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Total ionization cross-sections of CH4 and C3H8 molecules for impact of 10–28 keV electrons
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 246 (2006) 297–302 www.elsevier.com/locate/nimb
Total ionization cross-sections of CH4 and C3H8 molecules for impact of 10–28 keV electrons S. Mondal *, R. Shanker Atomic Physics Laboratory, Department of Physics, Banaras Hindu University, Varanasi 221 005, India Received 24 November 2005; received in revised form 13 January 2006 Available online 2 March 2006
Abstract The total ionization cross-sections of methane and propane molecules are measured for impact of 10–28 keV electrons. The cross-sections are found to follow the variation shown by Bethe formula as a function of electron impact energy. Also, the present results compare well with the available data in the literature. Further, the measured cross-sections of the above hydrocarbon molecules are found to correlate strongly to the total number of molecular electrons and to the molecular dipole polarizability. 2006 Elsevier B.V. All rights reserved. PACS: 34.80.Gs Keywords: Total ionization cross-sections; Fano–Bethe plots; Molecular dipole polarizability
1. Introduction Studies of the ionization processes in simple hydrocarbon molecules under impact of charged particles are of crucial importance in molecular collisions as they provide information on the basic principles of ionization in polyatomic molecules. Also, the interest of studying the charged particle induced ionization of hydrocarbon molecules lies in their applications, for example, in plasma physics, atmospheric physics and in upper planetary atmosphere. In particular, the constituent gases of the medium in upper planetary atmosphere are generally known to be hydrocarbons, such as, CH4, C3H8, etc. Dissociative ionization of these molecules under impact of galactic cosmic rays which consists of photons, electrons and ions produces highly reactive radicals. These radicals not only combine to form more complex molecules but also to bring significant changes in their concentrations due to chemical coupling between ionic- and neutral species. These nucleation of *
Corresponding author. Tel.: +91 9415450541; fax: +91 542 2368174. E-mail addresses: [email protected] (S. Mondal), rshanker@ bhu.ac.in (R. Shanker). 0168-583X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.01.025
new particles change the cloud formation in upper planetary atmosphere [1]. Investigations of such phenomena have made it fundamentally important for measurements of reliable total ionization cross-sections of hydrocarbons by electron impact. The total ionization cross-section values are also needed for calculations of different parameters involved in atmospheric plasmas. Moreover, these values serve as a normalization standard for determination of various absolute partial ionization cross-sections. Using a parallel plate ion collection technique, the total ionization cross-sections of CH4 for electron impact energy from threshold to 1 keV have been measured by Rapp and Englander-Golden [2]. Schram et al. [3] reported total ionization cross-sections of many hydrocarbons for impact of electrons in the range of 0.6–12 keV. Further, Duric et al. [4] determined the total ionization cross-sections of CH4 and C3H8 for impact of electrons from threshold to 240 eV. Recently, Nishimura and Tawara [5] have measured the total ionization cross-sections of several hydrocarbons, such as, CH4, C2H4, C2H6 and C3H8 for electron impact with energies from threshold to 3 keV. Absolute partial ionization cross-sections of CH4 by impact of electrons having energies from threshold to 1000 eV by Straub et al. [6] and
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from threshold to 510 eV have been measured by Orient and Srivastava [7]. The latter authors have obtained the absolute cross-sections by normalizing the sum of relative cross-sections to a known total ionization cross-sections of inert gases (Ne, Ar, Kr and Xe). However, on one hand, the relative partial ionization cross-sections of CH4 have been measured by Adamczyk et al. [8], by impact of electrons of energy 20–2000 eV by Chatham et al. [9] for electron energies ranging from threshold to 400 eV. Grill et al. [10] have measured relative partial ionization crosssections of C3H8 by impact of electrons having energies from threshold to 950 eV. These groups have determined absolute cross-sections by normalizing their relative values to the absolute values of Orient and Srivastava [7] at a specific energy. On the other hand, ionization behavior close to threshold for fragment ion production from CH4, C3H8 and some simple molecules under electron impact has been studied by Fiegele et al. [11]. Most of the experimental studies for electron impact ionization cross-sections of hydrocarbons mentioned in the above paragraphs have been reported for relatively low impact energies. However, data for high impact energies are scarce in the literature [12]. Among these experimental studies, only Nishimura and Tawara [5] and Schram et al. [3] have derived information from their data on the dipole oscillator strength and have compared values with the optical results. Also, these experimental data in the overlapping region of impact energy are not consistent among themselves. Therefore, it was thought worthwhile to perform a systematic measurements of the total ionization cross-sections of CH4 and C3H8 molecules for impact of 10–28 keV electrons for which no experimental data exist in the literature, to our knowledge. For understanding the details of electron impact collision processes occurring in the considered hydrocarbon molecules, we have compared our results with those obtained by Born approximation calculations and have derived the dipole oscillator
strength for these collision systems. The obtained values have been compared with those derived from optical as well as with other existing results. 2. Experimental 2.1. Apparatus The present measurements of total ionization cross-sections of CH4 and C3H8 molecules have been performed on a crossed-beam type experimental facility [13]. The collision induced ions were extracted and collected by a timeof-flight (TOF) spectrometer. Details of development of the experimental apparatus have been described previously elsewhere [14,15]. In the following, we give a brief account of the relevant components and parameters that were used in the present measurements. The schematic diagram of the experimental set-up is shown in Fig. 1. A mono energetic electron beam was obtained from a custom built electron gun. The beam was collimated and focused to a spot size of 3 mm at the scattering center, about 500 mm away from the mounting flange of the electron gun. For reducing the deflection of electron beam in the interaction zone due to the earth’s magnetic field, the inner wall of the scattering chamber was shielded with a sheet of 0.5 mm thick antimagnetic l-metal. A biased (60 V) Faraday cup was used to monitor the beam current after it transmitted through the target gas. The target gas was made to effuse from a hypodermic needle at 90 to the incident electron beam direction at a thermal velocity. The target gas pressure was kept at 2 · 104 Torr which satisfied the condition for a single collision. The collisionally induced multiply charged ions produced in the interaction region were extracted in a TOF spectrometer. The extraction of ions was made by an electric field strength of 190 V/cm. The applied electric field was set perpendicular to both the direction of ejected electrons entering the channel electron
Fig. 1. Schematic diagram of the experimental set-up.
