1 0 + 5 K) for each observed vibrational polyad and this result is independent of the wavelength (3 Ixm or 7.7 lxm) used to study the populations. The ratio of the populations of the ground, dyad and pentad states with respect to the total one for the experimental conditions of Fig. 5 were found to be equal to 0.58, 0.28 and 0.095, respectively. The same ratios for the initial conditions of the stagnation temperature 900 K are 0.55, 0.30 and 0.11. This means that within experimental accuracy relaxation of the vibrational energy was not found. The observed type of the distribution with the small rotational temperature within each polyad and the high vibrational total temperature was not taken into account in analysis of the effect of the vibrational energy on the dissociative chemisorption in experiments [2,3] for the methane beam-surface systern. In these papers the relative populations both between and within polyads were supposed to be unchanged during expansion of the beam and corresponded to the temperature of a nozzle. The present results point out the strong redistribution of the population between vibrational levels of the polyads due to supercooling in the molecular jet. For exampie, for the discussed case of the stagnation and dyad temperatures 900 and 210 K the populations of the P4 and u 2 vibrational states become 1.3 times higher and 2.2 times lower with respect to the appropriate populations before supercooling. For the molecules in dyad states cooled up to the temperature Tr0 equal to 100 K the corresponding coefficients for the depopulation of u 2 and overpopulation of u4 will be
D.K. Bronnikov et a l . / Chemical Physics Letters 249 (1996) 423-432
431
12 and 1,4, respectively. These estimations were done in supposition of the unchanged integral population of polyads during relaxation in the jet. Therefore, in discussing the observed increase in the sticking probability of methane [ 1 - 3 ] by the vibrational excitation of the molecular beam it is worth paying attention to the drastic increase in
distribution during energy relaxation under non-equilibrium conditions of the molecular jet or m o l e c u l e surface system. In the case of a molecular jet, no relaxation of vibrational energy between polyads was observed.
population of the u4 vibrational states and the strong depopulation of the other states in the polyads due to supercooling. The states of mode u4 are the lowest and, consequently, most populated in each polyad. In experiments [1-3] axisymmetric types of continuous molecular beam with stagnation temperatures around l000 K were used. Another experimental condition of jet expansion in our case does not allow the
Acknowledgement
prediction of the rovibrational distribution in these molecular beams from our data with high accuracy. Measurements of the vibrational distribution of molecules before and after interaction with a surface will give the most correct account of the role of vibrational energy in p r o m o t i n g d i s s o c i a t i v e chemisorption in beam experiments.
This work was partially supported by N A T O International Scientific Exchange Programs under Linkage Grant 921120 and in part by the International Science Foundation under Grant N M3T000. DKB and Y u G F thank the F O M Institute for Atomic and Molecular Physics, where the data of Section 3. I were taken, for its support and hospitality during several visits.
References
5, C o n c l u s i o n
[I] C.T. Rettner, H.E. Pfnur and DJ. Auerbach, Phys. Letters 54 (1985) 2716. [21 M.B. Lee, Q.Y. Yang and S.T. Ccyer, J. Chem. Phys. 87 (1987) 2724. [3] G.R. Schoofs, C.R. Arumainayagam, M C . McMaster and
A diode laser spectrometer is constructed for investigations of the state-to-state resolved interaction of a molecular beam of methane with a metal surface. The sensitivity of the diode laser spectrometer
R.J. Madix, Surface Sci. 215 (1989) 1. [4] A.C. Luntz and J. Harris, Surfacc Sci. 258 (1991) 397. [5] S.G. Brass, D.A. Reed and G. Ehrlich, J. Chem. Phys. 87 (1987) 4285.
was checked with a static gas under room temperature conditions. It was estimated for future experimerits that in the scattered molecular beam the detection limit can be reached for concentrations of t0125 × 10 J~ m o l e c u l e s / c m 3 for the rotational temperature 300 K. The double-pulse registration scheme
[6] J.T. Yates Jr., J.J. Zinck, S. Sheard and W.H. Weinberg, J. Chcm. Phys. 70 (1979)2266.
[71 A. Amrein, M, Quack and U. Schmitt. J. Phys. Chem. 92 (1988) 5455. [8] M. Hepp, G. Winnewisser and K. Yamada, J. Mol. Spectry. 146 (1991) 18 I; 164 (1994) 311.
[9] D.J. Nesbitt, J.W. Nibler, A. Schiffmann and W.B. Chapman, J. Chem. Phys. 98 (1993) 9513.
proposed for experiments with the molecular beam will provide the probability of eliminating the lowfrequency noise in absorption spectra of the scattered beam. The diode lasers of the spectrometer were used for measurements of the energy distribution in internal states in supersonic jets of methane. The rotational distribution of molecules within each vibrational polyad including the ground s t a t e w a s found to be Boltzmann-like with the same temperature. Calculations of population for a defined vibrational state or polyad were done for an observed type of distribution to analyze the evolution of the detailed
[10] J.C. Hilico, G.S. Baronov, D.K. Bronnikov, S.A. Gavrikov, 1.I. Nikolacv, V.D. Rusanov and Yu.G. Filimonov, J. Mol. Spectry. 161 (1993) 435. [11] G.S. Barnov, D.K. Bronnikov and S.A. Gavrikov, Soviet Phys. JETP 73 (1991)911. [12] M.E.M. Spruit, E.W. Kuipers, M.G. Tenner, J. Kimman and A W. Klcyn, J. Vacuum Sci. Technol. A 5 (1987) 496. [13] F.H. Gcuzcbrock, A.E. Wiskerke, M.G. Tcnner, A.W. Kleyn, s Stolte, A. Namiki, J. Phys. Chem., 95 (1991) 8409; A.E. Wiskerke, C.A. Taatjes, A.W. Klcyn, R.J.W.E. Lahaye, S. StoRe, D.K. Bronnikov and B.E. Hayden, J. Chem. Phys. 1(12 (1995) 3835. [14] A.I. Kuznetsov, D.M. Loukianov and H. Martin, Tunable diode laser applications, SPIE 1724 (1992) 128.
432
D.K. Bronnikov et al. / Chemical Physics Letters 249 (1996) 423-432
[15] J.C. Hilico, J.P. Champion, S. Toumi, VI.G. Tyuterev and S.A. Tashkun, J. Mol. Spectry. 168 (1994) 455. [16] J.P. Champion, J.C. Hilico, C. Wenger and L.R. Brown, J. Mol. Spectry. 133 (1989) 256-272. Il7] J.C. Hilico, S. Toumi and L.R. Brown, in: Laboratory and astronomical high resolution spectra, ASP Conf. Ser. 81 (1995) pp. 322-324. [18] L.R. Brown, M. Loete and J.C. Hilico, J. Mol. Spectry. 133 (1989) 273.
[19] O. Ouardi, Thesis. Universite de Bourgogne, Dijon (1988). [20] J.C. Hilico, D.K. Bronnikov, D.V. Kalinin, V.D. Rusanov and Yu.G. Selivanov, in preparation. [21] R.R. Gamache and L.S. Rothman, J. Quantum Spectry. Radiative Transfer 48 (1992)519-525. [22] T.N. Danilova, O.G. Ershov, A.N. Imenkov, 1.N. lvchenko, V.V. Sherstnev and Yu.P. Yakovlev, Tech. Phys. Letters 20 (1994) 172.