close

Вход

Забыли?

вход по аккаунту

?

A KINETIC STEADY-STATE MODEL FOR THE EXCITATION OF HELIUM ATOMS IN LOW-PRESSURE, MICROWAVE-INDUCED DISCHARGES

код для вставкиСкачать
INFORMATION TO USERS
This was produced from a copy of a document sent to us for microfilming. While the
most advanced technological means to photograph and reproduce this document
have been used, the quality is heavily dependent upon the quality o f the material
submitted.
The following explanation of techniques is provided to help you understand
markings or notations which may appear on this reproduction.
1.T he sign or “ target” for pages apparently lacking from the document
photographed is “Missing Page(s)” . If it was possible to obtain the missing
page(s) or section, they are spliced into the Him along with adjacent pages.
This may have necessitated cutting through an image and duplicating
adjacent pages to assure you o f complete continuity.
2. When an image on the Him is obliterated with a round black mark it is an
indication that the film inspector noticed either blurred copy because of
movement during exposure, or duplicate copy. Unless we meant to delete
copyrighted materials that should not have been filmed, you will find a
good image of the page in the adjacent frame.
3. When a map, drawing or chart, etc., is part of the material being photo­
graphed the photographer has followed a definite m ethod in “sectioning”
the material. It is customary to begin filming at the upper left hand comer
o f a large sheet and to continue from left to right in equal sections with
small overlaps. If necessary, sectioning is continued again—beginning
below the first row and continuing on until complete.
4. F or any illustrations that cannot be reproduced satisfactorily by
xerography, photographic prints can be purchased a t additional cost and
tipped into your xerographic copy. Requests can be made to our
Dissertations Customer Services Department.
5. Some pages in any document may have indistinct print. In all cases we
have filmed the best available copy.
University
M icrofilms
International
3 0 0 N. Z E E B R O A D , AN N A R B O R , Ml 4 8 1 0 6
18 B E D F O R D ROW, L O N D O N WC1R 4 E J , EN G L A N D
8112818
K o h l m il l e r , C h r is t o p h e r K ev in
. A KINETIC STEADY-STATE MODEL FOR THE EXCITATION OF HELIUM
ATOMS IN LOW-PRESSURE, MICROWAVE-INDUCED DISCHARGES
The Pennsylvania State University
University
Microfilm s
International
300 N. Zeeb Road, Ann Arbor, MI 48106
PH.D.
1981
The Pennsylvania State University
The Graduate School
Department of Chemistry
A Kinetic Steady-State Model for the
Excitation of Helium Atoms
in Low-Pressure, Microwave-Induced Discharges
A Thesis in
Chemistry
by
Christopher Kevin Kohlmiller
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
March 1981
I grant The Pennsylvania State University the
nonexclusive right to use this work for the University's
own purposes and to make single copies of the work
available to the public cn a not-for-profit basis if
copies are not otherwise available.
We approve the thesis of Christopher Kevin Kohlmiller.
Date of Signature:
Terence Hr-Z&Gby, Associate
Professor of Environmental
Chemistry, The Johns Hopkins
University, Co-Chairman of
Committee and Thesis Advisor
/Ji i
Joseph Jordan, Professor of
Chemistry, Co-Chairman of
Committee
/>< Jf*/
Z
=■
7
0
a ,
(
»7
h A. Dixon, Professor of
lemistry, Head of the
''Department of Chemistry
FYedrick W. Lampe\ Professor
of Chemistry
m i
Santiago R. Polo, Professor
of Physics
ABSTRACT
A kinetic steady-state model is theorized to pre­
dict the population density of excited atoms in reducedpressure helium discharges.
This model assumes inelastic
electron-impact excitations and radiative cascading from
higher states as the population processes and radiative
deactivation and associative ionization as the depopula­
tion processes.
The electron energy was experimentally
determined by a double-probe method to allow the
evaluation of the rate constants of the electron-impact
excitation reactions from known cross sections.
The
electron number density was also determined and was
assumed to fit a Druyvesteyn energy distribution.
The
relative population densities of the excited states of
helium in a microwave-induced discharge were measured
and compared with the calculated results.
The densities
of the excited states in doped discharges were also
measured.
TABLE OF CONTENTS
Page
ABSTRACT............................................ iii
LIST OF TABLES...................................... vii
LIST OF F I G U R E S ..................................
ix
ACKNOWLEDGEMENTS.................................... xii
I. HIGH-FREQUENCY DISCHARGES ..................
USED IN SPECTROCHEMICAL ANALYSIS
1
A.
Introduction............................
1
B.
The Early History of Discharges ........
2
C.
Basic Parameters and Processes..........
of hf Discharges
4
D.
HF Discharges Used for Spectral........
Analysis
7
1.
Inductively-Coupled Plasma..........
8
2.
Capacitively-Coupled Microwave. . . .
Plasma
14
3.
Inductively-Coupled Microwave . . . .
Plasma
17
4.
Comparison of hf Discharges.......... 24
II.
EXPERIMENTAL................................... 27
III.
POPULATION DENSITIES OF T H E ................... 37
HELIUM EXCITED STATES
A.
Introduction.............................. 37
B.
Emission Spectra of the Helium............ 37
Discharge
V
TABLE OF CONTENTS (continued)
page
C.
IV.
V.
Population Densities.....................
45
1.
Theory..............................
45
2.
R e s u l t s .....................
51
3.
Effect of Pressure Change ..........
on Number Density
58
4.
Effect of Doping Gases.
on Number Density
..........
62
ELECTRON ENERGY AND DENSITY ................
64
A.
Introduction............................
64
B.
Theory and Results......................
66
THE KINETIC STEADY-STATE THEORY ............
AND COMPARISON WITH EXPERIMENTAL
DATA
81
A.
Introduction............................
81
B.
Prediction of Excited-State ............
Number Densities Using the
Kinetic Steady-State Theory
83
1.
Mechanism.........................
83
2.
Rate Constant for Electron- . . . . .
Impact Excitation
88
3.
Determination of Ground State . . . .
Number Density
92
4.
Radiative Transition Probabilities. .
96
5.
Rate Constant for Homonuclear . . . .
Associative Ionization
96
6.
Total Lifetime of the jth State . . .
98
7.
Cascading..........................
99
8.
Effect of Pressure.............. • . .
100
vi
TABLE OF CONTENTS (continued)
page
9.
Effect of DopingG a s e s ............... 100
10.
Wall Reactions...................... 102
C. Comparison of Calculations................. 103
With the Experimental Results
D. Conclusions...............................117
REFERENCES.......................................... 119
vii
LIST OF TABLES
page
1.1
Comparison of the Inductively-Coupled
Microwave Plasma, the Microwave-Induced
Plasma and the Direct Current Plasma as
Excitation Sources
25
Specifications of the Varian AA-4
Monochromater
32
111.1
Atomic Oxygen Lines Observed in Reduced
Pressure Oxygen-Doped Helium Discharge
in the 800 to 300 nm Region
44
111.2
Blackbody and Filament Temperatures for
Standard Tungsten-Filament Lamp
47
III. 3
Spectroscopic Data for He(I) Transitions
50
111.4
Excitation Thresholds, Degeneracies, and
Population Densities of Excited States
of Helium at 1.0 Torr
52
111.5
Relative Number Densities of Observed
Excited States of Helium
56
III. 6
Population Ratios of the n = 3 and
n = 4 States of Helium
59
III.7
Ratios of the Population Densities
at Two Pressures (Torr) for the
Excited States of Helium
61
The Average Electron Energy and the
Positive Ion Density in the Discharge
as Determined by the Double-Probe
Method
75
Values of the Radiative Lifetimes, the
Rate Constants for Associative Ionization,
and the Effective Lifetimes, at 1.00 Torr,
for the Excited States of Helium
97
II.1
IV.1
V.l
viii
LIST OF TABLES (continued)
page
V.2
Rate Constants and Excited-State
Populations of S Family at 1.0 Torr
104
V.3
Rate Constants and Excited-State
Populations of P Family at 1.0 Torr
105
V.4
Rate Constants and Excited-State
Populations of D Family at 1.0 Torr
106
V.5
Calculated and Experimental Relative
Population Densities of Excited
States of Helium
112
V .6
Calculated Population Densities of ^S
States Between 0.4 and-4.0 .Torr
114
ix
LIST OF FIGURES
Page
1.1
Schematic Diagram of an InductivelyCoupled Plasma
11
1.2
Schematic Diagram of a CapacitivelyCoupled Microwave Plasma
15
11.1
Flow System for Emission Spectra Study
29
11.2
The Evanson Microwave Cavity and
Removable Cap
30
11.3
Diagram of Electronics Associated
With Intensity Calibration
33
11.4
Double-Probe Circuit
35
' 38
111.1
Emission Spectrum of Helium Discharge
at 1.0 Torr
111.2
Emission Spectrum of 2% -HydrogenDoped Helium Discharge at 1.0 Torr
40
111.3
Emission Spectrum of 1% NitrogenDoped Helium Discharge at 1.0 Torr
41
111.4
Emission Spectrum of 1% Nitrous OxideDoped Helium Discharge at 1.0 Torr
42
III. 5
Emission Spectrum of 1% Oxygen-Doped
Helium Discharge at 1.0 Torr
43
III. 6
Relative Values of the Emissitivity
of Tungsten, the Theoretical Spectral
Radiant Emittance of a Blackbody, and
the Recroded Signal from the Standard
Tungsten Lamp at 1850 K
49
III.7
Boltzmann Plot of the Experimental
Excited State Population Densities
at 1.0 Torr
57
X
LIST OF FIGURES (continued)
page
111 .8
Relative Population Densities of the
States in the Pressure Range 0.4 to
4.4 Torr
111.9
Relative Population Densities of the
States in the Hydrogen-Doped Helium
Discharge
S
60
3
D
63
IV.1
General Potential Diagram for the
Double-Probe Method
67
IV.2
Voltage-Current Characteristic of
the Double-Probe Method
70
IV.3
Experimental Voltage-Current
Characteristic of the Helium
Discharge at 1.0 Torr
74
IV.4
The Average Electron Energy and the
Positive Ion Density in the Helium
Discharge
76
IV.5
The Average Electron Energy and the
Positive Ion Density in the Doped
Helium Discharge
77
V.l
Relative Values of Electron Velocity,
Cross Section for Electron-impact
Excitation, Druyvesteyn Energy
Distribution, and the Rate Constant
for Electron-impact Excitation for the
3ls State
90
V.2
The Rate Constant of Electron-impact
Excitation as a Function of
.
Average Electron Energy for the S
States
91
V.3
Comparison of the Druyvesteyn and
Maxwellian Energy Distribution Functions
93
V.4
Calculated Population Densities of the ^S
States of the Helium Discharge
101
V.5
Calculated and Experimental
^
Relative Population Densities for S
States of Helium Discharge at 1.0 Torr
107
XX
LIST OF FIGURES (continued)
Page
V .6
Calculatedand Experimental
3
Relative Population Densities for S
States of Helium Discharge at 1.0 Torr
108
V.7
Calculated and Experimental Rela,
tive Population Densities for Ip and P
States of Helium Discharge at 1.0 Torr
109
V .8
Calculatedand Experimental
^
Relative Population Densities for D
States of Helium Discharge at 1.0 Torr
110
V.9
Calculated and Experimantal
Relative Population Densities for ~'D
States of Helium Discharge at 1.0 Torr
111
V.10
Calculatedand Experimental
^
Relative Population Densities for S
States of Helium Discharge
115
xii
ACKNOWLEDGEMENTS
I would like to thank Professor Terence Risby
for his guidance and assistance throughout this study.
I also thank Professor Lester Andrews of the University
of Virginia for his support and patience during the
writing of this dissertation.
Experimental assistance
from Dr. Joseph Dulka and Mr. Mark Ross is acknowledged.
The discussions with Professor Frederick Lampe and
Professor Gerd Rosenblatt were appreciated.
I thank
Professor Thomas Wiggins for the use of the tungsten
lamp, and Professor Robert Bernheim and Professor
Joseph Jordan for the use of other equipment.
CHAPTER I
HIGH-FREQUENCY ELECTRICAL DISCHARGES
USED IN SPECTROCHEMICAL ANALYSIS
A.
Introduction
Besides the three states of matter which are com­
monly experienced, a fourth state, the plasma state, also
exists,
verse.
and dominates (>99% (1)) throughout the uni­
This state is created when sufficient ionization
of gaseous atoms and molecules occurs such that the
behavior of the system is dominated by the electrons and
ions.
Strictly speaking, the term "plasma" should be
used only when the ionization of the gas is complete, and
such a system cannot be sustained under laboratory condi­
tions; the term "discharge" describes any system which is
partially ionized so that it will conduct electricity.
In common usage, the term "plasma" is often used for
laboratory discharges, and this practice will be followed
in this text, to be consistent with the original authors'
descriptions.
Electrical discharges can be produced by either direct
current (DC) or alternating current (AC) potential fields.
A combustion flame may also be considered a discharge, but
this term is usually reserved for systems which derive
their power from electrical sources.
The disruptive
discharges, i.e., the arc and spark, were the first to
be used for chemical analysis (2 ), and may still be the
most widely used, but will not be considered in this
review.
Despite the wide use of electrical discharges in
many areas of the physical sciences, no proven expla­
nation of the mechanism(s) of excitation in the discharges
has been presented.
The purpose of this thesis is to
examine one theory of excitation and compare the predicted
levels of excitation with experimentally determined values
This chapter will present a discussion of high frequency
electrical discharges used in spectroch^mical analysis
and the theories of excitation.
The subsequent
chapters present the important physical characteristics
of the discharge and how they may be obtained.
The last
chapter contains the comparison of the predicted and the
experimental values.
B.
The Early History of Electrical Discharges
McTaggert (3) has described the early history of
electrical discharges.
William Crookes in 1879 observed
the fluorescence in a partially evacuated glass container
in which he discharged a high-voltage current from an
induction coil (4).
William Watson, an English apothecary
had observed a similar phenomenon about 150 years
3
earlier (4).
Crookes found these "cathode rays" could be
bent by an electromagnet and considered them a fourth state
of matter, which he called "radiant matter" (4).
This
initial work led to the discovery of X-rays by Roentgen
and the electron by Thomson.
The works of C.T.R. Wilson
and J.S. Townsend in the early 1900's indicated that the
ionization of the gas molecules was due to collisions
with charged species (3).
The first use of the term
"plasma" to describe this state was by Langmuir in 1930
(5) .
The earliest use of high-frequency (hf) AC power
for the generating and sustaining of electrical discharges
was in 1925 (6 ).
Gerlach and Schweitzer appear to have
been the first to use an hf field for spectrochemical
analysis in 1931, when they used a Tesla coil for the
excitation and qualitative detection of mercury (7) .
Interest in the field did not develop until after World
War II and the development of radar.
The first use of a
microwave power generator to produce a discharge was by
Nagle in 1947 (3).
McCarthy's work in 1954 was the first
report of a chemical reaction studied in an hf discharge
(8 ).
The use of hf discharges for spectrochemical
analysis was suggested by Mavrodineau
in 1954 (2) and
reported by Badarau, et al., in 1956 for the analysis for
lead and barium using a nickel electrode in air (9).
Current hf techniques used for spectral analysis are dis­
cussed later in this chapter.
4
C.
Basic Parameters and Processes of hf Discharges
A very common method to sustain an electrical dis­
charge in the laboratory is the use of a high frequency
(hf) alternating current (AC) potential.
The discharge
is initiated by the introduction of electrons, usually
with a Tesla coil, in the hf field.
These electrons are
accelerated by the rapidly oscillating field and collide
with the neutral atoms and/or molecules in the gas (the
ions, also produced by the Tesla coil, are much less
affected by the hf field since their mass is so much
greater).
These collisions can be either elastic (in
which a small amount of the kinetic energy is transferred
from the electron to the molecule), inelastic (a much
larger amount of the kinetic energy of the electron is
transferred to the molecule, increasing its internal
energy), or superelastic
(the kinetic energy of the
electron is increased and the internal energy of the
molecule is decreased)
(10).