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299
multiplier (CEM) as well as to the direction of incident electrons. The extraction field was produced by applying an equal and opposite potentials to two horizontally mounted parallel plates (18 mm apart) enclosing the collision zone. The tip of the gas jet was positioned in the middle of two plates and pierced vertically into the lower plate from underneath. After extracting the ions, they were further accelerated into the drift tube biased at 215 V and were made to travel in a field-free region of about 22 mm path length. At the end of the drift tube, the ions were post-accelerated by applying a field of 900 V and were finally detected by the CEM biased at +3 kV. For measuring the total ionization cross-sections of the hydrocarbons using the above experimental facility, it was necessary to ensure an accurate alignment of the electron beam, the TOF spectrometer and the tip of the hypodermic needle with respect to the collision centre. 2.2. Data collection procedure Optimization for the full ion extraction and transmission efficiencies of the TOF was accomplished by measuring the total ion counts as a function of extraction and acceleration voltages applied on different electrodes of the TOF spectrometer. It is found that the number of ions increases with the extraction- and acceleration voltages and reaches a constant value. Hence, the optimized values for extraction and transmission voltages were those at which the corresponding ion counts obtain a constant value. Full detection efficiency of channeltron was ensured by setting the channeltron bias voltage at which the ion count rate becomes constant as a function of the biasing voltage. The ions collected by TOF spectrometer and detected by the channeltron were believed to originate from the target gas, this was confirmed by recording the TOF spectra of ions in coincidence with the electrons detected by a channeltron at 90 with respect to the incident beam direction. Fig. 2(a) and (b) show the typical time-of-flight spectra of ions produced from CH4 and C3H8 molecules respectively under impact of 10 keV electrons. It is to be noted that the charge states of the fragment ions produced from the parent molecules are not resolved in the spectra due to a poor time resolution of the employed TOF spectrometer. However, the positions of unresolved few fragment ions are marked by comparing the time-of-flight spectra of fragment ions produced from collisions of 200 eV electrons with CH4 and C3H8 molecules [16,17]. The total ionization cross-sections of the considered molecules were measured by detecting non-coincident total ion counts using the TOF spectrometer. The true total ion counts were obtained by subtracting the background ion counts from true plus background ion counts. The background ion counts were determined by measuring total ion counts produced from the residual gas alone present in the reaction chamber. From the detected total true ion counts Ni, the total ionization cross-section Qi was obtained by using a relation,
Fig. 2. Time-of-flight spectrum of fragment ions of (a) CH4 and (b) C3H8 measured in coincidence with secondary electrons of indiscriminated energy detected at 90 with respect to the incident beam direction for impact of 10 keV electrons.
