The atom-atom ionization process occurring in high-purity argon-xenon mixtures has been investigated by means of a conventional shock tube employing a microwave probe to monitor the electron-generation rate. All tests were conducted at approximately atmospheric pressure and at temperatures in the range between 5000° and 9000°K, corresponding to a neutral-particle density of 7.0 X 10^(17) cm^(-3). The cross-sectional slope constant for xenon ionized by collision with an argon atom is 1.8 X 10^(-20) cm^2/eV±20%, that is, equal to that for xenon ionized by collision with another xenon atom. The data for the reaction of argon ionizing xenon are consistent with an activation energy of 8.315 eV, that is, of the xenon-xenon, atom-atom ionization process. No data were obtained for xenon ionizing argon. Good correlation was obtained between the cross sections for electron elastic momentum exchange derived from the microwave experiment and those obtained from beam experiments. The argon-xenon ionization cross section implies that, for atom-atom processes in the noble gases at pressures ~ 1 atm and temperatures ~2/3 eV, the ionization cross section is independent of the electronic

structure of the projectile atom

Kelly, Arnold J.

English

Caltech Authors - Main

Reprinted from THE JOURNAL OF CHEMICAL PHYSICS, Vol. 45, No.5, 1733-1736, 1 September 1966 
Printed in U. S. A. 
Atom-Atom Ionization Mechanisms in Argon-Xenon Mixtures* 
ARNOLD J. KELLyt 
Daniel and Florence Guggenheim Jet Propulsion Center, Karman Laboratory of Jet Propulsion and Fluid Mechanics 
California Institute of Technology, Pasadena, California 
(Received 18 April 1966) 
The atom-atom ionization process occurring in high-purity argon-xenon mixtures has been investigated 
by means of a conventional shock tube employing a microwave probe to monitor the electron-generation 
rate. All tests were conducted at approximately atmospheric pressure and at temperatures in the range 
between 5000° and 90000 K, corresponding to a neutral-particle density of 7.0X1017 em-a. The cross-sectional 
slope constant for xenon ionized by collision with an argon atom is 1.8XlO-20 cm2/eV±20%, that is, equal 
to that for xenon ionized by collision with another xenon atom. The data for the reaction of argon ionizing 
xenon are consistent with an activation energy of 8.315 eV, that is, of the xenon-xenon, atom-atom ioniza-
tion process. No data were obtained for xenon ionizing argon. Good correlation was obtained between the 
cross sections for electron elastic momentum exchange derived from the microwave experiment and those 
obtained from beam experiments. 
The argon-xenon ionization cross section implies that, for atom-atom processes in the noble gases at 
pressures "'-'1 atm and temperatures "'-'i e V, the ionization cross section is independent of the electronic 
structure of the projectile atom. 
INTRODUCTION 
I N a previous paper,! the results of an experimental determination of the atom-atom cross section in 
pure argon, krypton, and xenon are summarized. The 
aim of the present study, using the same shock-tube 
and microwave diagnostic techniques, was to deter-
mine the effect of controlled amounts of impurity 
upon the atom-atom ionization process. The impurity 
will have an excitation level lower than that of the gas 
under investigation. Of particular interest were the 
interspecies ionization cross sections. Xenon was chosen 
as an appropriate impurity to be studied in conjunc-
tion with argon. The first excitation level of xenon 
(8.315 eV) is some 3.233 eV below that of argon 
(11.548 eV), and the argon-argon and xenon-xenon 
ionization reactions were well known and could be 
suitably taken into account. 
The details of the shock tube, the microwave diag-
nostic system, and the data reduction procedure are 
to be found in Ref. 1. A more elaborate exposition of 
these details is to be found in Ref. 2. Stringent pre-
cautions were taken in order to restrict the level of 
contamination of the test gas due to the experimental 
apparatus to less than 1 ppm. All of the argon-xenon 
mixture tests were conducted using premixed research-
grade gases purchased from the Linde Company. These 
gases had known impurity levels measured in the low 
parts-per-million range. 
Electron Generation Rate from Atom-Atom Interaction 
Pure Gas 
The preferred mechanism for atom-atom ionization 
of the noble gases at moderate pressures and temper-
* Work supported by the U.S. Air Force Office of Scientific 
Research under Contract AF 49 (638)-1285. 
t Graduate Student; now Senior Research Engineer, Jet Pro-
pulsion Laboratory, Pasadena, Calif. 