The inelastic collisions
cause ionization and excitation of the gaseous
molecules
(M) in the discharge:
M + e“ — >
M+ +
2e~
(1.1)
M + e“ — >
M* +
e~
(1.2)
These reactions are important since the ionization reac­
tion (1 .1 ) produces more electrons to sustain the discharge,
and the excitation reaction (1 .2 ) allows the energy of the
hf field to be transferred to the gaseous molecules through
the electrons.
The electrons cannot derive power from the field
on the average, since they are 90° out of phase with the
field (1 1 ), but do obtain energy because the elastic
collisions change the phase relationship.
energy changeslittle
in
The electron
these collisionssince
average fraction of theenergy
lost isgiven
the
by classical
physics to be 2m/M (11, 12) or about 0.1% (assuming
helium is the gas).
If the frequency of the external
field, f, is greater than the elastic collision frequency,
the distance the electron travels (x) due to the hf field
is
2 e E
x = --- 5—
moo
,T
(1.3)
where e is the electron charge, E is the field strength,
m is the mass of the electron and 00 is the angular fre­
quency (00 = 2 irf) .
in the research which is to be dis9
-1
cussed m this thesis, f = 2.45 x 10 sec
and E ^ 35
-4
volts/cm (13), the value x will be about 5 x 10
cm and
the energy obtained by the electron in one cycle is
e = e E x
or e ^ 0.02 eV.
(1.4)
Therefore the electron must undergo many
elastic collisions before it obtains sufficient energy
to produce an inelastic collision (e.g., ionization poten­
tial of helium is 24.6 eV). A detailed discussion of the
determination of the average electron energy is presented
in Chapter IV.
The species found in a discharge are not in thermo­
dynamic equilibrium, a fact known at least since Herzberg
in 1937 (14), yet many spectroscopists attempt to describe
a discharge by specifying its "temperature," which cannot
have any significant meaning unless it is related to a
defined equilibrium.
Sharp (2) has indicated a monatomic
discharge may be characterized by four temperatures.
(a) The electron temperature; TQ , which is deter­
mined by the kinetic energy of the electrons;
(b) The excitation temperature, T O , which characterizes the populations of various electronic
energy levels (also known as the spectroscopic
temperature);
(c) The ionization temperature, T^, which charac­
terizes the population of various ionization
states; and
(d) The gas temperature, T , which is determined
y
by the kinetic energy of the gaseous atoms or
molecules.
(For molecular discharge, temperatures must also be
determined for the dissociation equilibria, and for the
populations of the vibrational and rotational levels.)
If the four values of temperatures are equal, then the
discharge is in thermodynamic equilibrium; however, in
the discharge the values usually have the relation
7
Sharp (2)
and others have used the concept of "local
thermodynamic equilibrium" (LTE) to avoid this problem.
If the temperature change of a species along its mean
free path is small compared to its temperature, the
equilibrium is only slightly affected and LTE is said to
exist.
When conditions are such that even this approxi­
mation is poor, the concept of "partial LTE" is used to
indicate that the equilibrium is related only to the
species dominating the collisional processes (2, 15).
Obviously such an approach to understanding the
reactions in a discharge will depend largely on empiri­
cism.
This work attempts to avoid this approach by
using a general steady-state kinetic theory which should
lead to a greater understanding of the processes with
the discharges.
This will be introduced in Section D
and further discussed in Chapter V.
D.
HF Discharges Used for Spectral Analysis
In recent years, three hf techniques have been widely
used for spectral analysis (16) :
the inductively coupled
plasma (ICP), the capacitively coupled microwave plasma
(CMP), and the microwave induced plasma (MIP).
The initial
development of each will be reviewed separately, and the
theories of excitation in these discharges will also be
examined.
8
1.
Inductively-Coupled Plasma
The inductively-coupled plasma torch was developed
by Reed.in 1961 (17, 18).
He operated the plasma in a
quartz tube with an rf coil around the center, using
argon at one atmosphere and 10 kw at 4 MHz.
The plasma
was initiated with a small arc, or by heating a graphite
rod or a wire in the rf field.
The plasma was stabilized
by introducing the gas tangentially into the tube, creating
a low-pressure area in the tube center, which centered
the plasma and cooled the walls.
Reed did not use the
ICP for spectral analysis, but to grow single crystals of
refractory oxides and to melt zirconium oxide.
Reed measured the plasma temperature (16,000
K at
the plasma center) by assuming thermal equilibrium.
He
admitted that this assumption was unproven, but used as
evidence studies on dc plasmas and the short mean free
path of the electrons to support that the plasma is not
far from thermal equilibrium.
The first use of the ICP torch as a spectroscopic
source was by Greenfield and his colleagues who applied
for patents in 1963 (19).
This device consisted of
three concentric tubes, the outer two (quartz) to contain
the plasma, and the inner tube (borosilicate) to inject
the aerosol of the sample.
An annular, or doughnut­
shaped plasma formed, which allowed easy introduction of
the sample, and gave enhanced stability and sensitivity.
9
More recently, Greenfield has stated that despite the
many changes in design tried, this original device has
not been improved (2 0 ).
Greenfield first published the results of the ICP
in 1964 and showed its use as an emission source for cal­
cium and other metals and its freedom from electrode
contamination which affected the dc arc (21).
He has
also used the ICP for multi-element analysis of micro­
liter blood samples (22) and 32 other, varied samples
(20).
Detection limits from 1 to 100 ppb were obtained
for 22 metals using a 30-channel direct-reading spec­
trometer with fully automatic sequential sampling, and
the wide range of the ICP (1 ppb to 100%) was demonstrated.
Greenfield reviewed the concept of the temperature
of the plasma in a series of papers in 1975 (19, 23, 24).
Most authors working with an atmospheric ICP (19),
believed that the ICP is at LTE or near to LTE, although'
some felt the opposite.
Reported temperatures ranged
from 6800 to 15,000 K and decreased from the center.
For low-pressure ICP, it was accepted that divergence
from LTE occurred.
Independently of Greenfield, Fassel and his col­
leagues also developed the ICP torch as a spectroscopic
source in 1965 (25).
This work introduced the use of
laminar flow of the gas into the plasma, compared to the
tangential, turbulent flow used by Greenfield.
In 1969,
he demonstrated the superior detection limits of the ICP
10
on a wide scale (26, 27).
In a comparison of ICP to
atomic absorption for determination of metals, Fassel
and Kniseley showed that the detection limits were
comparable, but that the ICP had a greater range (trace,
minor, and major constituents) and that the ICP could be
used for multi-element analysis (28, 29, 30).
A schematic
diagram of their torch is shown in Figure 1.1.
Fassel
has also developed ICP for simultaneous multi-element
determinations (31).
Fassel and others studied the excitation properties
and the electron densities in the ICP and found the
addition of an easily ionized element does increase
the electron density, but does not have much effect on
the analyte line intensities (32) .
They did conclude
that LTE does not exist and suggested that the metastable
argon atoms were responsible for the excitation of the
analyte species.
This followed an earlier study in which
they were the first to suggest that LTE does not exist
in the ICP (33).
Other spectroscopists have examined the question
of the excitation processes of the ICP.
In 1970, Truitt
and Robinson listed several possible methods of energy
transfer, but did not consider electron collision (1-34).
Mermet (35, 36) was the first to conclude that LTE cannot
exist, by comparison of the excitation temperature
(4800 K at 40 MHz, 6200 K at 5 MHz) with the ionization
temperature (7000 K at 40 MHz, 8600 K at 5 MHz).
1.
13
12
3.
4.
quartz tubes
discharge
center
hf-coil
tuning system
5.
hf-generator
6.
gas unit
coolant gas
discharge gas
2.
7.
8.
9.
10.
carrier gas
nebulizer
11.
solution inlet
spectrometer
optical lens
12.
10
13.
11
Figure 1.1.
Schematic Diagram of an Inductively-Coupled Plasma
12
Kornblum and DeGalan (37, 38) tentatively agreed, suggesting
either metastable argon atoms or energetic electrons to
be responsible .for the excitation of the analyte species.
Visser, et al. (39), concluded that LTE does not exist
by comparison of the emission intensities of the atomic
hydrogen spectra in an argon discharge.
It has been
demonstrated that any study of the temperature in an ICP
must be obtained as a function of the spatial coordinates
in the plasma (37, 40).
Perhaps the most extensive study of the problem
of LTE in an ICP has been by Boumans and DeBoer.
They
had earlier examined the problem of temperature of dc
arcs.
Parameters of "effective temperature" (i.e.,
apparent temperature), "effective electron density," and
"effective analyte number density" were defined, but they
report that few situations exist where such values can be
used to explain the excitation in discharges (41).
Another
approach was to assume that LTE existed, but was perturbed
by the excess metastable argon species, which act as an
ionizer (Penning ionization) and as an ionizant (an easily
ionized species)
(42) .
This treatment qualitatively
explained some trends in the ICP, but not to a large degree.
In 1977, they reported that LTE cannot be assumed to exist,
as reported by Tschopel (16) in his review on excitation
in spectrochemical analysis.
In 1980, Kirkbright, et al. (43), determined the
central channel of an ICP was not in LTE from the
13
excitation temperatures measured from atomic iron popu­
lation levels.
in an ICP:
They discuss two theories for excitation
excitation by metastable argon atoms, and
direct electron collisional excitation.
They expect
electron impact would dominate the excitation and ioni­
zation processes because the value of Te must be higher
than T
since LTE does not exist, although ionization via
Penning ionization with excited argon atoms still should
occur.
The observation of upper level fluorine excited
states (14.5 to 18.5 eV) by Fry, et al. (44), indicates
that the excitation cannot occur by metastable argon
atoms (11.5 and 11.7 eV), or other excited argon atoms
(IP < 16.0 eV).
A number of reviews concerning the ICP have appeared
in the literature (2, 16, 24, 28, 45).
A recent innovation
was the development of a miniature system, to save gas
and power consumption (46, 47).
A low-power nitrogen
ICP has also been recently reported (48, 49).
A number of companies now market commercial instru­
ments, as ICP optical emission spectroscopy is challenging
atomic absorption methods as the optimum method for
routine trace metal analysis (28).
Falk, et al., have
shown that for atomic emission spectroscopy, excitation
in low-pressure discharges is better than by thermal
- excitation but worse than direct electron impact exci­
tation by comparison of the line intensities and the
ionization and dissociation rates (50, 51).
Some authors
14
have used ICP for atomic absorption and atomic fluore­
scence (24, 28), but little progress has been made.
2.
Capacitively-Coupled Microwave Plasma
The first capacitively-coupled plasma was reported
in 1941 by Cristescu and Grigorovici, who produced a
discharge by applying the output of a high-frequency
oscillator (60-90 MHz) to two plates separated by up to
15 cm (24) .
The capacitively-coupled microwave plasma (CMP)
produces a flame-like discharge, similar to the ICP.
It
was- developed by Cobine and Wilbur (52) . An electrode
is coupled through a wave guide to a microwave oscillator
and the plasma forms at the tip (Figure 1.2) .
The use
of the CMP for spectrochemical analysis was pioneered
independently by Jecht and Kessler (53) , Trapp and
Van Calker (54) , and Mavrodineau and Hughes (55).
Jecht and Kessler (53) reported the design and
some of the physical characteristics of the CMP.
The
electrons observed were produced by the gas in the dis­
charge and not emitted by the electrode.
Various gases
were investigated, and nitrogen was found to be the best,
apparently due to its metastable energy levels.
The gas
temperature was measured at 4000 K, but they report the
excitation is not purely thermal.
It proceeds preferen­
tially by electron excitation or in steps with metastable
states (16).
1 . microwave generator
2 . coaxial wave guide
3.
tuning stub
4.
burner tube
5. outer tube
6 . burner tip
7.
8.
9.
10.
11.
12.
plasma flame
quartz window
nebulizer.'
carrier gas
solution inlet
drain
10
11
Figure 1.2.
12
Schematic Diagram of a Capacitively-Coupled Microwave Plasma.
16
W. Tappe and J. Van Calker (54) studied the CMP,
using different frequencies and working gases (air, nitro­
gen, and argon).- The sensitivities of 28 elements in the
different gases were reported.
Using air as the working
gas, the temperature was 3000 to 4000 K, depending on the
height of the flame.
Mavrodineau and Hughes (55) used a CMP of 2 kW
output at 2450 MHz for an excitation source.
A comparison
of air, nitrogen, oxygen, helium, and hydrogen gases,
showed helium and hydrogen to be superior, by having
minimum background and allowing no oxidation.
They report
the neutral temperatures to be between 2900 and 3300 K,
but that the electron temperatures must be much higher,
as evidenced by the ability to excite the helium energy
levels.
The discharge, therefore, is not at thermal
equilibrium.
The analyte excitation is by energetic
electrons.
Goto, et al. (.56), used the CMP for analysis of
various metals, using nitrogen as the carrier gas, and
reported the detection limits.
To improve sensitivity
and precision, they suggest other carrier gases and
atomizing methods.
The temperature was considered to be
4500 K about 15 mm above the aluminum tip.
Murayama and Yamamoto (57) determined the detection
limits for 25 elements using an argon CMP.
The temper­
ature was measured at 6400 K, assuming local thermal
equilibrium by a comparison of the Doppler temperature
17
and the ionization temperature, at the flame axis and
in the outer zone of the flame.
The CMP has not been used as extensively as the
ICP.
One potential problem is the electrode, which
contaminates the sample, but this does not seem critical.
The technique has been reviewed by a number of authors
(16, 24, 59).
3.
Inductively-Coupled Microwave Plasma
In addition to the method of exciting a microwave
plasma using a CMP apparatus, it can also be excited by
placing an electrodeless discharge tube in a resonant
cavity, referred to as a microwave-induced plasma (MIP).
The energy is coupled to the gas contained in a non-conductive tube (usually quartz) with an external cavity.
Various cavities have been used (16); the'Evenson 1/4-wave
cavity (60) was used in this study and will be discussed
in Chapter II.
The first use of an MIP was to analyze isotopic
ratios of hydrogen (61) and of nitrogen (62) by Broida
and colleagues.
These were studied at about one torr
in nonflow systems.
Much of the early work on microwave
discharges concerned the study of the breakdown point
of various gases, as reviewed by McDonald (10).
The
breakdown point, the point at which the gas becomes a
discharge, is related to the properties of the gas, its
pressures, and the electric field strength of the micrqwave
18
frequency (in a DC discharge, the breakdown point is
also dependent on the material and the condition of the
electrode surface).
The widest use of the MIP has been as a detector
for gas chromatography.
This was developed by Cooke,
et al., (63) in 1965, who investigated the effects of the
discharge tube diameter and the pressure.
This was
closely followed by Lisk and Bache (64, 65), who applied
this system to the study of halogen or phosphorus con­
taining insecticides separated from mixtures.
They found
maximum sensitivity in argon by reducing the pressure to
about 200 torr (66) , and that using helium as the carrier
gas allowed determination of elements not observable using
argon (sulfur, chlorine, and bromine), but that the pres­
sure had to be maintained between five and ten torr (67).
Polymer build-up is often a problem in these analyses.
Braun, et al. (68), found that the addition of a trace
amount of oxygen to a low-pressure helium MIP reduced
the polymer build-up, and completely fragmented the
chromatographic effluent.
These effects have been
observed by other workers (69).
Runnels and Gibson (70) used the MIP for the analysis
of metals in solution.
They reported extremely sensitive
detection limits for the metals introduced as metal
chelates or as halide salts using only 25 watts of power
at atmospheric pressure.
A major problem in this area
has been the introduction of the sample, as the discharge
19
is easily extinguished and a number of authors have
described introduction systems to avoid this (71, 72, 73).
Recent advances have included the introduction of
two new cavity designs.
In 1976 Beenakker (74, 75) intro­
duced a cylindrical model (referred to as the TM q ^q
cavity) which operates at atmospheric pressure and does
not require desolvation of nebulized sample solutions.
Moisan (76) has designed a cavity which produces a
standing wave in the discharge cavity and has produced
discharges over 0.1 meter in length at atmospheric pres­
sure, and 2.5 meters at lower pressures.
The observed
surface wave plasma was not in LTE, as determined by
comparison of the gas and excitation temperatures, and
the electron temperature.