Qi ¼ C
Ni 1 cm2 ; N e P L3:34 1016
ð1Þ
where Ne is the total number of counts of the incident electrons, P is the target gas pressure in Torr, L is the effective path length of the electron beam in the target gas in cm and C is a constant depending on the geometry of the TOF spectrometer. The typical values of above parameters in the present experiment are: Ni = 2 348 400, Ne = 9.3 · 1013, P = 2 · 104 Torr, L = 0.5 cm and C = 6614 for 10 keV e–C3H8 collisions. The total uncertainty involved in the measurement of Qi arises due to the uncertainties in the parameters C, Ni, Ne, P and L; they are estimated to be 5%, 2%, 1%, 5% and 20%, respectively. Hence, the overall uncertainty in the measurement of Qi becomes nearly 22%. 3. Results and discussion 3.1. Total ionization cross-sections The measured total ionization cross-sections Qi of CH4 and C3H8 for impact of 10–28 keV electrons are listed in
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-16
2
Total cross section (10 cm )
Table 1. The Qi values are obtained without any normalization either with theory or any previous experimental data on a given impact energy. Fig. 3 shows the variation of electron impact total ionization cross-sections of CH4 as a function of incident electron energy. In this energy range only one datum at 12 keV from Schram et al. [3] has an overlap with our data. Nishimura and Tawara [5] have measured the total ionization cross-sections of CH4 at still lower impact energies (63000 eV). Their data are found to show the similar decreasing trend of the cross-sections with impact energy in their considered region of impact as that of the present measurements. However, generally all data points of Schram et al. reported in the impact energy range 600–12 000 eV are found to lie lower than the data points of both the present as well as of Nishimura and Tawara. Fig. 4 shows Qi values of the present work for 10– 28 keV e–C3H8 collisions as a function of incident electron energy and compares with those of Schram et al. [3] and Nishimura and Tawara [5]. A single datum at 12 keV of Schram et al. is found to underestimate the present measurements. However, data of Nishimura and Tawara follow a similar trend of variation of Qi with impact energy in their energy region of interest as our data do. For electron impact ionization of a molecule, the total ionization cross-sections are strongly correlated to the total number of electrons z and also to the molecular dipole polarizability a. As the number of target electrons increases in a molecule, their contribution to the total ionization cross-section becomes larger [18]. This is verified by comparing the total ionization cross-sections of CH4 and C3H8 as displayed in Table 1. This table shows that the cross-sections of C3H8 are about 300% larger than those of CH4 molecule for all impact energies. In order to examine the effect of total number of electrons and molecular dipole polarizability, the values of Qi/z and Qi/a are calculated and listed in Tables 2 and 3, respectively, for CH4 and C3H8. The values of a for CH4 and C3H8 are known to be 2.6 · 1024 cm3 and 6.3 · 1024 cm3, respectively. The comparison of Qi/z and Qi/a values in the region of present energies shows nearly a constant value for both molecules within the error of measurements of Qi. This indicates that the total number of molecular electrons and molecular polarizability play determinative roles in process of total ionization of a polyatomic molecule. The incident electron recognizes not only all electrons in the molecule but also influences the structure of molecular electron cloud, that is to say, the polarizability a.
1
0.1
1000
10000
Incident electron energy (eV)
-16
2
Total cross section (10 cm )
Fig. 3. Electron impact total ionization cross-sections of methane (CH4) as a function of incident electron energy; (m) present data; (r) Nishimura and Tawara [5]; (d) Schram et al. [3].
1
0.1 1000
10000
Incident electron energy (eV) Fig. 4. Electron impact total ionization cross-sections of propane (C3H8) as a function of incident electron energy; (m) present data; (r) Nishimura and Tawara [5]; (d) Schram et al. [3].
3.2. Fano–Bethe plot In order to obtain further information on the ionization mechanism for the considered collision systems, the electron impact total ionization cross-sections have been compared with the theoretical calculations based on the
Table 1 Total ionization cross-sections Qi (1016 cm2) of CH4 and C3H8 under 10–28 keV electron impact E (keV)
CH4 C3H8
10
12
14
0.155 0.5
0.13 0.44
0.11 0.382
16 0.36
18
20
0.098
0.086 0.29
22
24
28
0.26
0.074 0.25
0.065 0.22
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Table 2 Ratio Qi/z (1016 cm2) of the total ionization cross-sections Qi and the molecular electrons z versus incident electron energy (keV) E (keV)
CH4 C3H8
10
12
14
0.0155 0.0208
0.013 0.0184
0.011 0.0159
16
18
20
22
24
28
0.0098
0.0086 0.0121
0.026 0.0108
0.0074 0.0104
0.0065 0.0092
0.015
Table 3 Ratio Qi/a (108 cm1) of the total ionization cross-section Qi and the molecular polarizability a versus incident electron energy (keV) E (keV) 14
0.05 0.07
0.04 0.06
16
4pa20 R 2 4Eel ci ; M I ln Eel R
ð2Þ
where Eel is the incident electron energy, a0 is the Bohr radius, R is the Rydberg energy, M 2I is the square of the dipole matrix element and ci is a constant. The value of M 2I is related to the differential optical oscillator strength f as, Z 1 df R dE. ð3Þ M 2I ¼ dE E IP Here the integration is taken over the continuum, E is the energy of the continuum electrons. For the present collisions of high energy incident electrons, it is necessary to correct the incident energies for relativistic effect. This relativistic energy E0el is obtained using the following equation: " # 1 1 0 2 Eel ¼ m0 c 1 ; ð4Þ 2 2 ð1 þ Eel =m0 c2 Þ where m0 is the rest mass of electron and c is the velocity of light. Hence, Eq. (2) can be written in our energy range as, Qi E0el 4pa20 R
20 0.03 0.04
0.057
Bethe–Born approximation. For high velocity of incident electrons, the Bethe formula for total ionization cross-sections is given by [19] Qi ¼
18 0.04
¼ M 2I ln E0el þ C I ;
22
24
28
0.04
0.03 0.039
0.025 0.035
Fig. 5 shows the Fano–Bethe plots for variation of Qi E0el =4pa20 R versus ln E0el for CH4 and C3H8 molecules for impact of 10–28 keV electrons. Values of M 2I derived from these plots are listed in Table 4 and they are compared with values from optical measurements by other workers. The present M 2I value for CH4 seems to be in a reasonable agreement with that of Nishimura and Tawara [5] as well as with optical data [20]; however, it is found to be about 10% larger than the values of Schram et al. [3] and Adamczyk et al. [8]. Also, our value of M 2I for C3H8 agrees well with that for electron impact values obtained by other workers, but it deviates by about 212% from the value obtained from optical results. Such a discrepancy has also been observed by Nishimura and Tawara [5] between their
140 120
C3H8
100 2
12
0.06 0.08
80
'
10
QiEel /4π a0 R
CH4 C3H8
60 40
ð5Þ
CH4
M 2I
20
ln 4cRi .
