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Absolute total collision cross sections for Maxwellian beams of H2 and He scattered by room temperature H2 and He
Volume 27A, number
5
PHYSICS
ABSOLUTE TOTAL COLLISION OF H2 AND He SCATTERED
LETTERS
CROSS SECTIONS FOR MAXWELLIAN BY ROOM TEMPERATURE H2 AND
P. CANTINI, M. CAVALLIM,
15 Julv 1968
BEAMS He
M. G. DONDI and G.SCOLES
Gruppo Nazionale di Stmttura della Materia de1 C. N. R. Istituto di Fisica Sperimentule delPUniversitZl - Genova, Italy Received
22 April
1968
The absolute values of total collision cross sections for Maxwellian beams of H2 and He scattered by room temperature H2 and He are determined. The simple scattering chamber geometry adopted allows for an easy pressure calibration and avoids end corrections to the scattering length.
One of the difficulties of molecular scattering experiments has been, up to now, the determination of the absolute value of the scattering centers density in the interaction region. The scattering centers density just outside the interaction region (end corrections) has been a minor problem but not a negligible one [1,2]. Therefore, in spite of the usefulness of such measurements in the study of the attractive part of the molecular interaction potential, accurate determinations of the absolute values of the effective total collision cross sections are rarely found in the literature. This is especially truw for the so called permanent gases. For reference the reader is demanded to the recent extensive review by Bernstein and Mucker man [ 31. As a part of a program in molecular forces determination by molecular beavs scattering we carried out measurements of Qae$ Tl, T2 - g] [ 31 for the He - He, He - H2 and H2 - H2 systems. The beam cross section adopted is circular. The source is a conventional molecular effusion oven. The scattering chamber has, instead of the normal “channels” for the entrance and the exit of the primary beam, two well shaped circular holes. Near the holes the wall thickness is small in comparison with the hole diameters. The hole diameters are small in comparison with the chamber linear dimensions and with the molecular mean free path at all pressures of interest. Shortly, the gas effusion from the chamber is free molecular so that a flux measurement, which may be easily done in the high pressure side of the gas feeding system, is equivalent to a pressure measurement in the scattering chamber. One more advantage of the adopted geometry is that, in this situation, no end corrections 284
are necessary. For the usefulness of dynamical methods in pressure calibration see ref. 4. The detector is a bolometer detector described elsewhere [5]. The relevant dimensions of the system elements are given in table 1. Both source and scattering chamber were at room temperature. The gas purity was in any case better than 2Gas analyzed with a mass spectrometer downstream the last diaphragm in the gas feeding system, before, respectively, the scattering chamber and the source chamber. The results are reported in table 2. The Qeff reported in the first column are obtained by averaging respectively 6, 5, 8 and 4 values for the cross section obtained in different days. Each value differend from Qeff by no more than 3% and was obtained by a least squares analysis of 10 to 20 attenuation data. The attenuation was always inferior to 60% and the standard deviation u was: f 0.4% < u < f 2?& The absolute values of the cross sections are estimated to have been measured with an overall precision of f 5%; the extra 2% error arising from pressure calibration uncertainties. The Q(viw) reported in table 2 are obtained applying the well known correction due to Berkling et al. [ll] with the necessary changes arising from the fact that the output of our detector is proportional to the energy rather than to the number of the molecules. For that reason one should take in account a ~5 term multiplying the Boltzmann factor in the velocity distribution of the beam molecules. This is correct in the assumption that the accommodation coefficient of the beam particles at the detector surface is independent from the beam particle velocity. The values of the Q(viw) were estimated to
Volume 27A, number
PHYSICS
5
15 July 1968
LETTERS Table 1
Source diameter
43 = 0.27
mm
dcl = 0.773 * 0.005 mm holes diameter Scattering
‘dc2 = 0.717 * 0.005 mm
chamber length
Detector
6
- Scattering
Source
- Detector
chamber
1sc = 478 mm 0.2
ps
in the scattering in the source
chamber
vessel
in the utilization AP in the utilization
the scattering
1sc = 230 mm
distance
distance
in the source Pressure
11.3 f 0.1 mm
da = 1.0 f 0.1 mm
diameter
Source
=
vessel gas
vessel due to
-
1 X 10-5 Torr
-
1 X 10s6 Torr
Nevertheless an experimental analysis of the detector response to the beam velocities is presently in progress.