Winefordner and colleagues have devoted much atten­
tion to the physical properties of the MIP.
In 1971 (77),
they published a study of an argon MIP at atmospheric
pressure and concluded that local thermodynamic equili­
brium did not exist in the plasma from a comparison of
the rotational temperature (about 2000 K, using OH rota­
tional lines) and the excitation temperature (about
8000 K, using the absolute radiance from the argon lines).
In 1973 (78, 79), during a study of electrodeless-discharge
lamps (EDL), they found that the EDL temperature was very
important for the intensity output, and concluded that
the atmomization is thermal in nature.
They presented a
very complete study of microwave electrodeless discharges
20
in 1975 (13) .
Their comparison of the electron temperature,
T , and the gas' temperature (as approximated by the line
reversal temperature, T , of thalium line at 535.0 nm)
showed the non-LTE behavior of the discharge; i.e.,
Te > Tr
at least one order of magnitude.
Busch and Vickers (80) have also performed a sys­
tematic study of low-pressure microwaved-induced plasmas.
Again, the comparison of the spectroscopic (or excitation)
temperature and the electron temperature show that LTE
does not exist for such systems.
The lack of local thermodynamic equilibrium in
low-pressure MIP seems to be well accepted in the litera­
ture (16, 24), although the concept of "partial LTE" has
been used (2), which would seem to be confusing at best.
The actual means ofexcitation isstill not
resolved,
and has been examined by three groupsof workers.
The first model proposed (other than thermal equi­
librium) was the radiative ionization recombination (RIR)
model.
This model was originally proposed by Schulter
and applied to the MIP by Busch and Vickers (80).
This
theory allows that an equilibrium between ionization and
radiative recombination exists; i.e.,
k.
M + e” —
M
+
+ e
kn
M
+ e”
+ e“
M* + hvcon t .nuun
M* -£->■ M + hv
(1.5)
(1.6)
(1.7)
21
There are two distinct groups of electrons, a lowdensity, high-energy group that causes ionization, and a
high-density, low-energy group that undergoes recombina­
tion.
This theory has been further analyzed by Brassem
and Maessen (81,82), and Brassem, Maessen, and DeGalan
(83, 84), who evaluated the rate constants of Reactions
1.5 and 1.6 for the hydrogen atom from theoretical expres­
sions (k. = 4.0 x 10"9, k O 3^) = 1.5 x 10-13, k (41S)
1
P
P
= 6.1 x 10 3'^, and Ek = 1.2 x 10 3 cm3/sec).
The RIR model was used to predict the intensities
from excited-hydrogen levels (in a 1% H2/Ar and a 1%
H2/He discharge) and compared to the predicted values
assuming thermal excitation, which were both compared to
experimental data (84).
The RIR model was much more
successful than the thermal model (which was eight orders
of magnitude too low), but still underestimated the abso­
lute intensities by two orders of magnitude.
The authors
found no simple way to correct for this discrepancy, but
suggest the role of the metastable noble gas atoms may
be important.
Beenakker (85) examined the excitation processes in
a helium MIP at atmospheric pressure sustained in the
cavity of his design (74).
All the ion lines observed
originated from ionic levels within a limited range of
excitation energies (12.3 to 15.9 eV), yet numerous levels
are known just above and below this range and could have
been detected.
This eliminates the excitation by
22
electron impact since the electrons are known to have a
continuous range of energies.
He finds the most likely
mechanism to be
e“ + X — >• X+ + e“ + e"
(1.8)
He„ + X — ► X+ + He + e"
m
(1.9)
He 2
m
-I+ X —
+*
X
+ He + He
(1.10)
X+* — »- X+ + hv
(1.11)
X+ + e“ — ► X* + hv continuum
..
(1.12)
'
'
X* — ► X + hv
(1.13)
The atom is ionized by electronimpact (1.8) or Penning
ionization (1.9) .
The ion may be excited through collision
with a metastable helium molecule (I.10) and then emit its
characteristic frequency (1.11), or the ion may recombine
with an electron to form an excited atomic species (1.12),
and then radiatively relax to a lower state (1.13),
depending on the nature of species X.
A similar mechanism has been suggested by Houpt (86):
M + He2* (ca. 17.5 eV) —
M+ + 2He + e“
(1.14)
M + He2+ (ca. 21.5 eV) — >
M+ + 2 He
(1.15)
M + He* (19.8eV) — * M+ +
He + e~
(1.16)
M+ + e
M* —
(slow) — ► M*
M + hv
(1.17)
(1.18)
23
where (1.14) and (1.15) dominate at high pressures (730
torr) and (1.16) is important at low pressures.
These
models offer a theoretical basis to improve the intensity
of the MIP; i.e., at higher pressures the concentration
of helium molecules increases and the electron energy
decreases.
The Beenakker mechanism qualitatively explains
the species observed in the helium atmospheric MIP, but
has not been tested quantitatively.
When applied to an
argon atmospheric MIP, direct excitation by electron
impact could not be eliminated.
This model should be
considered "still speculative" (84), and cannot apply
to the discharges studied in this work.
The third approach proposes a general steady-state
kinetic theory as suggested by Lampe, Risby, and Serravallo
(87).
This LRS model attributes all excitation to colli­
sions with high energy electrons and has been referred
to as the corona-model (84).
The relevant reactions
in a low-pressure helium discharge would be
_
He + e
*
— *- He
_
+ e
(1.19)
He* + He — > He2+ + e”
(1.20)
He* — >- He + hv
(1.21)
The excited states of helium are formed through electron
impact (1.19) and are destroyed through homonuclear
association (1.20) or through radiative decay (1.21).
24
Although Maessen rejects this approach since the
electron density is too high for this model, he also
states that this approach gives results closer to the
experimental data than his RIR model (84) .
The purpose
of this work is to critically compare the theoretical
results of the LRS model with the experimental data and
to advance any possible improvements.
4.
Comparison of hf Discharges
Any comparison of these hf discharges is difficult
since often there are different apparatus types and con­
ditions used by various authors and since most authors
present their results with much optimism.
Tschopel (16)
compared the three techniques as excitation sources;
his table is reproduced in Table 1.1.
The MIP has the lowest cost, requires the lowest
power, and consumes the least gas, but is more susceptible
to interferences than the ICP, and is not as good an
excitation source in general, but is better than the CMP.
The cavity design of Beenakker (74) may improve the
evaluation of the MIP.
The ICP is best suited for the
routine analysis (28) .
It exhibits very little inter­
ference and allows very efficient sample introduction.
Its many reported uses in the literature indicates its
widespread acceptance.
In direct comparisons of the
CMP with the ICP, the ICP was found to be greatly
preferable (88, 89).
The detective limits of the MIP are
25
TABLE 1.1
Comparison of the Inductively-Coupled Plasma, the Capacitively-Coupled Microwave Plasma, the Microwave-Induced
Plasma, and the Direct Current Plasma as Excitation
Sources (16).
ICP
CMP
MIP
DCP
Instrumental complexity
+-
+
++
+
Running costs
-
+
++
'+
Efficiency; overall
evaluation
++
+
+-
+-
Powers of detection
++
+
++
+-
Total susceptibility
to interference
++
+
-
-
Matrix effects
++
+-
-
+-
Stable compound formation
++
+
-
+
Ionization interference
++
-
-
-
Electrode material
++
+-
+
-
Efficiency of sample
introduction
++
+-
+
-
Possibility of simultaneous
multi-element analysis
++
++
+-
++
Operation
+-
+
+
+—
Evaluation: Compared with the other excitation sources,
the source under consideration is ++, very good; +, good;
+-, neither good nor bad; -, bad.
26
comparable with the ICP, except for elements with
sensitive ionic lines (90).
The mechanisms of excitation in these discharges
are clearly not understood.
The general concept of
thermal equilibrium is no longer assumed by most workers.
Although it is possible that different mechanisms may
operate in the different discharges, it is possible that
these mechanisms are the same (91) . The kinetic steadystate model studied in this work should be applicable
to any hf discharge.
27
CHAPTER II
EXPERIMENTAL
The microwave discharge was originally intended as
a detector for a gas-chromatograph (69) so the system
was designed for continuous-flow.
A schematic diagram
of the system for the optical study is shown in Figure
II.1.
The microwave discharge was generated in a quarterwave Evanson (60) discharge cavity (Opthos Instrument
Company/ Rockville, Maryland), which was equipped with
two tuning stubs to allow the standing-wave ratio (SWR)
to be adjusted to a value not greater than 1.1 (SWR =
1.0 when the reverse power equals zero).
The power was
delivered by a Raytheon Microwave Power Generator which
was capable of providing between zero and 100 watts of
power at 2450 MHz.
The power and SWR were measured by
a Bendix MicroMatch (Model 725.4) .
The power was adjusted
to 75 watts in all experiments, after it was found that
further increases in power did not significantly increase
the intensity of the spectral emission.
was initiated using a Tesla coil.
The discharge
gas supplies with flow controllers
N:
fine control needle valves
C:
microwave cavity
D:
discharge cell
G:
microwave generator
L:
lens
M:
monochromator
A:
photomultiplier, power supply, and
amplifier
R:
recorder
Me:
McLeod gauge
P : absolute pressure gauge
Figure II.1.
Flow System for Emission Spectra Study.
29
Doping Gas
Helium
Me
To Vacuum
Figure II.1.
Flow System for Emission Spectra Study.
30
to generator
Removable Cap
(Actual Size)
tuning
stub
tuning stub
O
Air
Hose
Connection
Figure II.2.
Removable
Cap
The Evanson Microwave Cavity and Removable
Cap.
31
The flow rates of the gases were controlled by fineneedle valves (Hoke, No. 1315G4B).
The gases were obtained
commercially and were used without further purification.
The discharge cell, shown in Figure II.2, was constructed
from quartz, 1.3 cm od.
A cross was cut in the front of
the discharge cavity to aid in the placement of the lens
by focusing the discharge onto the slits of the mono­
chromator.
Specifications of the monochromator (Varian,
Model AA-4, Techtron Pty. Ltd., Melbourne, Australia)
are listed in Table II.1.
The radiation emitted was
detected by a photomultiplier tube (Hamamatsu, R466)
and the current was amplified (DC amplifier, Keithley
'600B Electrometer) and displayed on a strip chart
recorder (Varian A-25).
The system was maintained under reduced pressure
with a backing pump (Pressovac, Model 90550, Cenco
Instruments Company) and an oil diffusion pump (2 inch,
Cenco).
The pressure was measured with an absolute
pressure gauge (Model FA 160, Wallace and Tierman,
Belleville, New Jersey) and a McLeod gauge (Model 10-124,
VirTis Company, Inc., Gardiner, New York).
Emissions
not due to helium were never completely eliminated,
although the system was virtually leak-free, as measured
by the McLeod gauge (less than 5 mtorr).
The monochromator and detection system were cali­
brated in terms of spectral response with a tungstenfilament lamp (General Electric, 30A/T24/1)
(see
32
TABLE II.1
Specifications of the
Varian AA-4 Monochromator (69)
dispersing system:
focal length:
operative:
grating 50 mm x 50 mm, 638 lines/mm,
Ebert mounting
500 mm
f/10
spectral range:
186 - 1000 nm
wavelength accuracy:
+ 0.1 nm
wavelength reproducibility:
stray light:
slits:
+ 0.1 nm
0.2% at 200 nm
kinematic, coupled, opening to 300 ym
(band pass, 0.99 nm)
reciprocal dispersion:
resolving power:
3.3 nm/mm
32,000 (theoretical)
33
1
o
Lamp
Variable
Resistor
f
Standard
Resistor
t
(NDigital
Nanovoltraeter
I N I
Voltmeter
DC Power Supply
Figure II.3.
Diagram of Electronics Associated
With Intensity Calibration.
34
Chapter III).
This was accomplished by placing the lamp
such that its filament was located at the same spot as
the center of the discharge.
The electronics associated
with the lamp are shown in Figure II.3.
The lamp, when
operated at a constant current, produces a spectrum
similar to that of a blackbody source at a given tempera­
ture (measurements determined by the National Bureau
of Standards).
The current was determined by measuring
the voltage drop across a precision resistor (0.001 ohm,
temperature kept at 25.0° C with an oil bath).
The
determination of the spectral response was performed at
two currents (i.e., at two blackbody temperatures) and
the agreement was within 5%.
One difficulty encountered in this calibration was
evaluating the effect that the quartz tube had on the
radiation emitted by the discharge contained in the tube,
i.e., while both sources were encompassed by approximately
the same grade and thickness of quartz, the radiation from
the lamp passed through an optically flat window, while
the discharge radiation passed through a curved section
of tubing.
This problem became worse as the inside of
the discharge cell was etched by the reactive species.
This problem was partially overcome by moving the discharge
cell within the microwave cavity whenever the etching
became noticeable to the operator.
A schematic of the apparatus used in the electro­
static probe study is shown in Figure II.4.
The probes
Probes
Recorder
Variable Voltage
DC Voltmeter
Figure II.4.
Double-Probe Circuit.
36
were made of platinum wire, 0.5 mm in diameter, spaced
1.0 mm apart which were held in a glass sheath, 13 mm
from the center of the discharge.
The applied voltage
was supplied by a variable voltage supply (Heath Voltage
Reference Source) and was measured by a voltmeter
(Keithly Instruments, 160 Digital Multimeter).
The
voltage was varied between zero and 100 volts.
The
current was determined by measuring the voltage drop
across a standard resistance (448 ohm) with the recorder
in parallel.
Typical currents ranging 0 and 0.3 mA,
corresponding to about 200 mV at maximum were obtained
in this study.
The surface of the probes were prone to contami­
nation from the doping gases and had to be periodically
cleaned.
This became very noticeable when the probe
study of the pure molecular gases was attempted.
The
probe characteristics changed so rapidly that the study
could not be done.
Also, attempts to place the probes
exactly in the center of the discharge resulted in the
glass sheath melting; therefore the probes were always
placed at the edge of the cavity.
37
CHAPTER III
POPULATION DENSITIES
OF THE HELIUM EXCITED STATES
A.
Introduction
The intensities of the emissions from excited-
helium atoms in a microwave discharge were measured and
related to the relative number densities of the helium
excited states.
These populations were subsequently
studied by changing the helium pressure and by adding
molecular gases.
The radiative deactivation of excited-
helium atoms occur in the visible or near ultraviolet
regions and can be studied easily; however, transitions
1
3
from the lowest excited states (2 S and 2 S) to the
ground state (l^S) result in radiation in the vacuum
UV region (60.1 nm), and therefore the number densities
of these states were not determined.
B.
Emission Spectra of the Helium Discharge
The emission spectra of the low-pressure (0.5 to
5.0 torr) helium discharges were recorded as discussed
in Chapter II.
The spectrum of the helium discharge
at 1.0 torr is shown in Figure III.l.
The lines corres­
ponding to the He(I) transitions were identified from
800
I
700
1
600
I
500
I
400
I
300
Wavelength (nm)
Figure III.l.
Emission Spectrum of Helium Discharge
at 1.0 Torr.
39
standard references (92, 93).
Also present were lines
from transitions of H(I), N 2 (second positive system),
and N2+ (first negative system)
(94).
These bands are
due to leaks in the system and/or impurities in the
helium.
Increasing the pressure did not have any qualita­
tive effect on the spectra, but the intensities of the
lines did decrease as the pressure was increased.
The
amount of decrease was dependent, in general, on the
energy level of the initial state.
This is further
discussed in Section C.
The addition of the molecular gases (doping gases)
to the discharge caused the size and intensity of the
glow to decrease and greatly reduced the intensities of
the helium lines.
Additional lines in the spectra were
identified as due to the added species (Figures III.2,
III.3, III.4, and III.5).
The spectra of the doped
discharges were compared to the spectra produced from
discharges of only molecular gases; the non-helium lines
in these spectra were very similar in relative intensity
(within 10%).
This indicates the excitation mechanism in
both discharges is the same, i.e., collisions with ener­
getic electrons.
The data obtained from the oxygen-doped
helium discharges and the oxygen discharge are listed
in Table III.l.
40
8 Q0
700
600
500
400
Wavelength (nm)
Figure III.2.