Now, by where CI is another constant equal to plotting the experimental Qi E0el =4pa20 R values as a function of ln E0el , one obtains a curve whose gradient gives the value of M 2I corresponding to different molecules. These values provide information on the dipole-oscillator strength for total ionization of the target molecules, so to say on the strength of corresponding optical transitions.
0 9.2
9.4
9.6
9.8
10.0
lnE (eV) Fig. 5. Fano–Bethe plots: Qi E0el =4pa20 R versus ln E0el for 10–28 keV electron impact ionization of methane (j) and propane (d).
Table 4 M 2I values CH4 C3H8
10.2
' el
Present work
Nishimura and Tawara [5]
Schram et al. [3]
Adamczyk et al. [8]
Optical [18]
4.57 ± 1.14 16.12 ± 2.68
4.8 20
4.28 13.8
4.15
4.56 7.60
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electron data and the optical measurements [21] for larger hydrocarbons. For understanding this discrepancy, more extensive photo-absorption and photo-ionization data over a wide energy range are needed. Furthermore, from the above comparison of M 2I value for C3H8 and CH4 molecules, it is noted that M 2I for C3H8 is about 3.5 times larger than for CH4 indicating that the electron impact total ionization is produced in C3H8 more strongly via optical transitions than it is produced in CH4 molecule. 4. Conclusions In the present work, new experimental results on total ionization cross-sections of CH4 and C3H8 by impact of 10–28 keV electrons are presented. It is observed that the total number of target electrons and the molecular polarizability play important roles in electron impact ionization of a polyatomic molecule. The comparison of electron impact total ionization cross-sections for CH4 and C3H8 is found to confirm these observations. It is further observed that in the present impact energy range, the electron induced total ionization cross-sections for both CH4 and C3H8 agree well with calculations using the Bethe formula. Experimental values of M 2I for both CH4 and C3H8 molecules are obtained which agree reasonably well with previously reported values. Furthermore, it is noted that M 2I value for C3H8 is about 3.5 times larger than for CH4 molecule. Acknowledgements The authors acknowledge the financial support from Department of Science and Technology (DST), New Delhi for conducting this work under a research project: SP/S2/ L-08/2001. S. Mondal thanks the DST and the Council of Scientific and Industrial Research (CSIR), New Delhi
for providing research fellowships during the execution of this work. References [1] S.H. Lee, J.M. Reeves, J.C. Wilson, D.E. Hunton, A.A. Viggiano, T.M. Miller, J.O. Ballenthin, L.R. Lait, Science 301 (2003) 1886. [2] D. Rapp, P. Englander-Golden, J. Chem. Phys. 43 (1965) 1464. [3] B.L. Schram, M.J. van der Wiel, F.J. de Heer, H.R. Moustafa, J. Chem. Phys. 44 (1966) 49. [4] N. Duric, I. Cadez, M. Kurepa, Int. J. Mass Spectrom. Ion Proc. 108 (1991) R1. [5] H. Nishimura, H. Tawara, J. Phys. B: At. Mol. Opt. Phys. 27 (1994) 2063. [6] H.C. Straub, D. Lin, B.G. Lindsay, K.A. Smith, R.F. Stebbings, J. Chem. Phys. 106 (1997) 4430. [7] O.J. Orient, S.K. Srivastava, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 3923. [8] B. Adamczyk, A.J.H. Boerboom, B.L. Schram, J. Kistenmaker, J. Chem. Phys. 44 (1966) 4640. [9] H. Chatham, D. Hils, R. Robertson, A. Gallagher, J. Chem. Phys. 81 (1984) 1770. [10] V. Grill, G. Walder, D. Margreiter, T. Rauth, H.U. Poll, P. Scheier, T.D. Mark, Z. Phys. D 25 (1993) 217. [11] T. Fiegele, G. Hanel, I. Torres, M. Lezius, T.D. Mark, J. Phys. B: At. Mol. Opt. Phys. 33 (2000) 4263. [12] H. Nishimura, H. Tawara, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) L363. [13] S. Mondal, R. Shanker, Phys. Rev. A 72 (2005) 052705. [14] R.K. Singh, R.K. Mohanta, R. Hippler, R. Shanker, Pramana: J. Phys. 58 (2002) 499. [15] R.K. Singh, S. Mondal, R. Shanker, J. Phys. B: At. Mol. Opt. Phys. 36 (2002) 499. [16] P. Wang, C.R. Vidal, Chem. Phys. 280 (2002) 309. [17] H. Luna, E.G. Cavalcanti, J. Nickles, G.M. Sigaud, E.C. Montenegro, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 4717. [18] S. Mondal, R.K. Singh, R. Shanker, Pramana: J. Phys. 60 (2003) 1203. [19] W.F. Miller, R.L. Platzman, Proc. Phys. Soc. A 70 (1957) 299. [20] J.W. Gallagher, C.E. Brion, J.A.R. Samson, W. Langhoff, J. Phys. Chem. Ref. Data 17 (1988) 9. [21] R. Shoen, J. Chem. Phys. 37 (1962) 2032.