1 A. J. Kelly, J. Chern. Phys. 45, 1723 (1966), preceding paper. 
2 A. J. Kelly, "Atom-Atom Ionization Mechanisms and Cross 
Sections in Noble Gases and Noble Gas Mixtures," Ph.D. thesis, 
California Institute of Technology, 1965. 
atures involves two steps; a rate-controlling step in 
which one of the atoms is excited to the first excited 
state, and a second step in which the excited atom is 
ionized. If we define Qij(1 Vi-Vj /) as the ionization 
cross section, the ith species in two-body collisions 
with a member of the jth species, where Vi and Vi are 
their respective velocities, we can write the electron-
generation rate per unit volume as 
(1) 
Ni and N j are the neutral-particle densities of the 
ith and jth species, respectively, and f( ) denotes the 
velocity distribution. Because of the temperatures and 
pressures encountered in this study and the low levels 
of ionization attained, it is valid to assume that both 
species are in thermal equilibrium and that f(Vi) and 
f(vj) are Maxwell-Boltzmann distributions. 
Converting to center-of-mass coordinates, denoting 
the reduced mass (mimj) / (mi+mj) as J.lij and the 
relative velocity Vi-Vj as g, Eq. (1) can be written as 
~~~~j 41r C;ZT r2 ~: [exp (~:;g) ] Qij(g) g3dg, (2) 
where now gi* is the threshold relative energy at which 
the reaction begins. The relative interaction energy E 
is related to the relative center-of-mass velocity g as 
E= (tJ.lij)g2 which, for the case of threshold, becomes 
Ei* = (tJ.lij) gi*2. Substitution of a constant-slope ioni-
zation cross section,3 i.e., Qij=C;j(E-Ei*) , into (2) 
results in an expression for the atom-atom electron-
generation rate 
N e = (NiN J/1 +8ij)CijKij(1//3)3/2(2+/3Ei*) exp( -/3Ei *) , 
(3) 
where /3=1/kT and Kij=2(2/1rJ.lij) 1/2. 
3 Cf. Ref. 2 regarding the validity of constant-slope, approxi-
mation for energy dependence of atom-atom ionization cross 
section. 
1733 
1734 ARNOLD J. KELLY 
Binary Gas Mixture 
When a binary gas mixture undergoes atom-atom ionization, there are four electron-generation processes 
occurring simultaneously, two between like particles and two between unlike particles. The electron-generation 
rate for binary mixtures is therefore: 
Ne=!N12CnKn(1/{3)3/2(2+{3E'1) exp( -(3E.1) 
+N1N2C12K12(1/{3)3/2(2+{3E01) exp( -(3E*1) 
Species 1 ionized by Species 1, 
Species 1 ionized by Species 2, 
(4a) 
(4b) 
+N2N1C21K21(1/{3)3/2(2+{3E02) exp( -(3E*2) 
+!N22C22K22(1/{3)3/2(2+{3E02) exp( -(3E*2) 
Species 2 ionized by Species 1, 
Species 2 ionized by Species 2. 
(4c) 
(4d) 
It is assumed that the pure-gas cross-sectional slope 
constants (Cn, C22 ) and the threshold energies E01 
and E*2 are known. For interactions between unlike 
particles [Eqs. (4b) and (4c) ] it is assumed that the 
threshold energies for the reaction are determined by 
the characteristics of the particle undergoing reaction 
and are independent of the particle causing the excita-
tion. Thus, the threshold energy for an argon atom ex-
citing a xenon atom is 8.315 eV, the value observed for 
an argon atom exciting a xenon atom is 8.315 eV, the 
value observed for a xenon atom exciting another xenon 
atom. This assumption appears to be substantiated by 
experiment. Under these assumptions, there are two 
unknowns, C12 and C21. In argon-xenon mixtures for 
temperatures appropriate to this experiment, the dif-
ference between the threshold energies of argon and 
xenon is sufficiently large so that the exponential factors 
differ by as much as two orders of magnitude. Since the 
interspecies cross sections probably do not differ by 
more than an order of magnitude, the reaction with 
the lowest threshold energy is dominant. This is actually 
observed in the Arrhenius plots of the data for argon-
xenon mixtures, the slopes indicating a threshold energy 
the same as that for pure xenon. As a consequence of 
these considerations, we are required experimentally 
to determine only the interspecies cross section cor-
responding to the ionization of the species possessing 
the lower threshold energy. Although it is theoretically 
possible to determine both C12 and C21 by conductIng 
two independent experiments, this did not prove pos-
sible because the influence of the slower reaction was 
obscured by data scatter. 