Emission Spectrum of 2% HydrogenDoped Helium Discharge at 1.0 Torr.
300
41
800
700
600
500
400
Wavelength (nm)
Figure III.3.
Emission Spectrum of 1% Nitrogen-Doped
Helium Discharge at 1.0 Torr.
300
42
I
800
I
700
I
600
I
500
I
400
Wavelength (nm)
Figure III.4.
Emission Spectrum of 1% Nitrous OxideDoped Helium Discharge at 1.0 Torr.
3I 0
43
800
700
600
500
400
300
Wavelength (nm)
Figure III.5.
Emission Spectrum of 1% Oxygen-Doped
Helium Discharge at 1.0 Torr.
44
TABLE III.l
Atomic Oxygen Lines Observed in Reduced Pressure OxygenDoped Helium Discharge in the 800 to 300 nm Region3
X
(nm)
Transition*3
Energy of
Upper Level
(eV)
778
3s5 S-3p5P
10.74
726
3p3P-5s3S
12.70
715
Ss^D-Sp^D
14.46
700
3p3P-4d3D
12.76
645
H (I) 2p2 P-3d2D
5
5
3p P-5s S
616
3p5 P-4d5D
12.75
13.04
544
3p3P-6s3S
5
5
3p P- 6 s S
533
3p5P-5d5D
13.06
436
3s3 S-4p3P
12.36
394
3s5 S-4p5P
12.28
(656)
605
(12.09) •
12.66
13.02
aAlso observed were He (I) lines and molecular bands of
3 +
3 0- (First Herzberg System, A E - X E , and the Schumann3 - 3 "
o
Runge System, B E - X E ), and of OH (3064 A System,
9
A Z
+
2
- X IK)
^Reference 92
(94)
^
45
C.
Population Densities
The number of atoms in a particular excited state
can be determined from the intensity of the discharge
using theoretical relationships.
Although absolute
number densities cannot be determined, relative values can
be.
The changes of these values as the helium pressure
is varied, and as doping gases are added, are discussed.
1.
Theory
The population density of atoms, n^, in the excited
state j, is related to the intensity of the radiant power
emitted when the atoms radiatively deactivate to a lower
state by the Einstein equation (2)
P-» = hv n. A..
where P^ (erg/cm
3
(III.l)
sec) is the power of the emitted
radiation at wavelength X, v (cm“^) is the frequency
of the emitted radiation (v = c/\), and Aj^ (sec 1) is
the probability of transition (spontaneous emission) from
state j to state i.
The signal,
(amps), measured by
the picoameter is related to the output power by
= Px AV Rx
(III.2)
where AV is volume of the discharge examined and R
the response factor of thedetection system
the population densities of
at X .
theexcited states
A
is
Thus
can be
determined from the measured intensities of the emission
lines,
46
nj - h V AS" AV R,
if the value of
(III-3)
is knovm.
The value of the response factor will vary with the
orientation of the source with respect to the monochro­
mator and will vary with the wavelength due to the optics
of the monochromator and the surface characteristics of the
photocathode in the photomultiplier tube.
To evaluate
over the region of interest (300-750 nm), a radiation
source with a known output was used.
The monochromator
and detection system were, calibrated with a standard
tungsten-filament lamp, which had been previously compared
to a blackbody
source (Table III.2) .
The spectral radiant intensity I^T (power per unit
area) of the surface of an opaque body, such as a tungsten
filament, at temperature T , at wavelength X , in a
direction normal to the surface is defined by
* SXT PXT
(III'4)
g
where
is the spectral radiant emittance (power per
unit volume) of a blackbody at temperature T, and e^T
is a factor, varying from 0 to 1 , called the normal
spectral emissivity, or simply the exiiissivity.
The
emissivity of tungsten has been carefully studied and
the values measured by deVos (95) have been used.
The
filament temperature T , is related to the blackbody
n
temperature, T, by Wein's equation,
47
TABLE III.2
Blackbody and Filament Temperatures
for Standard Tungsten-Filament Lampa
(K)
Filament ^
Temperature
(K)
13.06
1200
1260
15.43
1400
1480
18.53
1600
1710
23.34
1850
1990
30.00
2130
2320
Current
(amperes)
Blackbody
Temperature
a0riginal calibration by Martha Wood of General Electric
Company on March 9, 1964.
^From Equation 111 .5,
0.4324 (95).
withX' = 665 nm and e
00:3
48
^ - -f- - .Tsr ln V t
t111-5’
where X' = 665 nm (Table III.2).
The spectral radiant emittance of a blackbody is
given by Planck's formula (96).
PB
=
XT
2h c V 5
[exp (hc/XkT) -1]
.
uu,6)
The signal from the tungsten lamp,
1111'7)
w
will depend on the area of the tungsten filament, AA ,
SX ~
eXT PXT AA" EX
and the monochromator response, R^. The relative values
B
W
of
and SX are s^own in FigureIII.6 .
By keeping the orientation and distance of the
tungsten filament to the monochromator the same as the
discharge, the values of R^ in Equations III.2 and III.7
are equal; i.e., the ratio of the experimental response to
the theoretical emittance of the discharge, is equal to
the ratio of the experimental response to
the theoretical
intensity of the tungsten lamp,
S
SW
^ T ^ ' e
A
P * AAW
at
( H I - 8)
*a t
The value of n^ can be determined from Equations III.l
and III.8 ,
_
.
AAW
nj - AV“hc
—
* eXTPAT
W~
SX ji
S,
X
,
(III.9)
I
900
I
800
Figure III.6 .
7^00
600
500
400
300
200
Relative Values of the Emissitivity of Tungsten, the
Theoretical Spectral Radiant Emittance of a Blackbody,
and the Recorded Signal from the Standard Tungsten
Lamp at 1850 K.
VO
50
TABLE III.3
Spectroscopic Data for He(I) Transitions'
p®
.W
AT
Ajl.
(sec ■*■)
x 1 0 10
x lO" 4 - 5
x 106
0.4251
0.4532
0.4615
0.4664
28.12
2.162
0.5738
0.2742
129
125
48.5
29.0
18.8
6.60
3.12
1.76
706.5
471.3
412.0
386.7
0.4276
0.4576
0.4673
0.4719
24.12
1.101
0.2372
0.1032
202
83.0
25.5
14.8
27.5
9.26
4.33
2.40
501.6
396.5
361.3
344.8
0.4536
0.4701
0.476,6
0.4796
2.037
0.1441
0.03890
0.01877
125
18.5
8.5
6.3
13.4
6.81
3.85
2.56
388.9
318.8
0.4715
0.4843
0.1111
0.005017
14.8
5.0
9.28
5.67
667.8
492.2
438.8
414.4
0.4321
0.4549
0.4500
0.4669
587.6
447.1
402.6
382.0
370.5
363.4
0.4414
0.4609
0.4690
0.4728
0.4749
0.4762
± 0.0002
728.1
504.8
443.8
416.9
aTB = 1850 K
Reference 92
'Reference 95
1
Equation 3.6
'Reference 93
(erg/cm
3
(ampere)
cAT
A"
(nm)
sec)
17.66
1.701
0.5046
0.2543
7.626
0.6250
0.1764
0.08682
0.05627
0.04236
210
108
45.0
25.5
230
53.5
20.0
12.8
10.0
8.5
65.1
19.3
8.89
4.94
71.7
24.4
11.9
5.87
4.53
3.03
51
and will depend on a set of constants (first term), values
that are determined by the wavelength and transition
studied (second term), and the discharge intensity,
.
B
W
The values of X, e^T , I^T ,
, and A ^ for the helium
transitions are listed in Table III.3.
Both the tungsten filament and the helium discharge
could be considered point sources (87), but this does
not consider the importance of the size of the discharge.
For this study, the ratio of the discharge volume to
the filament area was assumed to be the diameter of the
discharge tube, L (1.0 cm),
L =
(III.10)
AA
and the emission of radiation is assumed to be uniform
over this length.
This simplification is necessary to
allow the comparison of the intensity of the filament
(power/unit area) to the emittance of the discharge
(power/unit volume).
2.
Results
The number densities of the excited states of
helium obtained using Equation III.9 are shown in
Table III.4.
Obviously, these values cannot be correct
since the population densities of some states (e.g.,
1
16
“"3
n (3 D) = 3.9 x 10
cm ) are greater than the. ground
16
—3
state density (n(He) = 2.4 x 10
cm
at 1.0 torr and
400 K).
A discrepancy of this type was expected (97),
52
TABLE III.4
Excitation Thresholds, Degeneracies, and Population
Densities of Excited States of Helium at 1.0 Torr
.
03
(eV)
£
state
1
3
4
5
6
9.98
1.29
0.271
0.0739
10.3
1.17
0.233
0.0618
6
23.09
23.74
24.05
24.21
19.3
2.04
0.300
0.0554
6.43
0.679
0.100
0.0184
3
4
23.01
23.71
39.1
0.732
4.34
0.183
3
4
5
23.07
23.72
24.04
24.21
17.2
4.14
0.940
0.301
3.44
0.828
0.188
0.0602
23.06
23.72
24.04
24.21
24.31
24.37
39.2
9.69
2.62
0.646
0.148
0.0401
0.0114
0.0043
3
4
5
6
D
9.98
1.29
0.271
0.0739
(cm-3)
15
x 10
30.8
3.51
0.700
0.185
6
15
x 1 0 15
Hj/g
22.71
23.58
23.97
24.17
3
4
5
D
22.91
23.66
24.00
24.18
n.
3
(cm-3)
3
4
5
6
7
8
2.22
0.601
0.172
0.0645
53
but not at this magnitude.
The following discussion
examines the possible causes of this discrepency.
The assumption that the discharge is uniform has •
already been mentioned, and has been assumed by other
workers (84) . Winefordner, et al. (77) , found the
intensity of the argon lines in an argon discharge was
greatest at the discharge center and decreased rapidly
to zero at the discharge walls.
This has the effect of
decreasing the value of L, the discharge diameter, which
would increase the values of n. above those in Table III.4.
3
The assumption that the discharge is radiatively thin,
i.e., that self-absorption is minimal, is valid for the
population densities studied (98) , but any absorption
would cause the actual values of n^ to be greater than
those calculated in Table III.4.
The values of the emissitivity of tungsten were
taken from deVos (95), who studied a lamp similar to
that used in this study.
The emissitivity of the fila­
ments, however, cannot be assumed to be the same.
The
spectral characteristics of a surface are dependent on
many factors, such as impurities and texture, which are
not constant for all tungsten samples.
The lamp used
had been used intermittently over 15 years and should
be affected by this use.
The relative values of the
emissitivity should be the same as determined by deVos,
however, since any effect would not depend on X (97).
54
The absorption and/or diffraction by the discharge
walls were originally thought to be important, since
the discharge constantly sputters and deposits onto
these walls.
Memory effects have been noticed by other
workers who studied other compounds (77); however, for
pure noble gas discharges, no effects have been detected
(61).
Also, effects from stray light are negligible in
the visible and ultraviolet regions (69).
The assumption that
was the same for the tungsten
lamp and the discharge, depends on the geometrical
relation between the monochromator and the spectral
sources to be identical.
Again, problems are encountered
when comparing a flat surface to a volume; but by placing
the filament at the position of the discharge center,
this was accomplished, at least approximately.
Any
variance in aligning the tungsten filament exactly normal
to the monochromator could drastically reduce the values
W
^
of
, but would be independent of wavelength.
The assumption that the discharge radiation is
monochromatic is not accurate, but the widths of the
spectral lines are much less than the measuring band
width (0.1 nm).
Under the conditions of the discharge,
pressure broadening is probably the dominant effect (98).
The origin of the width is the energy spread in the
uncertainty principle.
AE • At — -Jjp
(III.11)
55
where the value of At can be approximated by the life­
time of the excited species.
The line width can be
approximated as
“ - swrst
(III-12>
and will depend on the inverse of the excited-state life­
time.
Most of the states studied will have lifetimes on
the order of 10
—8
second (see Chapter V), and therefore
-12
a line width about 10
cm.
Although the preceding discussion indicates the
causes for the unreliability of the absolute number
densities, it does not preclude the determination of the
relative values.
All the factors discussed should be
wavelength independent (except possibly AX), and there­
fore will affect all intensities uniformly.
The relative number densities of the helium-excited
states are listed in Table III.5.
The uncertainties
of these values are from the experimentally measured
W
values of
and
. The uncertainty of
was assumed
to be 1 % of full scale, and the uncertainty of
-9
assumed to be 0.50 x 10
amp, the minimum value
w
was
measured.
A Boltzman plot, i.e., In n^/g vs. energy of state
j is shown for the excited states in Figure III.7.
3
Although the 3 D population is the largest, its degeneracy,
15, is also the largest, and its population to degeneracy
TABLE III.5
Relative Number Densities of
Observed Excited States of Helium
Pressure (torr)
0.5
1.0
2.0
4.4
0.327
0.0298
0.00555
0.00141
0.327
0.0275
0.00496
0.00126
0.237
0.0181
0.00328
0.00081
0.167
0.0114
0.00205
0.00051
0.929
0.0744
0.0126
0.00330
0.972
0.0689
0.0118
0.00292
0.794
0.0487
0.00749
0.00190
0.628
0.0317
0.00470
0.00118
6
0.374
0.0334
0.00464
0.00084
0.409
0.0330
• 0.00441
0.00077
0.298
0.0225
0.00287
0.00050
0.204
0.0145
0.00178
0.00030
P
3
4
0.599
0.00955
0.623
0.00937
0.479
0.00672
0.350
0.00445
ln
D
3
4
5
0.438
0.0844
0.0182
0.00564
0.478
0.0848
0.0171
0.00513
0.426
0.0609
0.0116
0.00343
0.323
0.0402
0.00718
1.000
8
0.00110
0.887
0.136
0.0257
0.00691
0.00165
0.00062
' 0.717
0.0922
0.0162
0.00420
7
0.879
0.178
0.0398
0.0116
0.00289
3
4
5
6
3q
S
3
4
5
6
lp
P
3
4
5
6
3
4
3n
D
5
6
0.181
0.0369
0.00936
0.00259
0.00095
0 .00211
0.0 0 1 0 1
0.00037
Relative
Population
Density
n./g.
10 °
10
10
-2
-3
22.5
23.0
Figure III.7.
23.5
Energy (eV)
24.0
24.5
Boltzman Plot of the Experimental Excited-State Population
Densities at 1.0 Torr.
U1
58
ratio is the lowest of the n = 3 states.
The difference
in the n = 3 to the n = 4 states is quite drastic’ for the
S and’P families, but not for the D families.
This indi­
cates a deactivation mechanism available for the other
states that is not available for the 3^S, 3^S, 3^P, and
3
. . .
3 P states. This immediately suggests the homonuclear
associative ionization,
He* + He — p- He2+ + e"
(III. 13)
which is important for states with energy levels above
23.1 eV (99).
The ratios of the populations of the
n = 3 state to the n = 4 state for the six families are
listed in Table III.6 .
3.
Effect of Pressure Change on Number Density
The effects of changing the helium pressure on
the excited state number densities are shown in Figure
III .8 for the
states.
The other states show a similar
decrease in population as the pressure is increased.
As can be seen, the rate of decrease increases with the
principal quantum number, i.e.,
-dn (3^S) . -dn(41 S) „ -dn (5LS) , -dn(6 LS)
dP
dP
dP
dP
The major cause of this decrease is the lower average
electron energy as pressure is increased (discussed in
Chapter IV).
The higher excited states decreasing more
rapidly as the pressure is increased than the lower
59
TABLE III .6
Population Ratios of the
n = 3 and n = 4 States of Helium
Pressure (torr)
0.5
1.0
2.0
4.4
31 S/41S
11.0
11.9
13.1
14.7
33 S/43S
12.5
14.1
16.3
19.8
31P/41P
11.2
12.4
13.2
14.1
33P/43P
62.8
66.5
71.3
78.7
31 D/41D
5.2
5.0
7.0
8.0
33 D/43D
4.9
5.5
6.5
7.8
60
1.1
1.0
on
Population
0.8
0.7
Relative
Density
n./[n.
0.9
0.6
0.5
0
1.0
Figure III.8 .