(Ao2)
Beam target system
Q,ff(Ao2)
He - He
44.0
35.6
33 * 2 40 35
H2 - H2
78.8
63.7
65
H2 - He
52.3
46.6
43 f 1 f71 59 181 49.4*5.5[10]
He - H2
65.3
45.4
This work
< 1 Torr
5 X 10m5 < p, < 2.5 X 10e3 Torr
AP < 3 X 10m7 Torr
Table 2
80~. 1w )
pc
Other authors [6,7]
PI
[31 PI
decrease by a few percent for a 2% lowering of the accommodation coefficient with a doubling of the molecules velocity. This fact and the good agreement of our results with the more recent experimental results and theoretical calculations [12] existing in the literature suggest that a further correction due to the non constancy of the accommodation coefficient, if present, should not be very relevant.
References 1. E. W.Rothe and R. H. Neynaber, J. Chem. Phys. 42 (1965) 3306. 2. H.G. Bennewitz and H.D.Dohmann, Z. Physik 182 (1965) 524. 3. R. B. Bernstein and J. T.Muckerman, Adv. Chem. Phys. 12 (1967) 389. 4. H.G.Bennewitz and H.D.Dohmann, Vak. Tech. 1 (1965) 8. 5. M.Cavallini, G.Gallinaro and G.Scoles, Z. Naturf. 22a (1967) 413. 6. E. W.Rothe and R.H. Neynaber, J. Chem. Phys. 43 (1965) 4177. 7. G. E. Moore, S. Datz and F. Van der Valk, J. Chem. Phys. 46 (1967) 2012. 8. H.Harrison, J. Chem. Phys. 37 (1962) 1164. 9. H. J.Beier, Z. Physik 196 (1966) 185. 10. J.G.Skofronick, Rev. Sci. Ins. 38 (1967) 1628. 11. K.Berkling, R.Helbing, K.Kramer, H. Pauly, Ch. Schlier and P. Toschek, Z. Physik 166 (1962) 406. 12. R.B. Bernstein and F.A. Morse, J. Chem. Phys. 40 (1964) 917.
265
5
PHYSICS
ABSOLUTE TOTAL COLLISION OF H2 AND He SCATTERED
LETTERS
CROSS SECTIONS FOR MAXWELLIAN BY ROOM TEMPERATURE H2 AND
P. CANTINI, M. CAVALLIM,
15 Julv 1968
BEAMS He
M. G. DONDI and G.SCOLES
Gruppo Nazionale di Stmttura della Materia de1 C. N. R. Istituto di Fisica Sperimentule delPUniversitZl - Genova, Italy Received
22 April
1968
The absolute values of total collision cross sections for Maxwellian beams of H2 and He scattered by room temperature H2 and He are determined. The simple scattering chamber geometry adopted allows for an easy pressure calibration and avoids end corrections to the scattering length.
One of the difficulties of molecular scattering experiments has been, up to now, the determination of the absolute value of the scattering centers density in the interaction region. The scattering centers density just outside the interaction region (end corrections) has been a minor problem but not a negligible one [1,2]. Therefore, in spite of the usefulness of such measurements in the study of the attractive part of the molecular interaction potential, accurate determinations of the absolute values of the effective total collision cross sections are rarely found in the literature. This is especially truw for the so called permanent gases. For reference the reader is demanded to the recent extensive review by Bernstein and Mucker man [ 31. As a part of a program in molecular forces determination by molecular beavs scattering we carried out measurements of Qae$ Tl, T2 - g] [ 31 for the He - He, He - H2 and H2 - H2 systems. The beam cross section adopted is circular. The source is a conventional molecular effusion oven. The scattering chamber has, instead of the normal “channels” for the entrance and the exit of the primary beam, two well shaped circular holes. Near the holes the wall thickness is small in comparison with the hole diameters. The hole diameters are small in comparison with the chamber linear dimensions and with the molecular mean free path at all pressures of interest. Shortly, the gas effusion from the chamber is free molecular so that a flux measurement, which may be easily done in the high pressure side of the gas feeding system, is equivalent to a pressure measurement in the scattering chamber. One more advantage of the adopted geometry is that, in this situation, no end corrections 284
are necessary. For the usefulness of dynamical methods in pressure calibration see ref. 4. The detector is a bolometer detector described elsewhere [5]. The relevant dimensions of the system elements are given in table 1. Both source and scattering chamber were at room temperature. The gas purity was in any case better than 2Gas analyzed with a mass spectrometer downstream the last diaphragm in the gas feeding system, before, respectively, the scattering chamber and the source chamber. The results are reported in table 2. The Qeff reported in the first column are obtained by averaging respectively 6, 5, 8 and 4 values for the cross section obtained in different days. Each value differend from Qeff by no more than 3% and was obtained by a least squares analysis of 10 to 20 attenuation data. The attenuation was always inferior to 60% and the standard deviation u was: f 0.4% < u < f 2?& The absolute values of the cross sections are estimated to have been measured with an overall precision of f 5%; the extra 2% error arising from pressure calibration uncertainties. The Q(viw) reported in table 2 are obtained applying the well known correction due to Berkling et al. [ll] with the necessary changes arising from the fact that the output of our detector is proportional to the energy rather than to the number of the molecules. For that reason one should take in account a ~5 term multiplying the Boltzmann factor in the velocity distribution of the beam molecules. This is correct in the assumption that the accommodation coefficient of the beam particles at the detector surface is independent from the beam particle velocity. The values of the Q(viw) were estimated to
Volume 27A, number
PHYSICS
5
15 July 1968
LETTERS Table 1
Source diameter
43 = 0.27
mm
dcl = 0.773 * 0.005 mm holes diameter Scattering
‘dc2 = 0.717 * 0.005 mm
chamber length
Detector
6
- Scattering
Source
- Detector
chamber
1sc = 478 mm 0.2
ps
in the scattering in the source
chamber
vessel
in the utilization AP in the utilization
the scattering
1sc = 230 mm
distance
distance
in the source Pressure
11.3 f 0.1 mm
da = 1.0 f 0.1 mm
diameter
Source
=
vessel gas
vessel due to
-
1 X 10-5 Torr
-
1 X 10s6 Torr
Nevertheless an experimental analysis of the detector response to the beam velocities is presently in progress.
(Ao2)
Beam target system
Q,ff(Ao2)
He - He
44.0
35.6
33 * 2 40 35
H2 - H2
78.8
63.7
65
H2 - He
52.3
46.6
43 f 1 f71 59 181 49.4*5.5[10]
He - H2
65.3
45.4
This work
< 1 Torr
5 X 10m5 < p, < 2.5 X 10e3 Torr
AP < 3 X 10m7 Torr
Table 2
80~. 1w )
pc
Other authors [6,7]
PI
[31 PI
decrease by a few percent for a 2% lowering of the accommodation coefficient with a doubling of the molecules velocity. This fact and the good agreement of our results with the more recent experimental results and theoretical calculations [12] existing in the literature suggest that a further correction due to the non constancy of the accommodation coefficient, if present, should not be very relevant.
References 1. E. W.Rothe and R. H. Neynaber, J. Chem. Phys. 42 (1965) 3306. 2. H.G. Bennewitz and H.D.Dohmann, Z. Physik 182 (1965) 524. 3. R. B. Bernstein and J. T.Muckerman, Adv. Chem. Phys. 12 (1967) 389. 4. H.G.Bennewitz and H.D.Dohmann, Vak. Tech. 1 (1965) 8. 5. M.Cavallini, G.Gallinaro and G.Scoles, Z. Naturf. 22a (1967) 413. 6. E. W.Rothe and R.H. Neynaber, J. Chem. Phys. 43 (1965) 4177. 7. G. E. Moore, S. Datz and F. Van der Valk, J. Chem. Phys. 46 (1967) 2012. 8. H.Harrison, J. Chem. Phys. 37 (1962) 1164. 9. H. J.Beier, Z. Physik 196 (1966) 185. 10. J.G.Skofronick, Rev. Sci. Ins. 38 (1967) 1628. 11. K.Berkling, R.Helbing, K.Kramer, H. Pauly, Ch. Schlier and P. Toschek, Z. Physik 166 (1962) 406. 12. R.B. Bernstein and F.A. Morse, J. Chem. Phys. 40 (1964) 917.
265