EXPERIMENTAL RESULTS 
Ionization Cross Section 
Four different argon-xenon mixtures were studied; 
0.1 % (i.e., 1000 ppm xenon in argon) 0.48%, 5%, and 
20% xenon in argon. Because the results from the test-
ing of the 0.1% and 0.48% mixtures were not sub-
stantially different from those obtained when test-
ing pure argon, they have not been presented. The 
Arrhenius plots for the 5% and 20% mixture ratios are 
presented in Figs. 1 and 2, respectively. All these data 
were obtained at a nominal preshock pressure of 5 
torr, corresponding to a postshock neutral-particle 
density of 7.0X1017 cm-3• No attempt was made to 
investigate pressure dependence. 
The best fit to the data for both the 5% and 20% mix-
tures was obtained by letting C21 equal C22 = 1.8 X 10-20 
cm2/eV and, for consistency, C12 equal Cn =1.2XlO-19 
cm2/eV, with E'1=11.548 eV and E02 =8.315 eV, cor-
responding to the first excitation energy levels of argon 
and xenon, respectively. As was the case with the pure 
noble-gas ionization data,! diffraction effects associated 
with electron-density gradients lateral to the direction 
of the microwave beam have apparently shifted the 
low {3 ({3 ;:51.6) data below their true position. No cor-
rection has been applied in the data reduction pro-
cedure to compensate for this effect. The extent to 
which uncertainties associated with the known slope 
constants Cn and C22 and with the unknown slope con-
stant C12 would affect the determination of C21 can 
be judged from the relative contribution each reaction 
makes to the total electron-generation rate. Denoting 
the reactions by their cross-sectional slope constants, 
the fractional contribution that each makes to the 
electron population in shown in Table I for temper-
atures representing the extremes of the range studied. 
At worst, the ±15% uncertainty in Cn (d. Ref. 1) 
1.0 
o 
-1.0 
PURE XENON 
-2.0 (c •• = 1.8 x I020cm";EV, E.= 8.315 EV) 
-4.0 
-5.0 \ 
-6.0 PURE ARGON 
(S,=1.2XIO'·cm2/EV, E,=II.548 EV) 
-7.0~-""""'"",---,-,~-+",,--L..,-_...L.._---' 
1.200 1.400 1.600 1.800 2.000 2.i200 2.400 
f3 = Ilk T, EV' 
FIG. 1. Arrhenius plot for ionization of argon+5% xenon. 
0, 5 torr, N=6.96XlO17 em-S. Calculated using Cn = C12 = 
1.2 X 10-19 em'/eV; C'l= C'2= 1.8 X 10-'0 r.m'/eV. E,=11..'i48 eV, 
and E2=8.315 eV. 
ATOM-ATOM IONIZATION MECHANISMS 1735 
1.0 
o 
-1.0 
-2.0 
~ 
'2 
~. -3.0 
~ 
--= 
-4.0 
-5.0 
-6.0 
-7·f200 1.400 1.600 1.800 2.000 2.200 2.400 
{3 = l/kT, e:y' 
FIG. 2. Arrhenius plot for ionization of argon+20% xenon. 
0, 5 torr, N = 6.96 X 1017 cm-3• Calculated using Cu = C12 = 
1.2XlO-19 cm2/eV, C21=C22=1.8XlO-20 cm2/eV, E1=11.548 eV, 
and E2=8.315 eV. 
contributes ",,8% uncertainty to C21• Similarly, the 
error in C21 due to the uncertainty in C22 could at most 
amount to about 1 %. Finally, it is clear that even if 
the assumed value of C12 were in error by 100%, the 
resulting value of C21 would be affected by only 10% 
for the extreme case, low {3, 5% xenon in argon. No 
reasonable estimate of the slope constant C12 can be 
9.0 
B.O 
7.0 
6.0 
" 
-2 5.0 
" N 
1; 
I 
f- 4.0 
a 
3.0 
2.0 
1.0 
I 
"He:IGHWAV: & NICHOLS 
NASA TN 0 2651 
0~~--~--0~.7~00--~--~~--~~O~80~0~~~ 
{i1/2_ EVil. 