2.0
3.0
4.0
Relative Population Densities
of
States in the Pressure
Range 0.4 to 4.4 Torr.
61
TABLE III.7
Ratios of the Population Densities at
Two Pressures (torr) for the Excited States of Helium
rorrm vo
1.00
1.08
1.12
1.18
1.38
1.52
1.52
1.55
1.42
1.59
1.60
1.58.
n ^ in vo
0.96
1.08
1.07
1.13
1.22
1.41
1.58
1.54
1.26
1.54
1.59
1.61
n ^ in v o
0.91
1.02
1.05
1.09
1.37
1.47
1.53
1.54
1.46
1.55
1.61
1.65
ro ^
0.96
1.02
1.30
1.39
1.36
1.51
m ^ in vo
0.92
0.98
1.07
1.10
1.06
1.41
1.47
1.50
1.32
1.51
1.62
1.63
ro '3* in vo r~ co
0.88
0.98
1.08
1.23
1.16
1.15
1.13
1.33
1.44
1.35
1.57
1.52
1.24
1.48
1.59
1.65
1.62
1.59
•
62
excited states again indicates that homonuclear asso­
ciative ionization is important in the discharge.
The
ratios of the number densities at 2.0 torr to the number
densities at 1.0 torr are listed in Table III.7.
4.
Effect of Doping Gases on Number Density
As previously mentioned, the addition of 1 to 5%
of a molecular gas greatly reduced the intensity of the
discharge and, therefore, the populations of the excited
states.
Different gases— nitrogen, oxygen, hydrogen, and
nitrous oxide— were added, but all had about the same
effect.
Addition of 1% of the molecular gas caused the
number densities to decrease by a factor'of 10 for
nitrogen, oxygen, and nitrous oxide; and a factor of
5 for hydrogen.
This decrease was caused primarily by
the lower average electron energy (Chapter IV), but the
amount of decrease was greatest for the n = 3 states and
less for the higher states. This is illustrated for the
3
D family in Figure III.9 for the addition of 2% hydrogen.
This is indicative of the Penning ionization reaction,
He* + H 2 —
He + H 2 + e”
(III. 15)
which is known to occur for all excited states of helium.
The effect of this reaction is relatively greater for the lower
excited states since the upper excited states are more
affected by associative ionization, Reaction III. 14.
63
10
Pure Helium
-1
10
Relative
Population
Density,
10
10
-2
-3.
23.0
23.5
24.0
24.5
Energy (eV)
Figure III.9.
3
Relative Population Density of the D
States in the Hydrogen-Doped Helium
Discharge.
64
CHAPTER IV
ELECTRON ENERGY AND DENSITY
A.
Introduction
The mechanisms of fragmentation and excitation in
a
microwave-induced discharge can be related to the
average electron energy, (e), and the electron number
density, ng .
The distribution of electron energies
may be approximated by a Maxwellian distribution (87,
100) .
fM (e) = — (e) ” 3/2
M .
/fr
e1/2 exp
(-
4 e/(e))
-
(IV.1)
“2
but is represented more accurately by the Druyvesteyn
distribution (87, 100, 101).
f (e) = (|)3/2—
u
*
(e)“ 3/2 e1/2exp (-.55 e2/(e)2) (IV.2)
/n
This distribution does not provide an exact solution
unless the electric field strength is sufficiently low
to assume that inelastic collisions can be neglected,
which is rarely valid (1 0 0 ), but it does provide an
approximate solution.
Busch and Vickers (80), Brassem and Maessen (81,
82), and Brassem, Maessen and DeGalan (83, 84) have found
65
that the radiative ionization recombination (RIR) model
requires the postulations of two distinct groups of
electrons, a low-density high-energy group, and a
high-density low-energy group.
By using an experimental .
system similar to that used in this study, they were able
to determine the average energy of the former group and
the number density of the latter.
The other two para­
meters could only be estimated (84) , which is a serious
limitation to the RIR model.
The average energy and the population density of the
electrons in the discharge were determined by an electric
probe technique.
There exist two basic methods (102):
the single probe method (SPM) and the double probe
method (DPM).
Both methods consist of inserting one
(SPM) or two (DPM) small metallic electrodes into the
discharge.
These electrodes are attached to a variable
voltage supply and the current is measured as a function
of the applied potential.
The discharge ground becomes
the return electrode in the SPM.
The values of (e) and
nQ are determined from the current-potential relationship.
The SPM, first used by Langmuir in 1924 (103), may draw
a significant current from the discharge and perturb the
conditions it measures.
Therefore, the DPM was introduced
by Johnson and Malter in 1950 (104) since it withdraws
very little net current and exerts a negligible influence
on the discharge.
study.
The latter technique was used in this
66
B.
Theory and Results
The experimental design of the DPM has been des­
cribed in Chapter II, and it is shown schematically
in Figure IV.1.
The voltages
and V 2 indicate the
difference in potential between the surrounding discharge
and the probes P^ and P2, respectively.
The value of
Vc represents any potential difference between the dis­
charge surrounding P.^ and the discharge surrounding P2 By definition, the net current must equal zero,
therefore, the sum of the positive ion currents (i^
and
i ) must equal the sum of the electron currents (i..
p2
1
and i2) providing
i
+ i = i, + i,
= Zi
Pi
P2
1
2
that no negative ions exist.
represented by Ei.
(IV.3)
The total current is
The currents can be expressed in
the Boltzmann relationship (104),
i = A
j e~0V
(IV.4)
where A representsthe probe area, j represents the
random electron current density, and V represents the
voltage difference between the probe and the discharge.
The ratio of the electron charge, q, to the electron
temperature, Tg , is represented by 0 , i.e.,
0 = ^
(IV.5)
Since the average electron energy (e) is related to the
electron temperature TQ by
Sheath
Sheath
Probe 2
Probe 1
Area = A,
A.
1
Disonarge
Electron space current in discharge adjacent to
* Probe 1.
Electron space current in discharge adjacent to
h =
Probe 2.
Probe to discharge potential at Probe 1.
vi Probe to discharge potential at Probe 2.
V2 "
Potential difference between discharge adjacent
Vc =
to Probe 1 and Probe 2.
= Differential voltage applied between Probe 1 and
Probe 2.
31
Figure IV.1.
General Potential Diagram for the DoubleProbe Method.
68
Te = ^ ( e )
(IV. 6 )
0 is related to (e) by Equation IV.7.
0 = | q (e)"1
(IV. 7)
The sum of the currents can be expressed in terms of
the Boltzmann relation,
Ei = A 1 j^e ^1V1
+
^2^2e
2
(IV.8 )
The voltage difference applied between the probes, V^,
is equivalent to difference between the individual probe
voltages plus any voltage difference caused by any
inhomogenity in the discharge, V ; viz.,
Vd * VI ' V 2 +
Vc
(IV-9)
Combining Equation IV .8 and Equation IV.9 yields the
following equation:
In
Si
i2 1
= In A 2 ] 2 e?VC “t
tIt- V.
2 (e)
d
(IV. 10)
Since the first term on the right side of Equation
IV.10
contains only constants, the values of the probe areas,
electron random current densities, differences in plasma
potentials and the contact potentials do not affect the
magnitude of
(e)
.
It is assumed that the values of j do
not change with V or i, since with the DPM the net current
drain is so small.
Therefore Equation IV.10 can be rearranged to be
Equation IV.11,
69
Zi
12
A 131
exp
(IV.11)
[<0VC) + | -jfy Va]
+1
A 2D2
If the first derivative of this equation with respect
to
is taken and evaluated at
= 0 and rearranged
(i.e., i^ = 0 ), then the following equation is obtained:
(e) = | (G - G2)
"d V,
d i
Zi
(IV.12)
vd = 0
where
G =
Zi
Vd = 0
The graphical representation of this relationship is
shown in Figure IV.2.
Swift and Schwar (105) derived the following rela­
tionship for the determination of the positive ion
density, n+/ in the discharge:
Zi
n+
0.6 q A
(I
A - > 1/2
2 '(e)
where M is the mass of the positive ions.
(IV.13)
This equation
was derived for spherical probes, and is only approxi­
mately valid for this study since cylindrical probes
were used.
However, since electroneutrality exists,
the value of n+ will be proportional to Zi under any
conditions, and therefore relative values of n,T can be
obtained.
In the pure helium discharges, the positive
ion density is equal to the electron number density, nQ ,
70
i
Ei
Figure IV.2.
Voltage-Current Characteristic of
the Double-Probe Method.
71
and is approximately equal when the doping gases are
present, so the value of ng can be approximated by
Equation IV.13.
Lampe, Risby, and Serravallo (87), following Fite
(1 0 1 ), have suggested that the average electron energy
can be calculated from the discharge potential, assuming
the rate of energy loss of an electron in elastic
collisions with helium atoms can be equated to the power
delivered to the electron by the electric field.
The
power averaged over one cycle is represented by P:
•
1 ***1
P = y — r— — 5 * ? 0
- + 00 X
c
e
(IV.14)
where c is the mean speed of the electrons, Xg is the
mean free path of the electrons, m is the mass of the
electron, to is the frequency of the A C field, and E q
(volts/cm) is the field strength.
The energy loss per
collision averaged over one cycle is represented by AW:
AW = 2 |
2
9
W = g- (Sr
(IV.15)
If Equation IV.14 and Equation IV.15 are equated then
the following equation is obtained:
2
2
S T (S>
.
= 1
q 2 E2
X
2
- I "J 3 2.2
+ to X
c
'IV'16>
e
and this equation can be rearranged to provide a value
of (c)2 (to - 2 irv) ,
72
(c)2 = 2it2 v 2A 2
q2 E 2 M
o
ML +
1/2
) - 1
(IV.17)
The average electron energy can be found directly from
Equation 4.17:
(IV.18)
8A
m ir v
e
(Equation IV.18 corrects an error in Fite's derivation
(106)).
The application of this equation allows the
values of (e) to be measured experimentally providing
that the values of Le and E^
o can be determined.
The
mean free path of the electrons will depend on the helium
number density, n, and the cross section for the collision
between an electron and a helium atom, Qc>
The helium
number density is determined by the pressure and tempera­
ture of the discharge from the ideal gas law:
P
(IV.19)
The elastic-collision cross sections for electrons in
helium will depend on the electron energy, and have been
reported by Brown (12).
These values decrease almost
linearly from 5. sS2 at one electron volt to 2 .0 8 2 at
30 electron volts.
An average value of 4& 2 was assumed
The field strength of the discharge, Eq , was taken
from a report of Avni and Winefordner (13) who studied a
helium microwave discharge similar to that used in
73
this study.
The value decreased from 35 Vcm ^ at 1.0
torr to 10 Vcm.^ at 6.0 torr.
The voltage-current relation for the helium discharge
at 1.0 torr is shown in Figure IV.3.
The effects of
changing the pressure and adding doping gases are listed
in Table IV.1 and shown in Figures IV.4 and IV.5.
Also
shown are the theoretical values derived using Equation
IV.18.
2.0
The noise levels precluded measurements above
torr.
In this study the average electron energy reached
a maximum at pressures between 1.0 and 2.0 torr, although
the theory predicts that the value should increase as
the pressure is decreased.
The reason for this discre­
pancy is not clearly understood, but it may be the
increasing importance of the air leaks and/or impurities
in the helium discharge as the pressure is decreased.
Brassem and Maessen (81) found that the electron energy
increased almost linearly as the pressure was decreased
from 2.0 torr to 0.1 torr and obtained a maximum value
of about 13 eV (100,000 K).
They also found little
variation in the average electron energy when the micro­
wave power was increased from 50 W to 100 W.
Busch and
Vickers (80) found the ratio of the electron energies
between noble gas discharges was the same as the ratio
of the ionization potential of the discharge gases,
indicating the electron energy is primarily a function
A
i (amps)
X
i(T
5
20
V(volts)
-60
-40
20
40
20
-10
Ei
60
42.0 x 10
-5
amp
-20
30
Figure IV.3.
Experimental Voltage-Current Characteristic
of the Helium Discharge at 1.0 Torr.
TABLE IV.1
The Average Electron Energy and the Positive Ion Density
in the Discharge as Determined by the Double-Probe Method
n+
Helium
Pressure
(torr)
_3
(e)
(eV)
0.4
0.7
7.8
7.4
1.0
12.6
1.5
13.7
2.0
10.8
+ 1%
°2
1.0 + 2 %
°2
1.0 + 5%
7.2
1.85
2.08
1.73
1.73
1.75
4.7
0.69
+ 1 % n2
1.0 + 2 % n 2
1.0 + 5%
+ 2%
H2
1.0 + 3% h 2
1.0 + 5%
°2
1.0
N2
1.0
H2
•
5.1
1.19
0.69
00
1.0
(cm )
x 1012
1.59
5.1
1.24
5.3
1.06
6.1
1.48
5.5
1.41
5.2
1,18
76
(e), theoretic
-12
(cm
(e), experimen tal
x 10
12
Density, n
Ion
10
Positive
Average
Electron
Energy,
(e), (eV)
14
0
1.0
2.0
3.0
Helium Pressure (torr)
Figure IV.4.
The Average Electron Energy and the Positive
Ion Density in the Helium Discharge.
77
12 -
H2 : A , (e) ; A ,
n+
N2 : V
n+
•
1.8
/•\
v \
10 -
\
\
\
T \li
K
°2:
,(e);V ,
O , (e) ; 0 r n+
- 1.6
(eV)
e
o
(e)
CN
r-H
.1.4 S
1.2
Ion
-
Density
6 -
4 -
- 1.0
2 -
- 0.8
T
1
2
T
T
3
I
4
T
5
Doping Gas Added (Percent)
Figure IV.5.
The Average Electron Energy and Positive
Ion Density in Doped Helium Discharge •
Positive
Average
Electron
Energy,
8 -
78
of the ionization potentials, this conclusion could be
expected on the basis of electron impact ionization."
In this study the average electron energy was found
to decrease as the doping gases were introduced.
This
result can be explained by the increased number of non­
elastic collisions; e.g.,
e“ + 0 2 —
e" + 0 /
(IV.20)
which form vibrational and rotational excited states.
The cross sections for these reactions are known to be
much larger than the cross-sections for non-elastic
helium atom collision (107).
No relation was found
involving the amount of the doping as added, but this may
be due to the difficulty in controlling such small amounts
of the gases.
Brassem, et al. (83), found essentially
no change in the electron energy in a hydrogen-doped
helium discharge as the percentage of added hydrogen
was varied from 0 to 1 0 0 %; these results are in disagree­
ment with this work.
In general, they found the electron
energy to be approximately that of the pure noble gas
discharge up to a concentration of about 1 % of the added
gas.
Then the value decreased until at about 10%, when
the electron energy is about that of the pure added gas.
The electron density did not vary significantly in
the pure-helium discharge as the pressure was changed.
The maximum value of the electron density occurred at
the pressure corresponding to the lowest electron energy
value, but the reason for this is not known but has been
observed by other workers (81).
(Later attempts to
duplicate these results produced very different values
primarily due to corrosion of the electrodes.)
Brassem,
et al. (81), obtained similar results with a maximum
12
-3
number density, 3 x 10
cm , at 0.7 torr.
The addition of the doping gases was found to
decrease the electron densities by a factor of 2 or 3.
This is the result of the lower average electron energy
which results in fewer collisions having sufficient
energy to cause ionization.
The oxygen doping gas had
the greatest effect since it has the greatest electro­
negativity.
Braessem, et al. (83) , found the electron
density in the hydrogen-doped helium discharge did not
vary as the hydrogen concentration varied from 0 to 1 0 0 %;
these results are in disagreement with this work.
In
general, they found the opposite trend for electron
density as compared to electron energy:
little effect
below 1 % of the added gas, increase in electron density
between 1 and 1 0 %, and little change above 1 0 %.
It is of interest to examine the transition point
of 1% which has been reported by Brassem, et al. (83).
The maximum kinetic energy per elastic collision of the elec­
tron may be obtained (1 0 1 ) by the following equation:
80
If this equation is evaluated for an electric field of
35 V/cm then a maximum kinetic energy of 0.02 eV is
obtained.