Nuclear Instruments and Methods in Physics Research B 246 (2006) 297–302 www.elsevier.com/locate/nimb
Total ionization cross-sections of CH4 and C3H8 molecules for impact of 10–28 keV electrons S. Mondal *, R. Shanker Atomic Physics Laboratory, Department of Physics, Banaras Hindu University, Varanasi 221 005, India Received 24 November 2005; received in revised form 13 January 2006 Available online 2 March 2006
Abstract The total ionization cross-sections of methane and propane molecules are measured for impact of 10–28 keV electrons. The cross-sections are found to follow the variation shown by Bethe formula as a function of electron impact energy. Also, the present results compare well with the available data in the literature. Further, the measured cross-sections of the above hydrocarbon molecules are found to correlate strongly to the total number of molecular electrons and to the molecular dipole polarizability. 2006 Elsevier B.V. All rights reserved. PACS: 34.80.Gs Keywords: Total ionization cross-sections; Fano–Bethe plots; Molecular dipole polarizability
1. Introduction Studies of the ionization processes in simple hydrocarbon molecules under impact of charged particles are of crucial importance in molecular collisions as they provide information on the basic principles of ionization in polyatomic molecules. Also, the interest of studying the charged particle induced ionization of hydrocarbon molecules lies in their applications, for example, in plasma physics, atmospheric physics and in upper planetary atmosphere. In particular, the constituent gases of the medium in upper planetary atmosphere are generally known to be hydrocarbons, such as, CH4, C3H8, etc. Dissociative ionization of these molecules under impact of galactic cosmic rays which consists of photons, electrons and ions produces highly reactive radicals. These radicals not only combine to form more complex molecules but also to bring significant changes in their concentrations due to chemical coupling between ionic- and neutral species. These nucleation of *
Corresponding author. Tel.: +91 9415450541; fax: +91 542 2368174. E-mail addresses: [email protected] (S. Mondal), rshanker@ bhu.ac.in (R. Shanker). 0168-583X/$ - see front matter 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.01.025
new particles change the cloud formation in upper planetary atmosphere [1]. Investigations of such phenomena have made it fundamentally important for measurements of reliable total ionization cross-sections of hydrocarbons by electron impact. The total ionization cross-section values are also needed for calculations of different parameters involved in atmospheric plasmas. Moreover, these values serve as a normalization standard for determination of various absolute partial ionization cross-sections. Using a parallel plate ion collection technique, the total ionization cross-sections of CH4 for electron impact energy from threshold to 1 keV have been measured by Rapp and Englander-Golden [2]. Schram et al. [3] reported total ionization cross-sections of many hydrocarbons for impact of electrons in the range of 0.6–12 keV. Further, Duric et al. [4] determined the total ionization cross-sections of CH4 and C3H8 for impact of electrons from threshold to 240 eV. Recently, Nishimura and Tawara [5] have measured the total ionization cross-sections of several hydrocarbons, such as, CH4, C2H4, C2H6 and C3H8 for electron impact with energies from threshold to 3 keV. Absolute partial ionization cross-sections of CH4 by impact of electrons having energies from threshold to 1000 eV by Straub et al. [6] and
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from threshold to 510 eV have been measured by Orient and Srivastava [7]. The latter authors have obtained the absolute cross-sections by normalizing the sum of relative cross-sections to a known total ionization cross-sections of inert gases (Ne, Ar, Kr and Xe). However, on one hand, the relative partial ionization cross-sections of CH4 have been measured by Adamczyk et al. [8], by impact of electrons of energy 20–2000 eV by Chatham et al. [9] for electron energies ranging from threshold to 400 eV. Grill et al. [10] have measured relative partial ionization crosssections of C3H8 by impact of electrons having energies from threshold to 950 eV. These groups have determined absolute cross-sections by normalizing their relative values to the absolute values of Orient and Srivastava [7] at a specific energy. On the other hand, ionization behavior close to threshold for fragment ion production from CH4, C3H8 and some simple molecules under electron impact has been studied by Fiegele et al. [11]. Most of the experimental studies for electron impact ionization cross-sections of hydrocarbons mentioned in the above paragraphs have been reported for relatively low impact energies. However, data for high impact energies are scarce in the literature [12]. Among these experimental studies, only Nishimura and Tawara [5] and Schram et al. [3] have derived information from their data on the dipole oscillator strength and have compared values with the optical results. Also, these experimental data in the overlapping region of impact energy are not consistent among themselves. Therefore, it was thought worthwhile to perform a systematic measurements of the total ionization cross-sections of CH4 and C3H8 molecules for impact of 10–28 keV electrons for which no experimental data exist in the literature, to our knowledge. For understanding the details of electron impact collision processes occurring in the considered hydrocarbon molecules, we have compared our results with those obtained by Born approximation calculations and have derived the dipole oscillator
strength for these collision systems. The obtained values have been compared with those derived from optical as well as with other existing results. 2. Experimental 2.1. Apparatus The present measurements of total ionization cross-sections of CH4 and C3H8 molecules have been performed on a crossed-beam type experimental facility [13]. The collision induced ions were extracted and collected by a timeof-flight (TOF) spectrometer. Details of development of the experimental apparatus have been described previously elsewhere [14,15]. In the following, we give a brief account of the relevant components and parameters that were used in the present measurements. The schematic diagram of the experimental set-up is shown in Fig. 1. A mono energetic electron beam was obtained from a custom built electron gun. The beam was collimated and focused to a spot size of 3 mm at the scattering center, about 500 mm away from the mounting flange of the electron gun. For reducing the deflection of electron beam in the interaction zone due to the earth’s magnetic field, the inner wall of the scattering chamber was shielded with a sheet of 0.5 mm thick antimagnetic l-metal. A biased (60 V) Faraday cup was used to monitor the beam current after it transmitted through the target gas. The target gas was made to effuse from a hypodermic needle at 90 to the incident electron beam direction at a thermal velocity. The target gas pressure was kept at 2 · 104 Torr which satisfied the condition for a single collision. The collisionally induced multiply charged ions produced in the interaction region were extracted in a TOF spectrometer. The extraction of ions was made by an electric field strength of 190 V/cm. The applied electric field was set perpendicular to both the direction of ejected electrons entering the channel electron
Fig. 1. Schematic diagram of the experimental set-up.