FIG. 3. QT versus (:J-l for argon+5% xenon. 0, 5-torr data. 
Electron and atom temperature assumed equal. 
TABLE I. Relative reaction rates. 
Reaction 
Mixture 
(:J Cu C12 C21 C22 
5% xenon in argon 1.4 0.501 0.042 0.449 0.008 
1.8 0.230 0.020 0.737 0.013 
20% xenon in argon 1.6 0.098 0.040 0.794 0.068 
2.0 0.032 0.013 0.881 0.075 
made on the basis of this experimental work; the ma-
jority of the generated electrons, for the mixtures 
studied and the test conditions encountered, arise from 
argon ionizing xenon. 
The mixture data have associated with them error 
brackets which are equivalent to those for pure gases. 
The uncertainty introduced by possible variations from 
the specified mixture ratio is included in the brackets 
shown in the figures. Also shown in these figures are 
dashed lines representing the calculated composite 
atom-atom ionization behavior for a variation of 
±20% in the slope constant C21 from its most probable 
value, 1.8XlO-2o cm2/eV. This uncertainty is judged 
to be a reasonable estimate of the error with which this 
cross section is determined. For comparison, the pure 
argon and pure xenon results of Ref. 1 are included on 
these figures. 
Therefore, it is concluded that, within a probable 
error of about ±20%, the cross section for argon ioniz-
ing xenon is equal to the cross section for xenon-xenon 
ionization, as reported in Ref. 1. 
I 11.0 10.0 
9.0 
8.0 
" -2 7.0 
" N E 
u 
I 
f- 6.0 
a 
5.0 
4.0 
NASA TN 02651 
3.0 
0.700 0.600 
FIG. 4. QT versus (:J-' for argon+20% xenon. 0, 5-torr data. 
Electron and atom temperature assumed equal. 
1736 ARNOLD J. KELLY 
Electron-Atom Elastic Cross Sections 
. The tran~verse 24-GHz microwave probe,4 in addi-
tIon to sensmg electron density, provided data on the 
electron collision frequency and consequently permitted 
an electron-heavy component cross section to be cal-
culated. Because of the low level of ionization ( < 10-4) 
pres~nt during microwave interaction, it was possible 
to dIscount electron-ion and inelastic electron-atom 
collisions and to identify the collision frequency as that 
due to electron-atom elastic momentum-exchange en-
counters. Assuming that the electron gas has a Max-
wellian velocity distribution, the cross section obtained 
from these data is the Maxwell-averaged electron-atom 
elastic momentum-exchange cross section. The electron-
4 R. G. Jahn, Phys. Fluids 5,678 (1962). 
atom elastic momentum cross section determined from 
the data is denoted QT and is shown plotted as a func-
tion of {rl/2 in Figs. 3 and 4, assuming that the electron 
and atom temperatures were equal. Figure 3 presents 
results for 5% xenon in argon, and Fig. 4 for 20% 
xenon in argon. Electron-argon and electron-xenon 
cross sections .for elastic momentum exchange, based 
on beam expenments, Ref. 5, are shown for comparison. 
In making this comparison, these results have been 
weighted in accordance to the relative proportions of 
the two gases present in the mixtures. The correspond-
ence between the microwave and the beam results is 
good. 
6 J. E. Heigh.way ~nd L. D. Nichols, "Brayton Cycle MHD 
Power GeneratIOn WIth Non-Equilibrium Conductivity" Natl 
Aeron. Space Admin. Tech. Note D-2651 (1965). ' . 


Atom-atom ionization mechanism in Argon-Xenon mixtures

https://authors.library.caltech.edu/21545/1/176_Kelly_AJ_1966.pdf

Atom-atom ionization mechanism in Argon-Xenon mixtures

Abstract

Similar works

Full text

Available Versions

Caltech Authors - Main