Therefore if an electron is to obtain an
energy of 24.6 eV, it must undergo at least 1200 elastic
collisions.
Therefore, in a 1% doped discharge, the
electron would be very likely to have an inelastic
collision with a doping gas molecule before it obtains
sufficient energy to excite a helium atom.
This fact
suggests a problem with the interpretation of the data
which have been reported by Brassem, et al.
81
CHAPTER V
THE KINETIC STEADY-STATE THEORY
AND COMPARISON WITH EXPERIMENTAL DATA
A.
Introduction
Despite the wealth of publications which have used
electrical discharges in analytical chemistry (and other
branches of the physical sciences), no satisfactory
model has been developed to predict the active species
and their concentrations in these discharges.
Previous
models have relied on empirical relationships and/or
the assumption of thermodynamic equilibrium as discussed
in Chapter I.
This work examines a model that will pre­
dict the behavior of such discharges on the basis of a
steady-state kinetic theory.
A microwave-induced discharge was studied for
three reasons:
much work has been already reported
using such systems; the microwave discharge uses rela­
tively low power and uses less gas than other discharges
(16); and the apparatus was easily available.
Helium
was chosen as the gas to be studied due to its simpli­
city and the wealth of knowledge that already•existed.
82
In a helium electrical discharge at reduced pressure
(^1
torr), the major species expected to be present
in significant populations would be helium- ground state
atoms (He), helium atoms excited to the metastable states
1
3
(2 S, 2 S, (Hem )), helium atoms excited to higher elec­
tronic states (He^), helium ions (He+) , molecular ions
+
—
(He2 ), and electrons (e ). Other possible species are
not present in appreciable concentrations for the following
reasons.
+*
The excited helium ion (He
), requires a
minimum energy of 40.81 eV for formation (108), which is
much less than the average electron energy (see Chapter IV).
A similar argument holds for the doubly ionized helium
++
atom (He ), since it is formed with energy of 54.405 eV
(108) above the neutral ground state. The formation of
<
+*
excited He 2
ions via the associative ionization
reaction requires a minimum energy of 19.8 eV (the
minimum activation energy to excite He (l^S)), and since
the number density of the molecular ion must be much less
than the number density of the ground state atoms (by a
4
factor of 10 as estimated from the electron number
density), the number density of He2
+*
must also be very
low.
The helium molecule, He2, is thought to be repulsive
1 +
in its ground state, X 2^ (or if it does have a potential
well, it is ^10 K), and therefore does not have any
appreciable lifetime (109). The excited helium molecule,
*
3 +
He2 , does exist in a metastable state (a Eu), but this
83
state has been shown to be rapidly converted to a higher
energy state, A
(110).
1
+
, by a collision with an electron
This higher energy state has an optically allowed
transition to the ground state.
A complete study of a microwave-induced electrical
discharge should involve several measurement techniques:
emission spectrometry
(to measure [He^]), electrical
probes (to measure nQ
and (e), absorption spectroscopy
(to measure [Hem ] and
[He2 ]),and mass spectroscopy
(to measure [He ] and
[He2 ]).
This work represents a
study of the excited atomic states and utilizes the
first two techniques.
B.
Prediction of Excited-State Number Densities Using
the Kinetic Steady-State Theory
The steady-state theory provides a model for pre­
dicting the populations of the excited-states of helium
based on certain reactions which cause these states to be
populated or to be depopulated.
Other possible reactions
were considered, but were not included on the basis of
theoretical considerations.
The effects of gas tempera­
ture, pressure, and of foreign gases on the populations
of the excited states are also discussed.
1.
Mechanism
The mechanisms for the formation and destruction
of the jth state of helium will occur via the following
elementary reactions:
84
Excitation by Electron Impact:
. k
He + e" —
He.. + e"
(V.l)
Radiative Cascading from Higher States:
He, — £i-+. He. + hv
k
j
(V.2)
Radiative Deactivation:
A. .
He'j —
Hei + hv
(V.3)
Associative Homonuclear Ionization
(Hornbeck-Molner Reactions):
kA
' +
He. + He — s-* He, + e
D
£
(V.4)
There are a number of other possible reactions which
could populate the jth state, and they are as follows:
Dissociative Recombination:
He,+ + e“ — *- He. + He
Z
(V.5)
J
Recombination:
He+ + e” — *■ He. + hv
3
..
continuum
(V.6 )
Dissociative Collision:
He,* + He — ► He. + 2 He
^
(V.7)
J
Electron Impact of Metastable States:
He„ + e“ — >•
m
He. + e"
3
(V.8 )
Thermal Excitation from Metastable States:
He + He—
m
He. + He
j
(V.9)
Reaction V.5 has a large cross section (^10
—8
"3
cm /sec
(1 1 1 )), but the diatomic ion concentration is only approxi­
mately 1% of the total positive ion concentration (99).
The positive ion concentration is only 0.01% of the helium
neutral concentration (from the electron density measure­
ments pf Chapter IV).
Also it has been shown that Reaction
3
V.5 produces mostly excited atoms in the 2 S state (112) ,
and therefore will not affect the jth state populations.
Reaction V .6 must have a low cross section despite the
coulombic attraction since the reverse of the reaction has
-13
a lifetime of ^10
second, but the radiative lifetime for
allowed optical transitions is about 10
■"8
second (106).
Formation of the jth state through dissociative
collision, Reaction V.7, can also be safely ignored,
since the number density of the excited helium molecule
must be very small.
Electron impact of the metastable helium atoms
should have a larger rate of reaction than the electron
s'
impact of the ground state helium atoms, since the atom
should have a larger cross section in the metastable
state.
The contribution of this reaction can be
neglected, however, since the population density of the
metastable states must be considerably less than the
ground state population.
Although the populations of
metastable states were not measured, they can be esti­
mated to be about three orders of magnitude larger than
the n = 3 states, since the metastable lifetime is
86
longer than the lifetime of the other excited states.
If it is assumed that the rate constant for Reaction
V .8 is an .order of magnitude greater than the rate con­
stant for Reaction V.l, then the production of the jth
state through Reaction V .8 will be only approximately
0.1% of the production through Reaction V.l.
The collision between a metastable state and a
ground state atom could only produce higher excited
states if the thermal energies of the helium atoms in
the electrical discharge were sufficient.
The minimum
energy requirement would be approximately the difference
between the 2^S and the 3^S levels, 2.3 eV.
This
corresponds to a gas temperature of ^2000 K;
which is much higher than the estimated value of 400 K
discussed in Section V.B.3.
Other reactions which would depopulate the jth
state include
Excited Pair Ionization:
He. +
He. —
J
J
Hej +
He *
+ e"
(V.10)
^
He.. — »- He+ + He+ e"
(V.ll)
Collisional Deactivation:
He. +e“ — *•He
j
+
m
e”
(V.12)
These reactions have been neglected since the low number
densities of He^ indicate that the only reaction in which
it will be involved, would be in the collisions with
87
ground state helium atoms; i.e., the associative ioniza­
tion reaction, V.4.
Also the lifetimes of these species
are sufficiently small that there is a low probability
of collision of two excited species.
lisions have also been ignored.
All three-body col­
The possible effect of
the walls on the population of the jth state will be
discussed in Section V.B.10.
Possible reactions of the various species in the
helium electrical discharge with foreign species, such
as N2,
He. + N, — +J
He + N+ + N + e“
(V.13)
He + N2+ + e"
(V.14)
^
He.. + N 2 — ►
were investigated
by introducing
molecular gases (H2 , N2 / C>2, and
known amountsof
N 2 0) intothedischarge
and observing the changes in the discharge characteristics.
If only Reactions V.l through V.4 are important in
determining
the number density of the jth state, n^ ,
then the change in the number density with respect to
time will be related to the following equation:
= ke [He] ns + E
K
Nk - M
D
n.
(V.15)
-kA [He] n^
where [He] is the number density of the helium atoms and
nQ is the number density of the electrons.
When the
number density of the jth state reaches a constant value,
88
the steady state approximation may be used, and Equation
V.15
equals zero, so that
k
[He] n
+.SA-.
nj - x L - ~ E - H e -r
'
(v-16)
The number density of the jth state can be calculated
from rate constants, cross sections, and radiative life­
times of the various species which have been determined
by other workers and the experimentally measured para­
meters, electron density, and the number density of
helium ground state.
The distributions of the energy
of the electrons must also be determined, since the
values of kQ are dependent upon electron energy.
These
number densities can then be experimentally verified
by atomic emission measurements (Chapter III).
2.
Rate Constant for Electron-Impact Excitation
The rate constant for the population of the jth
state by electron impact, kQ , can, according to collision
theory be calculated from the reaction cross section, aQ ,
and the relative velocity of the two species.
This
latter term is approximated by the effective velocity
ve'
k
e
= a
e
v
e
= a
2 E 1/2
(^)
e m
(V. 17)
where e is the kinetic energy of the electron.
Equation v.17 can be applied when all the electrons
in the system have the same energy; however, the electrons
89
in a discharge are known to have a distribution of ener­
gies.
This distribution of energy has been approximated
by the Druyvesteyn relation (100),
fn «=) -
D
(4)V 2 ^ _
(e)-3/2 ,1/2
(V-18)
sr
2
exp (-.55
e
2/ ( e ) 2
)
where (e) is the average electron energy.
To determine the average value of the rate con­
stant, (kg) , kg must be integrated from
(the threshold
energy of the jth state) to infinity,
1/2
(ke,= /"oj ke de " I“oj CTe
fD (e> dE (V‘19)
The values of the cross sections as a function of electron
energy have been determined by St. John, Miller, and Lin
(113).
The relative values of a , v , f , and k
6
6
the 3^S state are shown in Figure V.l.
D
6
for
The integration
must be performed by graphical methods or by numerical
methods since Equation
cally.
V.19
cannot be solved analyti­
The integrations were terminated at 100 eV since
at this energy the value of kg was less than 0 .0 1 % of its
maximum value.
the
The results are shown in Figure V.2 for
states in the region 6 to 14 eV.
In a previous paper (87) on this model an approximate
solution to Equation
V.19
was used.
The solution
used was as follows:
= a (e-e0 j) exp [-b (e-e^)]
(V.20)
30
50
70
90
Electron Energy, £ (eV)
Figure V.l.
Relative Values of Electron Velocity, Cross-Section for
Electron-Impact Excitation, Druyvesteyn Energy Distri­
bution, and the Rate Constant for Electron-Impact
Excitation for the 3 S State.
°
Rate
Constant,
(k ) (cm /sec)
-11
-13
-15
-17
6
Figure V .2.
8
10
12
14
The Rate Constant of Electron-Impact Excitation as a Function
of Average Electron Energy for the
States.
92
and the electron population was assumed to fit a
Maxwellian distribution.
The methods used in this study
should yield more accurate values.
A comparison of the
Druyvesteyn distribution and the Maxwellian distribution
is shown in Figure V.3.
3.
Determination of the Ground State Number Density
The pressure of the system was measured after the
discharge region (Chapter II), and it was assumed that
the pressure was uniform throughout the system since it
was an open system.
The gas density is expected to be
different in the discharge region since the gas temperature
increases in the discharge region (1 0 0 ).
No attempt to measure the gas temperature in the
discharge was made.
The average energy electron was
determined, but since there is an obvious lack of thermal
equilibrium between the various species this value does
not reflect the gas temperature.
Bell (100) states a
typical ratio for the "electron temperature" and the "gas
temperature (T /T ) is approximately 100.
ss y
For this study,
2
the electron "temperature" is about 100,000 K (tQ = ^
(e) = 12.6 eV at 1.0 torr), which would result in a gas
temperature of approximately 1000 K.
Thermocouple
measurements in argon microwave discharges have yielded
similar results (2 ).
(e)
10
-1
10 -5.
10
- f t
10 "13
10
-17.
0
20
40
60
80
100
Average Electron Energy, (e) (eV)
Figure V.3.
Comparison of the Druyvesteyn and Maxwellian Energy
Distribution Functions.
VO
u>
94
It is doubtful that the gas temperature reaches
this value.
The heating of the gas is primarily by
electron impact.
He + e~ —
He' + e'-
where He' indicates the helium atom has gained thermal
energy and e' indicates that the electron has lost energy.
The average fraction of energy transferred from the
electron to the atom is related to the ratio of the mass
2m
of the two species (-^ 'v 3 x 10” ) . If the average
energy of the electron is 12.6 eV, then the helium atom
_3
will gain about 4 x 10
eV. This energy can be related
to temperature and the helium atom will gain 30 K per
collision.
The number of collisions between the helium
atoms and the electrons will be related to the total
elastic-collision cross-section, Qc , and the electron
number density.
The mean free path, 1, is defined as
the average distance a helium atom moves between electron
collisions is the mean free path, 1 „^,
rlS
= ‘W
1
(V-21)
where the cross-section will depend on the electron
energy. In the helium discharge at 1.0 torr (ng ^ 1.7
12
-3
x 10
cm , (e) ^ 12 eV) the cross-section is about
“16
2
3.5 x 10
cm , so the mean free path of the helium
atoms with respect to electron collisions is about 1.6
3
x 10 cm which is longer than the discharge length (the
95
electron mean free path will depend on the helium number
16
“3
density, ^2.4 x 10
cm
and therefore is about 1.2 x
10 ^ cm).
Therefore, each helium atom will experience
on an average less than one collision with an electron.
For this work it was assumed that the gas temperature
was only slightly above ambient, i.e., 400 K.
This is
the same temperature assumed by Teter (114), and close
to the temperature used by DeCorpo and Lampe (115).
The rate constants for the associative ionization reac­
tions were obtained from this latter paper.
Cher and
Hollingsworth (116) have reported a temperature of 399 K
in a nitrogen-doped helium discharge.
Therefore, it was
assumed the discharge temperature did not vary signi­
ficantly as the conditions were changed, within the
limits of this study.
Helium approaches ideal behavior at the pressures
and temperatures used in these experiments; therefore
the following equation may be used to estimate the number
density of the helium ground state atoms: •
[He] = £ = ^
= 2.42 x 1016 P (cm-3)
where P is measured in torr.
(V.21)
Equation V.21 is assumed to
be followed over the pressure range used and with the
addition of doping gases.
The actual value of T
does
have a large effect on [He], but since [He] affects
both the production, Reaction V.l, and destruction,
Reaction V.4, of the jth state, this effect is minimal.
96
.4.
Radiative Transition Probabilities
The radiative lifetimes, x , of the excited states
are listed in Table V.l.
These lifetimes are related
to the radiative transition probabilities,
t -
1
rA“ T
&Y
(V. 23)
■
and these values were taken from a paper by Gabriel and
Heddle (93).
The lifetimes of the states in the ^P family
are much shorter than the other states since the ^P
states are optically connected to the ground state, l^S
1
1
(i.e., n P — ► 1 S is an optically allowed transition).
The transition probability is a first order rate
constant and depends on the, frequency of the transition,
tOj^, and the transition moment integral (j-|y|i) (98),
64 ir4 w ..3
_
Aji = --- 3 h I*-■ (j IV Ii)
5.
(V. 24)
Rate Constant for Homonuclear Associative
Ionization
The reaction known as associative ionization was
first reported in 1923 (99) .
Hornbeck and Molnar have
published extensively on this reaction using the inert
gases (hence, these reactions are sometimes referred to
as the Hornbeck-Molnar reactions).
These workers showed
that the energetic onset of the He2+ ion (and Ne2+ and
Ar2+) is lower than the ionization potential of the helium
atom (23.1 eV compared to 24.6 eV) (99).