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299
multiplier (CEM) as well as to the direction of incident electrons. The extraction field was produced by applying an equal and opposite potentials to two horizontally mounted parallel plates (18 mm apart) enclosing the collision zone. The tip of the gas jet was positioned in the middle of two plates and pierced vertically into the lower plate from underneath. After extracting the ions, they were further accelerated into the drift tube biased at 215 V and were made to travel in a field-free region of about 22 mm path length. At the end of the drift tube, the ions were post-accelerated by applying a field of 900 V and were finally detected by the CEM biased at +3 kV. For measuring the total ionization cross-sections of the hydrocarbons using the above experimental facility, it was necessary to ensure an accurate alignment of the electron beam, the TOF spectrometer and the tip of the hypodermic needle with respect to the collision centre. 2.2. Data collection procedure Optimization for the full ion extraction and transmission efficiencies of the TOF was accomplished by measuring the total ion counts as a function of extraction and acceleration voltages applied on different electrodes of the TOF spectrometer. It is found that the number of ions increases with the extraction- and acceleration voltages and reaches a constant value. Hence, the optimized values for extraction and transmission voltages were those at which the corresponding ion counts obtain a constant value. Full detection efficiency of channeltron was ensured by setting the channeltron bias voltage at which the ion count rate becomes constant as a function of the biasing voltage. The ions collected by TOF spectrometer and detected by the channeltron were believed to originate from the target gas, this was confirmed by recording the TOF spectra of ions in coincidence with the electrons detected by a channeltron at 90 with respect to the incident beam direction. Fig. 2(a) and (b) show the typical time-of-flight spectra of ions produced from CH4 and C3H8 molecules respectively under impact of 10 keV electrons. It is to be noted that the charge states of the fragment ions produced from the parent molecules are not resolved in the spectra due to a poor time resolution of the employed TOF spectrometer. However, the positions of unresolved few fragment ions are marked by comparing the time-of-flight spectra of fragment ions produced from collisions of 200 eV electrons with CH4 and C3H8 molecules [16,17]. The total ionization cross-sections of the considered molecules were measured by detecting non-coincident total ion counts using the TOF spectrometer. The true total ion counts were obtained by subtracting the background ion counts from true plus background ion counts. The background ion counts were determined by measuring total ion counts produced from the residual gas alone present in the reaction chamber. From the detected total true ion counts Ni, the total ionization cross-section Qi was obtained by using a relation,
Fig. 2. Time-of-flight spectrum of fragment ions of (a) CH4 and (b) C3H8 measured in coincidence with secondary electrons of indiscriminated energy detected at 90 with respect to the incident beam direction for impact of 10 keV electrons.
Qi ¼ C
Ni 1 cm2 ; N e P L3:34 1016
ð1Þ
where Ne is the total number of counts of the incident electrons, P is the target gas pressure in Torr, L is the effective path length of the electron beam in the target gas in cm and C is a constant depending on the geometry of the TOF spectrometer. The typical values of above parameters in the present experiment are: Ni = 2 348 400, Ne = 9.3 · 1013, P = 2 · 104 Torr, L = 0.5 cm and C = 6614 for 10 keV e–C3H8 collisions. The total uncertainty involved in the measurement of Qi arises due to the uncertainties in the parameters C, Ni, Ne, P and L; they are estimated to be 5%, 2%, 1%, 5% and 20%, respectively. Hence, the overall uncertainty in the measurement of Qi becomes nearly 22%. 3. Results and discussion 3.1. Total ionization cross-sections The measured total ionization cross-sections Qi of CH4 and C3H8 for impact of 10–28 keV electrons are listed in
300
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-16
2
Total cross section (10 cm )
Table 1. The Qi values are obtained without any normalization either with theory or any previous experimental data on a given impact energy. Fig. 3 shows the variation of electron impact total ionization cross-sections of CH4 as a function of incident electron energy. In this energy range only one datum at 12 keV from Schram et al. [3] has an overlap with our data. Nishimura and Tawara [5] have measured the total ionization cross-sections of CH4 at still lower impact energies (63000 eV). Their data are found to show the similar decreasing trend of the cross-sections with impact energy in their considered region of impact as that of the present measurements. However, generally all data points of Schram et al. reported in the impact energy range 600–12 000 eV are found to lie lower than the data points of both the present as well as of Nishimura and Tawara. Fig. 4 shows Qi values of the present work for 10– 28 keV e–C3H8 collisions as a function of incident electron energy and compares with those of Schram et al. [3] and Nishimura and Tawara [5]. A single datum at 12 keV of Schram et al. is found to underestimate the present measurements. However, data of Nishimura and Tawara follow a similar trend of variation of Qi with impact energy in their energy region of interest as our data do. For electron impact ionization of a molecule, the total ionization cross-sections are strongly correlated to the total number of electrons z and also to the molecular dipole polarizability a. As the number of target electrons increases in a molecule, their contribution to the total ionization cross-section becomes larger [18]. This is verified by comparing the total ionization cross-sections of CH4 and C3H8 as displayed in Table 1. This table shows that the cross-sections of C3H8 are about 300% larger than those of CH4 molecule for all impact energies. In order to examine the effect of total number of electrons and molecular dipole polarizability, the values of Qi/z and Qi/a are calculated and listed in Tables 2 and 3, respectively, for CH4 and C3H8. The values of a for CH4 and C3H8 are known to be 2.6 · 1024 cm3 and 6.3 · 1024 cm3, respectively. The comparison of Qi/z and Qi/a values in the region of present energies shows nearly a constant value for both molecules within the error of measurements of Qi. This indicates that the total number of molecular electrons and molecular polarizability play determinative roles in process of total ionization of a polyatomic molecule. The incident electron recognizes not only all electrons in the molecule but also influences the structure of molecular electron cloud, that is to say, the polarizability a.
1
0.1
1000
10000
Incident electron energy (eV)
-16
2
Total cross section (10 cm )
Fig. 3. Electron impact total ionization cross-sections of methane (CH4) as a function of incident electron energy; (m) present data; (r) Nishimura and Tawara [5]; (d) Schram et al. [3].
1
0.1 1000
10000
Incident electron energy (eV) Fig. 4. Electron impact total ionization cross-sections of propane (C3H8) as a function of incident electron energy; (m) present data; (r) Nishimura and Tawara [5]; (d) Schram et al. [3].
3.2. Fano–Bethe plot In order to obtain further information on the ionization mechanism for the considered collision systems, the electron impact total ionization cross-sections have been compared with the theoretical calculations based on the
Table 1 Total ionization cross-sections Qi (1016 cm2) of CH4 and C3H8 under 10–28 keV electron impact E (keV)
CH4 C3H8
10
12
14
0.155 0.5
0.13 0.44
0.11 0.382
16 0.36
18
20
0.098
0.086 0.29
22
24
28
0.26
0.074 0.25
0.065 0.22
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301
Table 2 Ratio Qi/z (1016 cm2) of the total ionization cross-sections Qi and the molecular electrons z versus incident electron energy (keV) E (keV)
CH4 C3H8
10
12
14
0.0155 0.0208
0.013 0.0184
0.011 0.0159
16
18
20
22
24
28
0.0098
0.0086 0.0121
0.026 0.0108
0.0074 0.0104
0.0065 0.0092
0.015
Table 3 Ratio Qi/a (108 cm1) of the total ionization cross-section Qi and the molecular polarizability a versus incident electron energy (keV) E (keV) 14
0.05 0.07
0.04 0.06
16
4pa20 R 2 4Eel ci ; M I ln Eel R
ð2Þ
where Eel is the incident electron energy, a0 is the Bohr radius, R is the Rydberg energy, M 2I is the square of the dipole matrix element and ci is a constant. The value of M 2I is related to the differential optical oscillator strength f as, Z 1 df R dE. ð3Þ M 2I ¼ dE E IP Here the integration is taken over the continuum, E is the energy of the continuum electrons. For the present collisions of high energy incident electrons, it is necessary to correct the incident energies for relativistic effect. This relativistic energy E0el is obtained using the following equation: " # 1 1 0 2 Eel ¼ m0 c 1 ; ð4Þ 2 2 ð1 þ Eel =m0 c2 Þ where m0 is the rest mass of electron and c is the velocity of light. Hence, Eq. (2) can be written in our energy range as, Qi E0el 4pa20 R
20 0.03 0.04
0.057
Bethe–Born approximation. For high velocity of incident electrons, the Bethe formula for total ionization cross-sections is given by [19] Qi ¼
18 0.04
¼ M 2I ln E0el þ C I ;
22
24
28
0.04
0.03 0.039
0.025 0.035
Fig. 5 shows the Fano–Bethe plots for variation of Qi E0el =4pa20 R versus ln E0el for CH4 and C3H8 molecules for impact of 10–28 keV electrons. Values of M 2I derived from these plots are listed in Table 4 and they are compared with values from optical measurements by other workers. The present M 2I value for CH4 seems to be in a reasonable agreement with that of Nishimura and Tawara [5] as well as with optical data [20]; however, it is found to be about 10% larger than the values of Schram et al. [3] and Adamczyk et al. [8]. Also, our value of M 2I for C3H8 agrees well with that for electron impact values obtained by other workers, but it deviates by about 212% from the value obtained from optical results. Such a discrepancy has also been observed by Nishimura and Tawara [5] between their
140 120
C3H8
100 2
12
0.06 0.08
80
'
10
QiEel /4π a0 R
CH4 C3H8
60 40
ð5Þ
CH4
M 2I
20
ln 4cRi .
Now, by where CI is another constant equal to plotting the experimental Qi E0el =4pa20 R values as a function of ln E0el , one obtains a curve whose gradient gives the value of M 2I corresponding to different molecules. These values provide information on the dipole-oscillator strength for total ionization of the target molecules, so to say on the strength of corresponding optical transitions.
0 9.2
9.4
9.6
9.8
10.0
lnE (eV) Fig. 5. Fano–Bethe plots: Qi E0el =4pa20 R versus ln E0el for 10–28 keV electron impact ionization of methane (j) and propane (d).
Table 4 M 2I values CH4 C3H8
10.2
' el
Present work
Nishimura and Tawara [5]
Schram et al. [3]
Adamczyk et al. [8]
Optical [18]
4.57 ± 1.14 16.12 ± 2.68
4.8 20
4.28 13.8
4.15
4.56 7.60
302
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electron data and the optical measurements [21] for larger hydrocarbons. For understanding this discrepancy, more extensive photo-absorption and photo-ionization data over a wide energy range are needed. Furthermore, from the above comparison of M 2I value for C3H8 and CH4 molecules, it is noted that M 2I for C3H8 is about 3.5 times larger than for CH4 indicating that the electron impact total ionization is produced in C3H8 more strongly via optical transitions than it is produced in CH4 molecule. 4. Conclusions In the present work, new experimental results on total ionization cross-sections of CH4 and C3H8 by impact of 10–28 keV electrons are presented. It is observed that the total number of target electrons and the molecular polarizability play important roles in electron impact ionization of a polyatomic molecule. The comparison of electron impact total ionization cross-sections for CH4 and C3H8 is found to confirm these observations. It is further observed that in the present impact energy range, the electron induced total ionization cross-sections for both CH4 and C3H8 agree well with calculations using the Bethe formula. Experimental values of M 2I for both CH4 and C3H8 molecules are obtained which agree reasonably well with previously reported values. Furthermore, it is noted that M 2I value for C3H8 is about 3.5 times larger than for CH4 molecule. Acknowledgements The authors acknowledge the financial support from Department of Science and Technology (DST), New Delhi for conducting this work under a research project: SP/S2/ L-08/2001. S. Mondal thanks the DST and the Council of Scientific and Industrial Research (CSIR), New Delhi
for providing research fellowships during the execution of this work. References [1] S.H. Lee, J.M. Reeves, J.C. Wilson, D.E. Hunton, A.A. Viggiano, T.M. Miller, J.O. Ballenthin, L.R. Lait, Science 301 (2003) 1886. [2] D. Rapp, P. Englander-Golden, J. Chem. Phys. 43 (1965) 1464. [3] B.L. Schram, M.J. van der Wiel, F.J. de Heer, H.R. Moustafa, J. Chem. Phys. 44 (1966) 49. [4] N. Duric, I. Cadez, M. Kurepa, Int. J. Mass Spectrom. Ion Proc. 108 (1991) R1. [5] H. Nishimura, H. Tawara, J. Phys. B: At. Mol. Opt. Phys. 27 (1994) 2063. [6] H.C. Straub, D. Lin, B.G. Lindsay, K.A. Smith, R.F. Stebbings, J. Chem. Phys. 106 (1997) 4430. [7] O.J. Orient, S.K. Srivastava, J. Phys. B: At. Mol. Opt. Phys. 20 (1987) 3923. [8] B. Adamczyk, A.J.H. Boerboom, B.L. Schram, J. Kistenmaker, J. Chem. Phys. 44 (1966) 4640. [9] H. Chatham, D. Hils, R. Robertson, A. Gallagher, J. Chem. Phys. 81 (1984) 1770. [10] V. Grill, G. Walder, D. Margreiter, T. Rauth, H.U. Poll, P. Scheier, T.D. Mark, Z. Phys. D 25 (1993) 217. [11] T. Fiegele, G. Hanel, I. Torres, M. Lezius, T.D. Mark, J. Phys. B: At. Mol. Opt. Phys. 33 (2000) 4263. [12] H. Nishimura, H. Tawara, J. Phys. B: At. Mol. Opt. Phys. 24 (1991) L363. [13] S. Mondal, R. Shanker, Phys. Rev. A 72 (2005) 052705. [14] R.K. Singh, R.K. Mohanta, R. Hippler, R. Shanker, Pramana: J. Phys. 58 (2002) 499. [15] R.K. Singh, S. Mondal, R. Shanker, J. Phys. B: At. Mol. Opt. Phys. 36 (2002) 499. [16] P. Wang, C.R. Vidal, Chem. Phys. 280 (2002) 309. [17] H. Luna, E.G. Cavalcanti, J. Nickles, G.M. Sigaud, E.C. Montenegro, J. Phys. B: At. Mol. Opt. Phys. 36 (2003) 4717. [18] S. Mondal, R.K. Singh, R. Shanker, Pramana: J. Phys. 60 (2003) 1203. [19] W.F. Miller, R.L. Platzman, Proc. Phys. Soc. A 70 (1957) 299. [20] J.W. Gallagher, C.E. Brion, J.A.R. Samson, W. Langhoff, J. Phys. Chem. Ref. Data 17 (1988) 9. [21] R. Shoen, J. Chem. Phys. 37 (1962) 2032.