This observation
97
TABLE V.l
Values of the Radiative Lifetimes, the Rate Constants
for Associative Ionization, and the Effective Lifetimes,
at 1.00 Torr, for the Excited States of Helium
3
\
(sec)
x 10~8
t
1
s
3
4
5
6
3
4
5
6
3
4
5
6
5.32
8.98
15.1
24.0
3.64
6.38
11.0
18.3
0.171
0.393
0.755
1.29
3
4
9.66
13.8
3
4
5
1.54
3.78
7.27
12.3
6
3
4
5
6
7
8
1.39
3.22
6.01
10.7
14.5
20.7
k, (cm /sec)
A
'
x 10~1Q
.,
.
t(sec)
x 10~ 8
t/T
0
20
27
30
5.32
1.68
1.39
1.31
1.00
0.20
0.09
0.05
0
3.64
1.56
1.35
1.28
1.00
0.25
0.12
0.07
0.171
0.330
0.506
0.666
1.00
0.84
0.67
0.52
8.78
1.80
0.91
0.13
1.48
1.34
1.27
1.24
0.96
0.35
0.17
0.10
1.27
1.26
0.91
0.39
1.22
0.20
1.22
0.11
0.09
0.06
20
27
30
0.39
20
27
30
0.43
20
0.95
20
27
30
2.9
20
27
30
30
30
1.26
1.29
98
can be rationalized by postulating that this reaction is
a two-step process:
He + e" —
He* + e“
(V.25)
He* + He — ► He2+ + e“
(V.26)
The onset energy of 23.1 eV suggests that the metastable
states of helium 23S (19.8 eV) and 2^S (20.6 eV) could not
participate in Reaction V.25.
Also, for similar reasons
the following states, 23P (21.0 eV) , 2‘b? (21.2 eV) ,
33S (22.7 eV), and 3^S (22.9 eV) can not participate (114).
The associative ionization rate constants for the states
1 3
1
3
3 P, 3 P, 3 D , and 3 D were measured by Teter, et al.
(114) and their results demonstrated that the deactivation
of these states was pressure dependent.
DeCorpo and Lampe
(115) determined the cross sections for reaction (V.25)
3
1
1
for the states n D, n D, and n P. These data were inter­
preted by Lampe, Risby, and Serravallo (87) to indicate
-9
-3
a rate constant of 2.7 x 10
cm
for all states with
n > 3.
This work modifies the Lampe, et al., approach
by assuming that the value of kA increases with n (i.e.,
the values of the collision diameters increase with n (115)).
The values chosen for kA (Table V.l) are such that their
—9 —3
average yields a value close to 2.7 x 10 cm
6.
Total.Lifetime of jth State
It is of interest to compare the effects of asso­
ciative ionization reaction and of the
radiative relaxa­
tion on the expected total lifetime of the excited states.
99
Table V.1 shows the comparison between the radiative
lifetime,. Xj, and the total lifetime, tj
(V. 27)
= { Aji + kA
for the excited states of helium.
The fraction of the
population that will deactivate radiatively is given
by t/x.
For the n1? family of states, the radiative
lifetime is clearly the dominant effect, as these states
are optically connected to the ground state, 11 S.
For
the other families, the lifetimes are limited by the rate
of the associative ionization reaction for n > 3, and
are limited by the radiative lifetime for n = 3.
The
effect of associative ionization is more important at
higher pressures, but the radiative lifetime remains the
dominant term when n = 3 over the pressure range studied.
7.
Cascading
The effect of populating excited states by cascading
from higher excited states is more important for the
triplet states than for the singlet states.
To obtain
estimations of the cascading contributions, population
densities of the n = 5 and n = 6 states and the nF
family of states had to be assumed.
The cascading term
was corrected for the fraction of the kth state that
depopulated by associative ionization,.
(V.28)
100
8.
Effect of Pressure
The increase in the helium pressure decreases the
expected electron energy and therefore the value of the rate
constant for electron-impact excitation.
The decrease of
the electron energy is due to the decreased electron path
length/ as shown in Equation IV.18.
The calculated excited-
state concentrations would therefore also be expected to de­
crease as the pressure is increased.
The relation between
the pressure and the calculated value of [n^S] is shown in
Figure V.4.
The low population densities below 1.0 torr are
due to the low experimental values of electron energy.
9.
Effect of Doping Gases
Equation V.16 does not include a term to account for
the presence of foreign species in the discharge, yet
it is well-known that the discharge -is changed dramati­
cally when doping gases are added.
A large portion of
this change is the result of a lower average electron
energy caused by the large cross-section for the colli­
sions between molecular gases and electrons (107), e.g.,
e~ + 0 2 —
0^ + e~
(V.29)
where 0 2 indicates the molecule is in a rotationally or
vibrationally excited state.
Much of the energy of the
discharge is thus transferred to the vibrational energy
levels of the molecular gas.
The excited-state helium atom may deactivate through
a collision with the molecular species,
101
10
10
Population
Density, n. (cm
10
10
10
10
10
1
2
3
4
Helium Pressure (torr)
Figure V.4.
Calculated Population Densities of
States of the Helium Discharge.
S
102
.He,.* + 0 2 — £-*- He + 02+ + e"
k
,
He^* + 0 2 — ^
+ 0^ (or 02*)
(V.30)
(V.31)
Reaction V.30 is known as Penning Ionization and has rate
constants of 2 x 10 "^0 cm^/sec for C>2 , 1 x 10-10 for N2 , and
5 x 10 ^
for H 2 for the 2^S state (99, 116).
It is assumed
that the rate constants for the higher excited states are
within an order of magnitude of the rate constants for the
metastable states, since the energies of the helium excited
states are much greater than the ionization potentials of the
-9
3
molecular gases. Using 2 x 10
cm /sec as the upper limit
of the rate constant, and 2.4 x 10"^ cm”^ as the molecular
gas concentration (1 %), the lifetime of the excited-state
helium atom would be 2 x 10
•ionization.
_6
second with respect to Penning
This is much greater than the lifetimes listed
in Table V.l, and indicates that Reaction V.30 may be neglec­
ted.
The magnitude of Reaction V.31 is not known, but the
probability of the excited helium atom not relaxing to the
ground state in such a collision must be quite small.
10.
Wall Reactions
The lack of knowledge about the effects of the
walls surrounding the discharge is the "major blind spot"
(101) in understanding discharge chemistry.
The walls
serve as sites for the production and removal of electrons
and ions, and also provide catalytic
surfaces.
However,
in this study, it can be shown that the wall effects on
103
the number density of the excited states of helium are
negligible and this statement is rationalized by the
following discussion.
A helium atom at 400 K will have an average velocity
of 2 x 10
5
cm/sec and for the states studied, the maximum
probable lifetime before either radiative relaxation or
associative ionization is 5.3 x 10
—8
1
sec (3 S).
Therefore,
during the lifetime of an excited state, the helium atom
will have a path length of about 1 x 10
_2
cm.
This path
is much less than the diameter of the discharge tube,
(2.5 cm), and therefore, less than 1% of the excited
species would be expected to deactivate through wall
collisions.
It should be noted that wall collisions will
contribute to the "gas temperature" of the discharge
(Section 3).
C.
Comparison of Calculations with the Experimental
Results
The results obtained by the use of Equation V.16
are shown in Tables V.2-V.5 and in Figures V.5-V.9, and
are compared with the experimental results obtained for
a pressure of 1.0 torr.
The ordinate values are in
relative units to allow for the calibration uncertainty
as explained in Chapter III.
As observed from these figures, the steady-state
theory does predict an approximate exponential relation
between the population density and the energy level of a
104
TABLE V. 2
Rate Constants and Excited-State Populations of S Family
at 1.0 Torra
(ke)b
3
cm /sec
EA. .
31
-1
sec
x IQ' 12
x 106
kA
/
cm 3/sec
in-10
x 10
taji
'VS
cm-"3
[nj^CAS
cm” 3
cm” 3
x 109
x 109
x 109
0.
9.63
0.28
9.91
20.
1.33
0.012
1.34
31S
4.35
18.8
41S
1.90
11.14
5*8
0.659
6.62
27.
0.382
0.0017
0.384
6 1S
0.309
4.16
30.
0.168
0.0001
0.168
33S
10.8
27.5
43S
3.22
15.68
53S
1.20
9.06
0.
48.9
10.2
59.1
20.
6.27
0.05
6.32
27.
2.02
«...
2.02
a2.42 x 10-*-® helium atoms/cm3, 1.72 x 10^ 3 electrons/cm3
b (e) = 12.6 eV
cignores contribution from cascading
105
TABLE V.3
Rate Constants and Excited-State Populations of P Family
at 1.0 Torra
<ke)b
/
cm3/sec
m -12
x 10
s1?
15.3
41?
6.21
33P
8.44
EA.,
sec
-1
x 106
584.7
254.3
10.35
x 10"9
x 109
[nj]
-3
cm
9
x 10
3.26
0.01
3.27
'"j'S
kA
/
cm 3/sec
x 10
cm" 3
0.39
2.56
20
0.43
’■Hj^CAS
cm-3
277
—
3
2.56
280
3
3
a2.42 x 1 0 ^ helium atoms/cm , 1.72 x 10^2 electrons/cm
b (e) = 12.6 eV
cignores contribution from cascading
106
TABLE V. 4
Rate Constants and Excited-State
Populations of D Family at 1.0 Torr
ZA. .
“VS
(ke)
3,
cm /sec
x 10“2
sec
x 106
3XD
3.63
65.1
4^D
0.672
26.44
20
1.87
—
1.87
S-'-D
0.374
13.76
27
0.985
—
0.985
6 1D
0.186
8.13
30
0.479
__
0.479
33D
3.14
71.7
43D
1.17
31.05
20
9.18
53D
0.669
16.65
27
5.10
6 3D
0.386
9.34
30
2.94
-1
kA
3,
cm /sec
.n — 10
x 10
0.95
2.9
taji
cm" 3
j]CAS
cm" 3
cm" 3
x 109
x 109
x 109
11.2
24.9
0.15
0.73
0.05
—
11.4
25.6
9.23
5.10
2.94
a2.42 x lO3"^ helium atoms/cm3, 1.72 x 103"2 electrons/cm3
b (e) = 12.6 eV
cignores contribution from cascading
, experimental
, calculated
23.0
23.5
24.0
Energy (eV)
Figure V.5.
Calculated and Experimental Relative Population Densities
for 1S States of Helium Discharge at 1.0 Torr.
O/ experimental
Q, calculated
23.0
Figure V. 6 .
23.5
Energy (eV)
24.0
108
Calculated and Experimental Relative Population Densities for 3S
States of Helium Discharge at 1.0 Torr.
O f experimental
10
P
© , calculated
A , experimental
P
, calculated ^P
10
23.0
23.5
24.0
Energy (eV)
Figure V.7.
109
Calculated and Experimental Relative Population Densities for
1
3
P and P States of Helium Discharge at 1.0 Torr.
O / experimental
O , calculated
23.0
23.5
24.0
Energy (eV)
Figure V. 8 .
Calculated and Experimental Relative Population Densities for
110
States of Helium Discharge at 1.0 Torr.
Of experimental
O' calculated
23.0
23.5
24.0
Energy (eV)
Calculated and Experimental Relative Population Densities
3
for D States of Helium Discharge at 1.0 Torr.
Ill
Figure V.9.
112
TABLE V.5
Calculated and Experimental Relative Population Densities
of Excited States of Helium
e
(eV)
Experimental
(cm~3)
Calculated
(cm"3)
Exp/Calc
22.91
23.66
24.00
24.18
0.254
0.0329
0.00691
0.00188
0.0354
0.00479
0.00137
0.00600
7.2
6.9
5.0
3.1
22.71
23.58
23.97
24.17
0.786
0.0896
0.0228
0.00473
0.211
3.7
3.9
3.2
0.492
0.0519
0.00765
0.00141
0.0117
0.00914
6
23.09
23.74
24.05
24.21
3
4
23.01
23.71
1
1
3
4
5
23.07
23.72
24.04
24.21
0.437
0.105
0.0240
0.00521
0.0407
0.00668
0.00352
0.00171
10.7
15.8
23.06
23.72
24.04
24.21
24.31
24.37
1.003
0.247
0.0565
0.0153
0.00437
0.00164
0.0914
0.0330
0.0182
0.0105
—
10.9
7.5
3.1
1.5
.
03
3
4
5
6
3
4
5
6
3
4
5
6
3
4
5
6
7
8
0.0226
0.00721
—
42.1
5.7
——
1
0.0254
—
6.8
3.1
—
—
113
particular state.
This relation is due to the mechanism
of the steady-state theory; i.e., the collisions with
energetic electrons, and is not due to a thermodynamic
equilibrium in the discharge.
agree well within each family.
The shapes of the curves
In general, the experi­
mental data show that the population density decreases
faster with increasing threshold energy (or with n),
than the theory predicts (Table V.5).
This is parti-
cularly noticeable for the upper levels of the
family, Figure V.9.
3
D
This indicates that one or more
additional reactions are occurring in the discharge; e.g.,
Hej + He
He. +
n 2* —
Hei + He"
*■ Hei +
n 2+
(V.32)
(or 02+ ) + e~
Hej - s s r * Hei
(V.33)
tv-34)
Reaction V.'33 seems the most probable, since radiative
relaxations of the species N 2 * species were observed in
addition to the spectra resulting from the radiative
relaxations of He^. Also the Penning ionization reaction
would affect the populations of the higher excited states
more than the lower excited states since the value of
the collisional diameter increases with n.
The variation of the populations of the
states
as the helium pressure is increased from 0.5 to 2.0 torr
is shown in Table V .6 and Figure V. 10 and the steady-state
theory agrees with those experimental results for the
114
TABLE V.6
Calculated Population Densities of
States Between 0.4 and 4.0 Torr
)
g
x 10*
41S
/
(cm“3%
)
g
x 10s
0.4
0.0534
0.00587
0.00306
0.00135
1.0
9.64
1.33
0.382
0.168
2.47
0.660
0.316
Pressure
(torr)
1.5
(cm
26.3
5XS
(cm-3)
g
x 10*
(cm"3)
x 109
2.0
7.10
0.495
0.155
0.0567
4. 0a
0.0450
0.00083
0.00030
0.00014
1
a (e) = 7.0 eV/ n = 1.75 x 10
Figure V.4.
e
A
cm
extrapolated from
115
.
10
10
ro
S
O
10
Relative
Population
Density
c
10
-2
-3
O O A V, calculated
O Q A V, experimental
10 -4
0
1
2
Helium Pressure
Figure V.10.
Calculated and Experimental Rela^
tive Population Densities for -*-S
States of Helium Discharge.
116
pressure range 1.0 to 2.0 torr.
of
The low values
below 1.0 torr are the result of the low
value of (e) which was not expected and probably indicates
the failure of the double probe theory (Chapter IV).
Extrapolation to calculate the values at 4.0 torr also
gave poor results.
The decrease of (e) with the pressure
increase, causes the value of (ke) to decrease.
Also as
the pressure increases, the relative value of the asso­
ciative ionization reaction increases, and
therefore, the populations of higher energy states
decrease more rapidly than the 3^S state.
This relation3
ship is observed for the other families of states: s,
XD, and 3D.
The effects of the addition of the doping gases,
nitrogen, oxygen, hydrogen, and nitrous oxide are very
similar.
The population densities of the excited helium
atoms decreased, typically by a factor of 1 0 , upon addi­
tion of 1 % of the doping gas, and continued to decrease
with the addition of more molecular gas.
This decrease
cannot be explained solely by the reduction in the
average electron energy for these doping gas experiments.
Also for reasons discussed earlier, the results cannot be
explained by Penning ionization.
Therefore, a reaction
of the type of
k.
He.. + N2* — i-*. He + N 2
+ e“
may be a possible important reaction.
(V.35)
On the basis of the
117
experimental data, the contribution due to Reaction V.35
would appear to be comparable to that 'of the associative
ionization reaction, yet the concentration of the doping
gas is only a fraction (0 .0 1 ) of the helium atom concen­
tration.
Assuming all of the doping gas molecules were in
excited states, the rate constant for Reaction V.34 would
need to be about 100 times greater than the value of the
_7
rate constant for associative ionization, or about 3 x 10
3
cm /sec. This value is much larger than could be justified
for this reaction, and therefore Reaction V.34 cannot explain
the behavior of the doped discharges.
The roles of the elec­
tron-molecular ion dissociative recombination reactions may
be significant.
Also, the assumptions in the Penning
ionization discussion may be incorrect.
D.
Conclusions
The steady-state kinetic theory is shown to be an
accurate model for predicting the relative population
densities in a pure helium microwave-induced electrical
discharge at reduced pressures on the basis of the
experimentally determined electron energies and densi­
ties.
The inability to compare absolute population
densities is the result of the difficulties in obtaining
experimental population densities from emission spectra.
The chemistry of the discharge is drastically
changed upon the addition of molecular gases and becomes
much too complicated for such a model.
The model does
118
predict the direction of the change, but does not
successfully estimate the magnitude of the change.
There is much interest in obtaining a better under­
standing of the processes in these discharges since
their use is substantial.
Winefordner and colleagues (40)
are studying the relative distribution of species in ICP
electrical discharges with a laser-excited fluorescence
technique to determine the spatial resolution which is
necessary to fully understand the processes occurring in
the discharge.
Also the ion-electron radiative recombi­
nation model has been recently applied to atmospheric
microwave discharges (117).
The mechanisms proposed in this study should be
considered tentative since not all the species were
measured.
Further work should include atomic absorption
studies to determine the number densities of the meta­
stable species and their role in the reaction occupying
in the electrical discharge.
Also mass spectroscopic
studies should yield information about the number densities
of the positive and negative ions in the discharge.
Although there is still a great deal of information
to be gained about the excitation and fragmentation of
molecules in electrical discharges, it is proposed that
this study should eliminate much of the speculations
involved in this field and suggest further areas for
research.
119
REFERENCES
1.
G. V. Marr, Plasma Spectroscopy, Elsevier Publishing
Company, Amsterdam, 1968.
2.
B. L. Sharp,
3.
F . K . McTaggert, Plasma Chemistry in Electrical
Discharges, Elsevier Publishing Company, Amsterdam,
1967.
B. Jaffe, Crucibles, The Story of Chemistry,
Fawcett World Library, New York (1957).
4.
Sel. Ann. Rev. Anal. Sci., 4_, 37 (1976).
5.
L. Tonks and I. Langmuir, Phys. Rev., 34, 876.
6.
G .Glocker and S . C . Lind, The Electrochemistry of
Gases and Other Dielectrics, John Wiley and Sons,
New York, 19 39.
7.
W. Gerlach and E. Schweitzer, Z. Allgem. Chem., 195,
255 (1931) .
8.
R. L. McCarthy, J. Chem. Phys., 22, 1360 (1954).
9.
E. Badarau, M. Giurgea, Gh. Giurgea, and A. T. H.
Trutia, Spectrochim. Acta, 11, 441 (1957).
10.
A. D. MacDonald, Microwave Breakdown in Gases, John
Wiley and Sons, Inc., New York, 1966.
11.
F. Kaufman, "The Production of Atoms and Simple
Radicals in Glow Discharges," in Chemical Reactions in
Electrical Discharges, Advances in~Chemistry Series,
Volume SO, R. F. Gould (Editor), American Chemical
Society Publications, Washington, 1969.
12.
S. C. Brown, Basic Data of Plasma Physics, The M.I.T.
Press, Cambridge, 1967.
13.
R. Avni and J. D. Winefordner, Spectrochim. Acta, 30B,
281 (1975).
14.
G. Herzberg, Atomic Spectra and Atomic Structure,
Dover Publications, New York, 1944.
120
15.
J. Jarosz, J. Mermet, and J. Robin, Spectrochim. Acta,
33B, 365 (1978).
16.
P. Tschopel, "Plasma Excitation in Spectrochemical
Analysis" in Comprehensive Analytical Chemistry,
Volume 9, G. Svehla (Editor), Elsevier Publishing
Company, Amsterdam, 1979.
17.
T.
B. Reed, J .Appl. Phys., 32, 821
(1961).
18.
T.
B. Reed, J. Appl. Phys., 32, 2534 (1961).
19.
S. Greenfield, H. McGeachin, and P.
Talanta, 23, 1 (1976).
B. Smith,
20.
S. Greenfield, I. L. Jones, H. McGeachin, and P. B.
Smith, Anal. Chim. Acta., 74_, 225 (1975) .
21.
S. Greenfield, I. L. Jones, and C. T. Berry, Analyst,
82, 713 (1964).
22.
S. Greenfield and P. B. Smith, Anal. Chim. Acta, 59,
341 (1972) .
23.
S. Greenfield, H. McGeachin, and P. B. Smith, Talanta,
22, 1 (1975).
24.
S. Greenfield, H. McGeachin, and P.
22, 553 (1975).
B. Smith, Talanta,
25.
R. H. Wendt and V. A. Fassel, Anal. Chem., 37, 920
(1965) .
26.
V. A. Fassel and G. W. Dickenson, Anal. Chem., 40,
247 (1968).
27.
G. W. Dickinson and V. A. Fassel, Anal. Chem., 41,
1021 (1969).
28.
V. A. Fassel and R. Knisely, Anal. Chem., 46, 1110A
(1974) .
29.
V. A. Fassel and R. Knisely, Anal. Chem., 46, 1155A
(1974) .
30.
V. A. Fassel, Science, 202, 183 (1978).
31.
R. K. Winge, V. A. Fassel, R. N. Knisely, E. DeKalb,
and W. J. Haas, Spectrochim. Acta, 32B, 327 (1977).
32.
P. J. Kalnicky, V. A. Fassel, and R. N. Knisely,
Appl. Spectr., 31, 137 (1977) .
121
33.
W. B. Barnett, V. A. Fassel, and R. N. Knisely,
Spectrochim. Acta, 25B, 139 (1970).
34-.
D. Truitt and J. W. Robinson, Anal. Chim. Acta,
51, 61 (1970).
35.
J. M. Mermet, Spectrochim. Acta, 30B, 383 (1975).
36.
J. Jarosz, J. M. Mermet, and J. P. Robin, Spectrochim.
Acta, 33B, 55 (1978).
37.
G. R. Kornblum and L. DeGalan, Spectrochim. Acta,
32B, 71 (1977).
38.
G. R. Kornblum and L. DeGalan, Spectrochim. Acta,
32B, 455 (1977).
39.
K. Visser, F. M. Hamm, and P. B. Zeeman, Appl. Spect.,
30, 34 (1976).
40.
N. Omenetto, S. Nikdel, R. D. Reeves, J. B. Bradshaw,
J. N. Bower, and J. D. Winefordner, Spectrochim.
Acta, 35B, 507 (1980) .
41.
P. W. J. M. Boumans and F. J. DeBoer, Spectrochim.
Acta, 3IB, 355 (1976).
42.
P. W. J.' M. Boumans and F. J. DeBoer, Spectrochim.
Acta, 32B, 365 (1977).
43.
J. F. Alder, R. M. Bombelka, and G. F. Kirkbright,
Spectrochim. Acta, 35b , 163 (1980).
44.
R. C. Fry, S. J. Northway, R. M. Brown, and S. K.
Hughes, Anal. Chem., 52, 1716 (1980) .
45.
A. F. Ward, Airier.’ Lab., 10, 79 (1978).
46.
R. N. Savage and G. M. Hiettje, Anal. Chem., 51,
408 (1979).
47.
R. N. Savage and G. M. Hieftje, Anal. Chem., 52, 1267
(1980) .
48.
R. M. Barnes and S. Nikdel, Appl. Spect., 30, 310
(1976) .
49.
R. M. Barnes and G. A. Meyer, Anal. Chem., 52, 1523
(1980) .
50.
H. Falk, E. Hoffman, I. Jaeckel, and Ch. Ludke,
Spectrochim. Acta, 34B, 333 (1979).
122
51.
H. Falk, Spectrochim. Acta, 32B, 437 (1977).
52.
J. D. Cobine and D. A. Wilbur, J. Appl. Phys., 22,
835 (1951).
53.
U. Jecht and W. Kessler, Z.. Anal. Chem., 198, 27
(1963) .
54.
W. Trappe and J. VanCalker, Z. Anal Chem., 198, 13
(1963) .
55.
R. Mavrodineanu and R. C. Hughes, Spectrochim. Acta,
19, 1309 (1963) .
56.
H. Goto, K. Hirokawa, and M. Suzuki, Z. Anal. Chem.,
225, 130 (1967) .
57.
S. Murayama, H. Matsumo, and M. Yamamoto, Spectrochim.
Acta, 23B, 513 (1968) .
58.
S. Murayama, Spectrochim. Acta, 25B, 191 (1970).
59.
R. K. Skogerboe and G. N. Coleman, Anal. Chem., 48,
611A (1976) .
60. . F. C. Fehsenfeld, K. M. Evenson, and H. P. Broida,
Rev. Sci. Inst., 36, 294 (1965).
61.
H. P. Broida and J. W. Moyer, J. Opt. Soc. Am., 42,
37 (1952).
62.
H. P. Broida and M. W. Chapman, Anal. Chem., 30,
2049 (1958) .
63.
A. J. McCormack, S. C. Tong, and W. D. Cooke, Anal.
Chem., 37, 1470 (1965).
64.
C. A. Bache and D. J. Lisk, Anal. Chem., 37, 1477
(1965) .
65.
C. A. Bache and D. J. Lisk, Anal. Chem., 38, 783
(1966) .
66.
C. A. Bache and-D. J. Lisk, Anal. Chem., 38, 1757
(1966).
67.
C. A. Bache and D. J. Lisk, Anal. Chem., 39, 786
(1967) .
68.
W. Braun, N. C. Peterson, A. M. Bass, and M. J.
Kurylo, J. Chrom., 55, 237 (1971).
123
69.
F. A. Serravallo, Doctoral Thesis, The Pennsylvania
State University, 1975.
70.
J. H. Runnels and J. H. Gibsoii, Anal. Chem., 39,
1398 (1967).
71.
H. Kawaguchi and B. L. Vallee, Anal. Chem., 47,
1029 (1975).
72.
K. M. Aldous, R. M. Dagnall, B. L. Sharp, and T. S.
West, Anal. Chim. Acta, 54, 233 (1971).
73.
L. R. Layman and G. M. Hieftje, Anal. Chem., 47,
194 (1975).
74.
C. I. M. Beenakker, Spectrochim. ACta, 31B, 483
(1976) .
75.
C. I. M. Beenakker and P. W. J. M. Boumans,
Spectrochim. Acta, 33B, 53 (1978).
76.
J. Hubert, M. Moisan, and A. Richard, Spectrochim.
Acta, 33B, 1 (1979).
77.
K. Fallgatter, V. Svoboda, and J. D. Winefordner,
Appl. Spect., 2J5, 347 (1971) .
78.
R. F. Browner and J. D. Winefordner, Spectrochim.
Acta, 28B, 263 (1975) .
79.
R. G. Michel, J. Coleman, and J. D. Winefordner,
Spectrochim. Acta, 33B, 195 (1978).
80.
K. W. Busch and T. J. Vickers, Spectrochim. Acta,
28B, 85 (1973).
81.
P. Brassem and F. J. M. J. Maessen, Spectrochim.
Acta, 29B, 203 (1974).
82.
P. Brassem and F. J. M. J. Maessen, Spectrochim.
Acta, 3OB. 547 (1975).
83.
P. Brassem, F. J. M. J. Maessen, and L. DeGalan,
Spectrochim. Ac ta, 31B, 537 (1976).
84.
P. Brassem, F. J. M. J. Maessen, and L. DeGalan,
Spectrochim. Acta, 33B, 753 (1978) .
85.
C. I. M. Beenakker, Spectrochim. Ac ta, 32B, 173 (1977)
86.
P. M. Houpt, Anal. Chim. Acta, 8 6 , 129 (1976).
124
87. . F. W. Lampe, T. H. Risby, and F. A. Serravallo,
Anal. Chem., 49, 560 (1977).
88 .
P. W. J. M. Boumans, F. J. DeBoer, F. J. Dahman,
H. Hoelzel, and A. Meier, Spectrochim. Acta, 30B,
449 (1975).
89.
G. F. Larson and V. A. Fassel, Anal. Chem., 48,
1161 (1976).
90.
C. I. M. Beenakker, B. Bosman, and P. W. J. M.
Boumans, Spectrochim. Acta, 33B, 373 (1978).
91.
P. W. J. M. Boumans, Spectrochim. Acta, 35B, 57
(1980) .
92.
A. R. Striganov and N. S. Sventitskii, Tables of
Spectral Lines of Neutral and ionized Atoms, Plenum
Press, New York, 1968.
93.
A. H. Gabriel and D. W. 0. Heddle, Proc. Roy. Soc.
London, A258, 124 (1960).
94.
R. W. B. Pearse and A. G. Gaydon, The Identification
of Molecular Spectra, 3rd Edition, Chapman and Hall
Ltd., London, 1965.
95.
J. C. deVos, Physica, 20, 690 (1954).
96.
S. Katzoff (Editor), Symposium on Thermal Radiation,
NASA, San Francisco, 1964.
97.
G. Rosenberg, private communication.
98.
W. A. Guillory, Introduction to Molecular Structure
and Spectroscopy, Allyn and Bacon, Inc., Boston
(1977).
99.
F. W. Lampe, "Ionizing Collision Reactions of
Electronically Excited Atoms and Molecules," in
Ion-Molecule Reactions, Volume 2, J. L. Franklin
(Editor), Plenum Press, New York, 1972.
100 . A. T. Bell, "Fundamentals of Plasma Chemistry,"
in Techniques and Applications of Plasma Chemistry,
J. R. Hollahan and A. T. Bell (Editors), Wiley
Interscience, New York, 1974.
101 . W. L. Fite, "Chemical Physics of Discharges," in
Chemical Reactions in Electrical Discharges, Advances
in Chemistry Series, Volume 80, R. F. Gould (Editor),
American Chemical Society Publications, Washington,
1969.
125
102.
P. M. Chung, L. Talbot, and K. J. Touryan, Electrical
Probes in Stationary and Flowing Plasma, SpringsVerlog, New York, 1975.
103.
I. Langmuir, Phys. Rev., 28, 727 (1926).
104.
E. 0. Johnson and L. Maiter, Phys. Rev.,
(1950).
105.
J. D. Swift and M. J. R. Schwar, Electrical Probes
for Plasma Diagnostics, Elsevier Publishing
Company, New York, 1969.
106.
F. W. Lampe, private communication.
80, 58
107.
A. V. Phelps, "Basic Parameters for Electrical
Discharges in Gases," in Chemical Reactions in
Electrical Discharges, Advances in Chemistry Series,
Volume 80, R. F. Gould (Editor), American Chemical
Society Publications, Washington, 1969.
108.
C. E. Moore, Selected Tables Of Atomic Spectra,
U. S. Government Printing Office, Washington, 1965.
109.
A. P. J. vanDeursen and J. Reuss,
63, 4559 (1975).
J. Chem. Phys.,
110.
C. B. Collins and W. W. Robertson, J. Chem. Phys.,
40, 701 (1964).
;
111.
J. Boulmer, P. Davey, J. F. Delpech, and J. C. '
Gauthier, Phys. Rev. Let., 30, 199 (1973).
112.
M. Ceret and F. Lambert, C. R. Acad. Sci., Ser. B,
77, 275 (1972).
113.
R. M. St. John, F. L. Miller, and C. C. Lin, Phys.
Rev., 134, A 888 (1964).
114.
M. P. Teter, F. E. Niles, and W. W. Robertson,
J. Chem. Phys., 44, 3018 (1966).
115.
J. J. DeCorpo and F. W. Lampe, J. Chem. Phys.,
51, 943 (1969).
116.
M. Cher and C. S. Hollingsworth, "Chemiluminescent
Reactions of Excited Helium with Nitrogen and Oxygen"
in Chemical Reactions in Electrical Discharges.
Advances in Chemistry Series, Volume 80, F. Gould
(Editor), American Chemical Society Publications,
Washington, 1969.
117.
S. R. Goode and D. C. Otto, Spectrochim. Acta, 35B,
569 (1980).
VITA
Christopher Kevin Kohlmiller was born in South
Bend, Indiana on September 19, 1953.
After graduation
from Cathedral Preparatory School, Erie, Pennsylvania,
in June 1971, he entered the University of Nore Dame and
received a Bachelor of Science degree in Chemistry in
May 1975.
He entered the Graduate School of the
Pennsylvania State University in June, 1975, where he
held the position of teaching assistant for four years.
He has been an Instructor of Chemistry at the University
of Virginia since September, 1979.
Документ
Категория
Без категории
Просмотров
0
Размер файла
3 719 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа