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Characterization and catalytic activity of dispersed transition metal oxide particles on carbon substrates

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Title:
Characterization and catalytic activity of dispersed transition metal oxide particles on carbon substrates
Creator:
Davis, Jack G., 1950-
Publication Date:
Language:
English
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vi, 139 leaves : ill. ; 28 cm.

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Subjects / Keywords:
Analyzers ( jstor )
Atoms ( jstor )
Carbon ( jstor )
Electrons ( jstor )
Energy ( jstor )
Orbitals ( jstor )
Oxides ( jstor )
Permanganates ( jstor )
Photoelectrons ( jstor )
Vapor deposition ( jstor )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Iron oxides ( lcsh )
Manganese oxides ( lcsh )
Photoelectron spectroscopy ( lcsh )
X-ray spectroscopy ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1988.
Bibliography:
Includes bibliographical references.
Additional Physical Form:
Also available online.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Jack G. Davis, Jr.

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University of Florida
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Full Text







CHARACTERIZATION AND CATALYTIC ACTIVITY OF DISPERSED
TRANSITION METAL OXIDE PARTICLES ON CARBON SUBSTRATES













By

JACK G. DAVIS, JR.


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

1988


fl -'r LF'













ACKNOWLEDGMENTS


I would like to express my appreciation to Dr. Vaneica Young for
her guidance and very helpful suggestions during the course of my
research project. I would also like to thank members of my
research committee who were also of help.
Paul McCaslin, Linda Volk, Mike Clay, and Peter ten Berge all
made my stay at the University of Florida much more enjoyable by
their friendship and advice.













TABLE OF CONTENTS

page
ACKNOWLEDGMENTS .......................................... ii
ABSTRACT ................................................... v
CHAPTERS
1 INTRO DUCTION ..................................... 1
Fundamental Principles of X-Ray Photoelectron
Spectroscopy ................................... 1
Instrum entation .................................. 3

2 BACKGROUND OF THEORETICAL RESEARCH UNDERTAKEN..17
Overview of Molecular Orbital Theory .............. 17
Approximations to Molecular Orbital Theory ......... 31
3 THE EFFECT OF VARIATION OF MOLECULAR GEOMETRY
OF A TRANSITION METAL OXIDE CLUSTER ON THE
VALENCE BAND DENSITY OF STATES .................. 38
Background ................................... 38
Modification of CNDO2/U Algorithm ............... 43
Construction of VBDOS curves ................... 50
4 PHOTOEMISSION STUDIES OF VAPOR DEPOSITED AND
SOLUTION DEPOSITED MANGANESE OXIDES AND
SOLUTION DEPOSITED IRON OXIDES ON CARBON FOIL ..... 57

Introduction .................................. 57
Variable Angle XPS (VAXPS) .................... 59
Quantitative Analysis by XPS .................... 61
Preparation of Samples ........................ 64
R results ....................................... 70









CHAPTERS
5 EFFECT OF DISPERSED MANGANESE OXIDES ON THE
DECOMPOSITION OF PERMANGANATE SOLUTIONS........104

Introduction .................................. 104
Kinetics of Reactions .......................... 106
Experim ental ................................. 110
R results ...................................... 118
Correlation of Rate Law Expressions
with Experimental Data ......................... 125
6 CONCLUSIONS AND FUTURE WORK................... 129
APPENDIX
STATISTICAL ANALYSIS OF XPS VALENCE BAND DATA ...........133
REFERENCES .............................................. 135
BIOGRAPHICAL SKETCH ...................................... 139














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CHARACTERIZATION AND CATALYTIC ACTIVITY OF DISPERSED
TRANSITION METAL OXIDE CLUSTERS ON CARBON SUBSTRATES

By

JACK G. DAVIS, JR.

December 1988

Chairperson: Vaneica Y. Young
Major Department: Chemistry
After modification of a CNDO2/U algorithm, a valence band
density of states curve (VBDOS) is constructed from the resulting
eigenvectors and eigenvalues for a distribution of MnO dimer
structures. The resulting curve shows a remarkable similarity to the
X-ray photoelectron spectroscopy (XPS) spectrum of a thick
continuous film of MnO.
In order to investigate the properties of small particles using
XPS, they must be isolated on supports. Different methods of
preparing dispersed oxides on carbon foil supports are investigated.
In particular, vapor and solution deposition are used to fabricate
various transition metal oxides on carbon foil. Vapor deposition is
used to disperse MnO and Mn203 on the carbon substrate and solution
deposition is used to disperse MnO2 and Fe203 on the substrate. Data








acquired by XPS from the samples of both methods indicate that two
completely different surfaces result. Vapor deposition yields a
surface in which the particles are confined to the surface. Solution
deposition yields a surface whereby the particles have been
incorporated into the surface. The electronic structure of these
particles are investigated using valence band photoemission.
When the dispersed Mn oxides on carbon foil are placed in
permanganate solution, it is found that the dispersed MnO has a
greater effect on the autocatalytic decomposition of permanganate
than does dispersed Mn203. It is also found that dispersed Mn203 has
a greater effect on this reaction than either the bulk or continuous
film of the Mn(lll) oxide. Dispersed MnO2 on carbon foil are judged to
have too high an effect on the reaction, possibly because of the
particles which are incorporated into the surface.













CHAPTER 1
INTRODUCTION


Fundamental Principles of X-Ray Photoelectron Spectroscopy



The analytical methodology of X-Ray Photoelectron Spectroscopy
(XPS) is an effective means for the chemical analysis of surfaces. In
XPS, a solid is bombarded with X-Ray radiation, typically of energies
of either 1487 or 1254 eV. Photoemission of electrons from the
surface region of the solid occurs. The ejected photoelectrons are
dispersed according to their kinetic energy (if an electrostatic
analyzer is used) and then counted. The intensity of the signal is a
function of the number of counts at a given kinetic energy.
Conservation of energy requires that

hv= B.E. + K.E. + aspect, (1)


where hv is the energy of the incident X-Ray radiation, B.E. is the
binding energy and K.E. is the kinetic energy of the photoelectron and
aspect is the spectrometer work function. The value of aspect. will
vary from instrument to instrument, thus each instrument must be
calibrated for this quantity. From the measured kinetic energy of the
photoelectron its binding energy can be calculated by

B.E. = hv K.E. aspect. (2)









From the binding energies of photoelectrons, chemical information

can be deduced about the surface.


Electron Detector / .
X-Rays e
Anod / \Sample e \
ee e e \
ee eI-
Filament e e e e e Vacuum

""'
' \^^ Photoelectrons >



Figure 1-1. Schematic Representing Basic XPS Principles.


X-Ray bombardment of a surface can produce another type of

electron other than a photoelectron. Upon the photoemission of an
electron, a vacancy will develop after ejection. An electron with
lower binding energy from another subshell can move in and fill the

vacancy. This movement results in the dissipation of energy which

can cause a third electron, known as an Auger electron, to be

ejected. Auger electrons are denoted by three upper case letters. The
first letter represents the subshell containing the electron which is

ionized by the incident X-Ray radiation, the second represents the

subshell containing the electron which fills the vacancy, and the
third the subshell from which the Auger electron is ejected. The
signal intensity or peak height is affected by parameters which do
not affect the binding energies. One such parameter is the

differential cross section for photoionization [1], which is given by








do(E)/dQ= GT(E)/4 [1 + BP2(cos(0)]. (3)
It is seen that the intensity is a function of the total cross section
for photoionization, which is the probability of observing an
electron of a given energy for ionization, and the angle 0 between
the incident photon beam and the direction of ejection of the
photoelectron. The B term is known as the asymmetry parameter
and is a term which is characteristic of a given molecular orbital.
The value of B indicates what the preferred direction of the
photoelectrons will be with respect to the incident photon beam. If
B=+2 as is the case for a spherically symmetric distribution of
charge (an atomic s orbital), then the phrLtoelectrons will be
preferentially ejected at angles of 900 to the photon beam [1]. For
orbitals having angular momentum (i.e. p, d or f), B values will be
less than +2, which will cause the photoelectron to be preferentially
ejected at different angles. If the intensity is plotted against 0 for
many different values of B it is found that there is a "magic angle"
of 54.70 where the intensity is independent of 0. When
spectrometers are operated at this magic angle, total cross sections
can be used directly in quantitative analysis.


Instrumentation

General Principles

An X-ray photoelectron spectrometer is composed of a x-ray
source, a sample analysis chamber (SAC), an electron or energy
analyzer, and a detector system, which is usually interfaced with a
computer. X-rays are generated by bombarding a material (target)








with high energy electrons. When these electrons impinge upon the
target they knock out its electrons, which creates vacancies. The
photons are generated as a result of the higher energy electrons of
the target filling the vacancies created by the ejection of the lower
energy electrons. This process creates photons of various energies
which then pass through either a Be or an Al window. This acts to
partially filter the bremsstrahlung or x-ray continuum from the
desired Kx rays. Even after filtration, however, only about 50% of

the photons are of the desired energy. The contribution to the
photoelectron spectrum by the bremsstrah ung is not important
because it is distributed over 2 KeV while the Ka rays are

concentrated in a peak of 1eV FWHM [1]. In addition to the Kco 1,2

line, other lines are present due the to difference in energy between
the LII and LIII levels. This difference is important because Ka 3,4

gives satellites in the spectra. With monochromatization it is
possible to reduce the width of Al Kx 1,2 radiation to as little as 0.2

eV [2]. X-ray radiation can be monochromatized by allowing it to
impinge upon a crystal which will cause it to be dispersed. After
dispersion, radiation of a particular energy can be selected by means
of a slit. This method is known as slit filtering. Another method
involves the matching the dispersion of the crystal with that of the
spectrometer. In this technique the X-rays are dispersed by the
crystal before they reach the sample. Their dispersion will cause
the resulting photoelectrons to come out at slightly different
energies, depending on their position along the target. This
dispersion is compensated for by the spectrometer so all electrons
will be ejected as if they came from atomic orbitals having the









same energy [1]. Still another means to reduce the inherent line

width of the radiation is the fine focusing method, which uses a

rotating anode to concentrate the beam before it impinges upon the

crystal. Its advantages are that it gives more photons after

emergence from the monochromator and does not put any

restrictions on the sample. Monochromatization removes those lines

responsible for source satellites in the spectra.


Crystal


Anode


Anode


Sample


Electron
Lens


Sample


Figure 1-2.


Schematics showing different types of
monochromatization.
a) Slit Filtering
b) Dispersion Compensation




















Rotating Sample
Anode

Figure 1-2.--continued
c) Schematic showing the fine focusing method of
monochromatization.


It also removes all of the high energy brehmsstrahlung radiation,
which is responsible for the decomposition of organic samples and
some inorganic salts. The one disadvantage is that there is a large
intensity loss for those instruments which employ a large sample
area like the retarding grid instruments [2]. Figure 1-2 illustrates
the above methods of monochromatization.
To avoid collisions between the X-rays and photoelectrons with
the surrounding gas molecules, it is necessary to contain the source
and sample in a high vacuum sample analysis chamber (SAC). In our
instrument typically pressures as low as 10-9 torr are achieved.
With some degree of effort, namely by placing liquid nitrogen in the
cold trap of the SAC, pressures as low as 5 X 10-11 torr are
possible. The next major component of an X-Ray Photoelectron
Spectrometer is the electron or energy analyzer. Photoelectrons are
generated with a very broad spectrum of energies. Before an electron








with a particular kinetic energy can be counted by the detector
system it must be separated from photoelectrons which have kinetic
energies different from itself. The function of the electron analyzer
is to perform this separation. The spectrum of photoelectron kinetic
energies relative to the sample is not identical to the spectrum of
photoelectron kinetic energies relative to the electron analyzer,
because the sample and the spectrometer share a common ground, as
seen by Figure 1-3. However, they are in one-to-one correspondence,
since they differ by a constant factor, as shown by the following
equations:


Ekin = E'kin + (0sam-0spect)
hv = EbinE + E'kin + 0sam
hv = EbinE + Ekin + aspect.







Sample Electron Analyzer Det.


I I

vacuum ki Ek
level Ekin
Ii vYBcuum level
$am_--_n_ specl Fermi level



Figure 1-3. Diagram showing principles for the calculation of
binding energies.








EbinF is the Fermi level referenced binding energy of the electron in
the sample. Thus, binding energies will be measured correctly only
when the Fermi level of the sample is pinned to the Fermi level of
the spectrometer. This is not possible for insulators, and the
problem is further aggravated by sample charging which results
from the photoemission process. The work function of the
spectrometer is determined by calibrating it with a known standard,
for example, the binding energy of the Au4f electron, which has a
literature value of 83.8 eV. Auxiliary referencing must be employed
for insulators. Most common are the gold decoration technique or
referencing to the Cis contamination peak.
There are three main types of analyzers which perform these
functions. The two most important are the retarding grid and
dispersion types. The retarding grid analyzer forces the electron to
traverse a potential difference between two grids. This analyzer has
a poor resolution and is not employed in any commercial x-ray
photoelectron spectrometer. The dispersive type analyzer, which is
most commonly used today, separates photoelectrons either
according to their momentum or energy by making them traverse
either a magnetic or electrostatic field respectively. The earliest
dispersion analyzers were of the magnetic type. In this type
analyzer, the photoelectrons are sorted according to their
momentum. The equation which relates the magnetic field, with the
path and momentum of the photoelectron is given by


B(po)=mi)/epo.








The magnetic field is B, m and i) are the mass and velocity of the
electron and Po is the radius of the orbit of the electron. Double

focusing can be understood by looking at Figure 1-4. If the
photoelectron enters the analyzer; at an angle 0 to po (the optic

circle), in the xy plane or at an angle g. with respect to the z-axis,
then it will return to the optic circle after it has traversed an angle
of ,'2 or 255 degrees. In other words, the analyzer has the ability
to redirect the deviation of the photoelectron whether it deviates in
or out of the plane of po. The major advantage of the magnetic

dispersion analyzers is that a greater field can be supplied for the
study of high energy (>5000eV) photoelectrons. At this energy
relativistic effects become significant and the optics needed to
study such electrons are better understood for magnetic
instruments[1].








1 ~rmage
OpticeCirde x



^^ Source


Figure 1-4. Principle of Magnetic Double Focusing Electron Analyzer.








One disadvantage of this type analyzer is that of cost. A magnetic
analyzer comparable to an electrostatic one would cost
approximately ten times as much. Another disadvantage of the
magnetic analyzer instruments is their sensitivity to stray
magnetic fields. If a resolution of 0.01% is desired the stray field
must be reduced to 0.1 mG over a very large volume. To achieve this
reduction of stray magnetism, very large compensating coils must
be used. This makes the instrument as a whole very space consuming.
Also, the stray fields must be monitored continuously [2].
Besides magnetic dispersive analyzers, there are also
electrostatic type analyzers, which are more commonly used today
because they cost less to construct and are less cumbersome. Their
principle disadvantage is that they are unsuitable for studies
involving high energy photoelectrons. If one is analyzing electrons
with an eV greater than 2000, relativistic effects become
noticeable. The optics for dealing with these effects are better
understood for magnetic than for electrostatic analyzers. In an
electrostatic analyzer, the photoelectron is dispersed according to
its kinetic energy along a predescribed path. This is done by forcing
the photoelectron to traverse an electrostatic field instead of a
magnetic one. Such a field is achieved by placing a potential between
two plates. The geometry of these plates determines the type of
electrostatic analyzer. Several of the possible geometries of the
plates are hemispherical and cylindrical. In our instrument
hemispherical plates are employed. If we look at Figure 1-5 we can
see a schematic diagram of a hemispherical electron analyzer.
Equation (5) shows the relationship between the voltage between the








plates, the kinetic energy of the photoelectron, and the radius of its

orbit in the analyzer.



Electron Anal Uzer




e.rd..L n--'- /--i Multichennel
Retardeti Dn
Secti on__ __ Detectar


/Semp]e
X -Reus

Figure 1-5. Schematic illustration of electron analyzer with
retardation section.


V=E/e(R2/R 1 -R 1/R2) (5)


This equation states that when a particular voltage is being applied

between the plates, only photoelectrons of a particular kinetic

energy will be able to completely traverse space between the plates
and reach the detector. To measure the kinetic energies of all
photoelectrons which are generated, the voltage is continuously
varied over some specified range, usually with the aid of a computer
which has been interfaced with the system. To reduce or lessen the
tolerances of many of the mechanical components of the
spectrometer, the photoelectron passes through a retardation
section prior to its entry into the analyzer. If the kinetic energy of
the electron is reduced from Ekin to some final EO, the relative








resolution required from the analyzer is reduced from AEkin/Ekin to
AEkin/EO. If, for example, a spectrometer is required to achieve a
resolution of 0.1eV for 10O00eV electrons or 0.01% as the result of
retardation, it would be required to achieve a resolution of 0.1ev for
100eV electrons. Retardation does reduce the intensity of the signal,
however, so a trade-off between intensity and resolution results.
After the photoelectrons have been dispersed according to their
kinetic energies, they must be detected and counted. Almost all
detectors in XPS utilize continuous-dynode electron multipliers of
the "channeltron" type [3-5]. These devices consist of glass tubes
which have been doped with lead and then treated in such a way so
as to leave the surface coated with a semiconducting material with
a very high secondary electron emissive power [3]. A voltage of a
few kV is placed between the ends of these tubes and electron
multiplications of the order 106-108 are achieved by repeated wall
collisions as electrons travel down the inside of the tube [6]. As the
voltage between the plates of the analyzer is swept, the electron
counts at different kinetic energies is usually stored with the aid of
a computer. Computer control is advantageous because it is
desirable to make repeated scans over a spectral region to average
out instrument drifts and to eliminate certain types of noise [6]. In
many cases repeated scans are mandatory. Weak signals can result
due to a small amount of the analyte or if the take-off angle (angle
between the sample and the analyzer about which more will be
covered in a later chapter) is at or near zero. The output from the
electron multiplier can be linked directly to a plotter or printer for
a single continuous sweep. The data system also allows one to








perform peak fits whereby .spectral data can be resolved into
Gaussian or Lorentzian distributions. For example the Oi s spectra
can be resolved into a given number of these distributions which can
then be compared to literature values. By doing so, various chemical
species on the surface which contain oxygen can be deduced. Besides
performing peak fits, it is possible to deconvolute XPS spectra so
as to mathematically remove instrumental linewidth contributions.
This term is not to be confused with peak fit.


Instrument Employed

The instrument utilized for this work is the KRATOS XSAM 800.
This instrument has a dual anode (either Mg or Al can be selected) x-
ray source, a sample analysis chamber which can be pumped on by
either a roughing, turbomolecular, ion, or titanium sublimation type
pump, a hemispherical electron analyzer which includes a
retardation section to reduce the kinetic energy of the
photoelectrons before entering the analyzer, a detector consisting of
a electron multiplier and a data system (A Digital Micro PDP-11
with 256 K bytes of RAM) to control the scanning of the
photoelectrons and to collect and store the data. Peak fits are also
possible at the convenience of the operator.
The X-ray source consists of a filament assembly which is
essentially a tube with tungsten filaments which have been coated
with thorium on either side. The thorium has a lower work function
than the tungsten which makes the emission of electrons more
efficient. The anode is a hollow metal rod with one end open so as








to allow cooling water to pass through and the other end capped
with copper. The copper end resembles a roof with one side plated
with Al and the other side with Mg. To generate x-rays, the
emission stabilizer circuitry is first activated. This is a new circuit
design by KRATOS which is supposed to generate a more stable
emission of electrons from the filaments. After the emission
stabilizer is activated, the high voltage power supply is switched
on. Before this can occur, three safety interlocks must be satisfied.
First, the pressure of the cooling water to the anode must be
sufficient; second, the ion pump to the x-ray source must be on; and
third, the ion gauge must be switched on. If these interlocks are
satisfied, the power can be turned on. The desired voltage of the x-
ray radiation is dialed up. Usually a value of 15kV is selected. The
emission current is selected, and usually a value of 15mA is chosen.
At this point the x-rays can be generated either by computer
command or local command. When the Al anode is selected, the x-
rays have an energy of 1487 eV, and when the Mg anode is chosen,
the radiation is 1254 eV.
The sample analysis chamber (SAC) normally is kept at pressures
between 10-9 to 10-11 torr. To achieve this extremely low
pressure, it must be pumped in stages. First a roughing pump is used
to evacuate the chamber to approximately 0.5 torr. After this
pressure is obtained, a turbomolecular pump is used to bring the
vacuum down to the 10-3 torr region. The ion pump is switched on
and in conjunction with the turbomolecular pump evacuates the
chamber down to 10-6 torr. The valve between the SAC and the
turbomolecular pump is closed and the ion pump brings the vacuum








down to the operating range of 10-9 torr. The specifications of the
machine state that it is capable of reaching a pressure as low as
5X10-11torr. To reach this pressure, however, it is necessary to add
liquid nitrogen to the cold trap in the SAC. This procedure is very
time consuming and is usually not necessary. To improve the
efficiency of the ion pump, it may be used in conjunction with a
titanium sublimation pump.
After the SAC has been pumped down to the 10-9 torr range and
the X-ray source has been activated, data can be acquired. This can
be done with or without computer control. Almost always computer
control is the option chosen. As stated previously the computer is a
Digital Micro PDP-11 with the RT-11 operating system and 256K
bytes of RAM. DS800, the software written by KRATOS, allows the
user to acquire and process data off line. To acquire data, one simply
chooses that option from the master menu which first appears after
the system is booted. After the data acquisition menu appears one
selects the regions) which is (are) to be scanned, the number of
sweeps to be performed in that region and the time allowed for each
sweep. In addition, the operator has the choice of excitation source
(either Al or Mg), low or high magnification, low or high resolution,
and analyzer mode (either FRR or FAT). After the parameters have
been selected, data acquisition can begin. One chooses the run option
and assigns a file name to that run. The file name can be anything
with six or fewer characters. One parameter that the computer
cannot control on our instrument is the angle between the analyzer
and the sample (sometimes referred to as the take off angle). This
has to be adjusted manually. After the data has been collected and








stored, it can be viewed by choosing the off line processing option.
After this option is chosen the data file name is typed in and the
data appears in the form of spectra. The y-axis represents the
intensity of the signal (number of photoelectron counts for a given
kinetic energy) and the x-axis can represent either the binding or
kinetic energy of the photoelectrons. It is also possible to perform
depth profiling, which is done in conjunction with the ion gun. The
ion gun creates argon ions which are directed as a beam to the
sample. The beam strips away successive layers of the sample and
the composition of each layer is determined. One of the
disadvantages of this technique is that it destroys the sample. If one
is using the sample in a catalytic experiment it might be preferable
to use the sample after it has been analyzed. Also, matrix effect
data is not attainable. Very rarely is the analyte going to be
unaffected by the matrix in which it resides. Depth profiling works
from the premise that all of the molecules are going to be sputtered
at an equal rate, which is not the case. For example, in my work with
dispersed manganese dioxide on carbon substrates, one factor which
causes the molecules to be sputtered at different rates is the
difference in the weights between the manganese and carbon atoms.














CHAPTER 2
BACKGROUND OF THEORETICAL RESEARCH UNDERTAKEN


Overview of Molecular Orbital Theory


Fundamental Principles



One aspect of the research that is undertaken here involves the
effect of variation of the molecular geometry of clusters of the
formula (MnO)2 on the XPS valence band density of states (VBDOS).
To show this effect, results of molecular orbital theory are
compared with XPS valence band spectra. This comparison is
possible as a result of the theory of Koopman [7-8], which states
that the negative of an eigenvalue or molecular orbital energy (-6) is
equal to the binding energy (B.E.) of the photoelectron as given by

- = B.E.


By making comparisons between eigenvalues and XPS valence band
data, information can be deduced about the electronic structure of
discontinuous clusters of deposited material on the surface of a
substrate. Using the postulates of quantum mechanics, the
eigenvalues can be obtained from the wavefunction of a system, as
discussed briefly below.








The particle, detected by XPS, can be regarded as a wave, with
the wavelength given by the de Broglie relation given by
mv=p=h/(X)
or X=h/p, (6)

where p is the particle momentum and h is Planck's constant [6].
This wave behavior of the electron can be characterized by a wave
function P(r,t) which contains all the information possible about it
[9]. The Schrodinger equation, which allows eigenvalues to be
extracted from the wavefunction, can be derived from the de Broglie
relationship and the classical time-independent wave equation. It is
given by


ih/4n 2(a/at) I(r,t) = -(h2/8n2m) AP(r,t) + V(r,t)T'(r,t), (7)


where A is the Laplacian operator o2/ax2 + a2/ay2 + a2/az2. This
equation describes the motion of a particle when it is under the
influence of a potential V(r,t). The Laplacian operator and the
potential acting together on W(r,t) form the Hamiltonian operator,
which represents the total energy of the system. The wavefunction
T(r,t) must meet certain conditions, however, in order for the
equation to be valid. These conditions derive from the postulate of
quantum mechanics which states that a system of particles must be
described by a square-integrable function. Thus '(r,t) = T (ql,q2,q3,-
.... W* wi, w2, w3, .*, t), where the q's are the space coordinates, the

w's are the spin coordinates, and t is the time coordinate. T*T is the
probability that the space spin coordinates lie in the volume element








dr (=dti, dr2, -) at time t, if is normalized. To be acceptable the
function must be single valued, nowhere infinite, continuous, with a
piecewise continuous first derivative [8] as seen in Figure 2-1.


a) Not Single Valued


b) Not Continuous


x


c) Has Infinite
Value



x

d) Acceptable




-x


Figure 2-1.


Illustrations of unacceptable and acceptable
wavefunctions.


ii


j00


/00








The more familiar form of the' Schrodinger equation (7) is

HT = ET, (8)
where H is the Hamiltonian operator and E is the energy. Equation (8)
is an example of a class of equations called eigenvalue equations as
shown by


Opf=cf, (9)

where Op is an operator, f is a function called an eigenfunction and c
is a constant called an eigenvalue. Therefore T is an eigenfunction.
In equation (7) V is the potential energy, and the second derivatives
of the wavefunction are related to the kinetic energy. This is so
because the second derivative of P with respect to a given direction
of measure is the rate of change of slope (i.e. the curvature) of P in

that direction. A wave function with more curvature will yield a
greater kinetic energy. This is in agreement with the de Broglie
relationship which states that a wave with a shorter wavelength
will have a greater kinetic energy. Since we have a constant E, the
wave must have more curvature in regions where the potential
energy is low and visa versa [8]. The wavefunctions which are
associated with a particle are related to its momentum by equation
(6). In addition, the wavefunctions are eigenfunctions of the
Schrodinger equation (8) and must meet the conditions which are
illustrated in Figure 2-2. Also, the absolute square of the
wavefunctions (i.e. Il12) is proportional to the probability density
for finding a particle. If is an eigenfunction of equation (8), then
k' is also an eigenfunction, where k is a constant. Since k can be any







number, a problem arises as to which value k should be. Since the
absolute square IT'12 is proportional to the probability density for
finding an electron,




AT HigherE

-=- Lower E

(a)

Ej




(b)
Figure 2-2. Illustration showing relationship between wave
curvature and energy.
(a) When the potential energy V=0, the higher energy
has more curvature (more wiggly). (b) As V increases
the wavefunction becomes less wiggly [8].


then the probability of finding a particle between x=-oo and x=-o
must be 1. The following equation is given by

k*k f I*(x)T(x)dx =1. (10)

If selection of the k multiplier is made such that (10) is satisfied,
then the wave function T' = kT is normalized. If two different







eigenfunctions 'ga, 'b are integrated over x, they must give zero as
a result, as shown by equation (11)


J 'Pa'Pbdx=0. ab (11)


Such wavefunctions are orthogonal. If wavefunctions are normalized
and orthogonal, they are said to be orthonormal.
A second postulate states that when a dynamical variable of an
operator is measured, that the measurement is one of the
eigenvalues of that operator. If a large number of identical systems
have the same function T then the average number of measurements
on the variable M is given by

Mav = J T*MP dr. (if T is normalized) (12)

By linking the postulates together, and knowing the Hamiltonian
operator represents the total energy of the system, the average
value for the energy of a large number of identical systems can be
obtained. This is given by equations (13) and (13a).

E = J W*HT de (if T is normalized) (13)

The bra-ket form of (13) is
E = I H I (13a)

In molecular orbital calculations, the energy of the system is
minimized according to equation (13). Before this can be done
however, it is necessary to formulate the Hamiltonian operator for
the system and the form of the wavefunction T'. To formulate the








Hamiltonian operator, one must account for the total energy of the
system. Terms must be formulated for the kinetic energy of the
electrons, the potential between the electron and the nucleus and
the electrostatic repulsion between electrons. Formulation of these
terms results in an equation given by

n N n n-1 n
H = -(1/2) Ai2 I I ( Zu/r.ti) + I 1/rij. (14)
i=1 I=1 i=1 i=1 j=i+1

The letters i and j are indices for the n electrons and is an index
for the N nuclei. In principle wavefunctions can be symmetric or
antisymmetric. An antisymmetric wavefunction has equal amounts
of area represented by (+) and (-) regions. Symmetric wavefunctions
do not. This principle can be seen in Figure 2-3.

a)







b)





Figure 2-3. Figure showing principle of antisymmetric and
symmetric wavefunctions.
a) antisymmetric; b) symmetric
The Heisenberg uncertainty principle states that the ability to "see"
electrons in an atom would perturb it so strongly that it could not be








assumed to be in the same state after measurement. Therefore there
is no way of distinguishing electron (1) at position rli, from electron
(2) at position r2. If we want to know r, we can only average
together rl and r2. Since we cannot distinguish electron (1) from
electron (2), the wavefunction can not be written as simply the
product of one electron functions 0 of the form

V = 01(1)02(2)03(3)... (15)

Since electrons are fermions, which are particles with half integral
spin, the wavefunctions are required to be antisymmetric with
respect to electron exchange. This behavior is accounted for if the
wavefunctions are written in the form of a Slater determinant [6].
For example, for a two electron system, the wavefunction would be
given by the following equation:


T 1 0 (1) 42 (1)
V4=-
V2 *(2) 0 (2)


The general form for the Slater determinant is

0(1)02(1).... n (1)
1
01(2)02(2) Wn(2)
/n!
01(n)2(v) nn)

In molecular quantum mechanics it is very important to calculate
eigenvectors and eigenvalues which represent electrons moving in a








"self consistent field" or SCF. The reason for this importance is seen
by looking at the last term in the equation for the Hamiltonian
operator (14), which is the interelectronic repulsion operator.
Because electrons repel each other, the electron density is more
diffuse than it would otherwise be. Electron (2) "sees" electron (1)
as a smeared out, time averaged cloud. Electron (2) "sees" electron
(1) as a smeared out, time averaged cloud. Electron (2) is thus
screening the positive nucleus from electron (1). Since the nucleus
is being screened, electron (1) will occupy a less constricted orbital
than it otherwise would. If electron (1) is in a ls orbital, its orbital
as a result of this screening is represented by

Is'(1)= qt3/ir exp(-rl ). (electron (1)) (16)

A numerical value for C, which is related to the screened nuclear
charge seen by electron (1), can be determined. Likewise electron (2)
is being screened by electron (1) in its expanded orbital C. A value
for ' can therefore be determined for electron (2). C' will be
different from C because the shielding of the nucleus by electron (1)
is different from the previous step. Each change in C for electron (1)
necessitates a change in '. This process is continued until the two
values (i.e. C and C') converge. When this happens electrons (1) and (2)
are being screened by the same amount. The potential due to the
nucleus and charge cloud of each electron causes the orbital for each
electron to be self consistent. The electrons move in a self
consistent field [8].








The one electron wavefunction Oi for a molecular orbital must be
expressed in some mathematical form. The manner in which this is
done is to express it as a linear combination of atomic orbitals
(LCAO). If Oi is the molecular orbital it can be expressed by
Oi = I cjixj, (17)
where the Xj's are the atomic orbitals and the cji's are the
coefficients. The coefficients of the atomic orbitals are known as an
eigenvector. The atomic orbitals Xji can be written as a function of
the following variables:
X(r,O,S) =Rnl(r)Ylm(O,O). (18)
The variables r, 8, and 0 are expressed in terms of spherical polar
coordinates as illustrated by Figure 2-4. The Ylm(0,0) part has
angular dependence and is explained by spherical harmonics.
Z
x=r sin8 cos
y=rsin 8 sin r /
z=r cos 8

0 v





x-



Figure 2-4. The relationship between spherical polar (r,e,p) and
cartesian coordinates (x,y,z).
It can further be broken down as exemplified by the equation given
by








YIm(9,0) = Olm(e)Dm(O). (19)


To be sure that the wavefunction will be unchanged if 0 or 0 is
replaced by (0+2n) or (0+2n)the spherical harmonics depend upon the
angular-momentum quantum numbers I and m, which arise in the
solution of differential equations involving angular coordinates 0
and 0. The radial part of the atomic orbital Rnl(r) is a function of
exponential decay function (exp) and can take either the Slater-type
[10] form
rn-1 exp(-Cr) (20)

or the Gaussian type form
rn-1 exp(-r2). (21)


The Slater type orbital is used in the research undertaken in this
dissertation. Slater functions behave better in the region of r=0 and
do not fall off as sharply as do the Gaussian type orbitals [11].
The orbital exponent is a function of how "spread out" the orbital
is. The formula for is given by

S= (Z-s)/n*, where n* is the effective principal number,

s is the screening constant and Z is the atomic number. The greater
the screening by the other electrons, the smaller will be the value of
and the more diffuse the orbital will be. The effect of the value of
CL on the orbital is shown by Figure 2-5.










/ Larger "inner" STO


R(r) /



-Smaller "outer" STO

0/
0 r

Figure 2-5. Schematic showing the effect of the Slater exponent
on the radial portion of an atomic orbital.


Self-Consistent Field Theory

As was mentioned in the previous section, it is necessary to
determine eigenvalues and eigenvectors which are the result of
electrons moving in a self-consistent field. From equation (13), the
energy is obtained by allowing the Hamiltonian operator H to operate
on the probability density {*-'. H can be broken down into a one
electron part Hi and a two electron part H2 as illustrated by

H = Hi + H2. (22)
The one electron part is a function of the kinetic energy of the ith
electron and the potential between that electron and the nucleus. If
summed over all electrons we have
HI = Hcore (p), (23)
P
where Hcore (p) = (-1/2) Ap2 ZArpA-1. (24)
A







The two electron part of equation (22) is H2 = ,. rpq-1 (25)
p
Equation (13a) is given by
E = <'| H IT>,
where E = <'1 Hi IT> + <'1 H21'>. (26)


The wavefunction must be written as a Slater determinant so that
electron exchange can be incorporated into it. Allowing a
permutation operator P to act on the wavefunction is the equivalent
to writing the wavefunction as a Slater determinant. The
expectation value of the one electron operator is


Hii = Jf 'i(1) Hcore "i(1) drli. (27)


The two electron Hamiltonian is a function of the two electron
operator 1/rpg (equation 25). This operator gives the electrostatic
coulomb repulsion energy between two charge clouds [8]. A matrix
element of this electrostatic coulomb repulsion is defined as


Jij = fJf 1i*(1)Wj*(2) (1/rpq) 'k(1)W 1(2) d'rldT2. (28)


The value of this integral represents the repulsion between electron
(1) on orbitals Ti and Wk and electron (2) on orbital Tj and 'F1. Since
the charge clouds are everywhere negative, their product causes J to
be everywhere positive. The entire matrix would represent the
electrostatic repulsions between all orbitals in the molecule
including differential overlap where i*()TWk(1). Another integral








that results from the evaluation of the two electron Hamiltonian is
the exchange integral denoted by K. This integral gives the
interaction between an electron "distribution" and another electron
in the same distribution [8]. The exchange integral is given by


Kij = JJf i*(1) Tj*(2) (1/rpq) 'j(1) Ti(2) dti d'r2. (29)


By collecting terms the formula for the total electronic energy is
given by
n n n n
E = 2 Hii + ,Jii+ I I (2Jij- Kij) (30)
i i i j(i)
and the orbital energies are given by

n
e= H + ,{ 2Jij Kij}. (31)

The derivation of the Fock operator is very complex and it is not
necessary for it to be presented here. If interested in its derivation
consult reference 8 appendix 7. By utilization of the previously
mentioned terms, the Fock operator is given by


F = [Hcore + X(2Jj (1) Kj(1))]. (32)
(1) j
which leads to the following equation in the eigenvector form.

Foi = 4i (33)

Self consistency is achieved by making an initial guess at the
molecular orbitals ij. These MOs are used to construct a Fock








operator, which is used to solve for the new MOs (i.e.()'). These are
then used to construct a new F' and so on until no significant change
is detected. The solutions are said to be self-consistent.


Approximations to Molecular Orbital Theory


Basic Principles of Complete Neglect of Differential Overlap (CNDO)


The SCF principles that were outlined above involve very lengthy
algorithms (some methods have more than 80,000 lines of code) and
as a result, require a considerable amount of computer memory and
CPU time in order to execute. As a result, approximations have been
applied to SCF principles. Thus considerably shorter codes (typically
between 1200-1600 lines) requiring less computer memory are
obtained. One of the best known examples of approximate molecular
orbital theory is complete neglect of differential overlap (CNDO)
written by John A. Pople and associates in 1965 [12-13]. Such an
approximate method is also referred to as semiempirical because
the eigenvectors and eigenvalues no longer result solely from the
principles of quantum mechanics. Experimental data is used in the
formulation of the Fock matrix.
The first approximation in CNDO which is applied to SCF theory
applies to the formulation of the overlap integral matrix. This
matrix is composed of values which show the degree of overlap
between the various atomic orbitals in the molecule. The
approximation consists of replacing the overlap matrix by a unit








matrix whereby all elements are zero except the diagonal elements
which are 1. In the normalization of Roothaan's equations J.(FIO-
eSgi)C'Ui = 0 [14]. By ignoring differential overlap, S -u =0 for Iu In
other words, the atomic orbitals are treated as if they were
orthogonal and as a result, the Roothaan equations reduce to
X FgCu = eiCgi where Fg is the Fock operator, C-ui is the
eigenvector or coefficients to the same atomic orbital as the Fock
operator and the Ei's are the eigenvalues or molecular orbital
energies. This approximation becomes more severe as the
internuclear distance decreases, however, because it causes larger
and larger electron populations to be ignored. The second
approximation results in a simplification of equation (28), which
computes the matrix elements of the electrostatic coulomb
repulsion between charge clouds. The approximation neglects all
differential overlaps in two electrons integrals. Differential overlap
occurs when i*(l1)Pj(1)0, where probability density is coming
from electron (1) over orbitals i and j. Such electron densities are
exceedingly numerous and also exceedingly small. Ignoring
differential overlap means than equation (28) vanishes unless i=k
and j=l. This has the obvious benefit of reducing the number of
integrals that need to be evaluated. The third approximation, which
results from the second, is to reduce the number of coulomb
repulsions to one value per atom pair. Differential overlap can be
monoatomic, where iYk is on the same atom or diatomic where
'PiFk is on different atoms. For the monoatomic case neglect of
differential overlap causes invariance of rotation to be negated. This
means that rotation of an atom with respect to another atom will








result in a different set of eigenvalues and eigenvectors. To restore
invariance, there is an additional approximation made. The remaining
two electrons integrals will not be dependent upon the nature of the
atomic orbitals, but on the atoms to which Tj and k belong [11].
This can be shown as

(iilkk) = FAB for all i on atom A and for all k on atom B.

r'AB is the average electrostatic repulsion between any electron on
atom A and any on atom B [11]. The value of FAB is given by

FAB = ifJ SA2(1) (1/r12) SB2(2) dtldt2. (34)

As equation (34) shows all orbitals are taken to be of the "s" type.
The fourth approximation is to neglect differential overlap in the
interaction integrals involving the cores of other atoms where


(i|VBjk) = VAB if i=k. If ick the integral vanishes.

VAB is the interaction between any electron on atom A with the
core of atom B. Therefore, any differential overlap between two
atomic orbitals on atom A will be ignored in the calculation of this
interaction.
The last approximation made in CNDO is to allow off diagonal
matrix elements in the Hamiltonian to be proportional to the
overlap integrals. This is shown by


Hik = P3ABOSik,


(35)








where PABo is the bonding parameter, which is characteristic of a
particular atom. As the overlap increases, the bonding capacity of
the overlap will increase [11]. With all these approximations, the
Fock matrix elements can be computed and are given by


Fgg = Ugt + ( PAA 1/2 Pg) FAA + (PBB FAB VAB) and (36)
B(AA)
Fgu = P3ABOS u 1/2 Pp) FAB. I,u (37)


Equation (36) can be rearranged into
Fjj = Utg + (PAA 1/2 Pgg) FAA + [-QB FAB + (ZB FAB VAB)]
B(A)
(38)
and the total energy can then be derived. This is shown by


E Total = (1/2) Pg (Hg + Fl) + _,ZAZBRAB-1. (38a)
Ilv A To achieve self-consistency an initial guess is made of the
molecular orbital coefficients. The diagonal elements of the Fock
matrix (i.e. Fg) come from experimental values for the ionization
potentials ( i.e. Ug in equation (38)). The off diagonal elements (i.e.
FgI)) are replaced by PABOSgu. The electrons are then assigned to
M.O.s with the lowest energy (i.e. lowest eigenvalues). The density
matrix, which is given by
OCC
PU = c icJ)i, (39)
i
is calculated from the coefficients of the occupied atomic orbitals.
This matrix is used to formulate a new Fock matrix Fg). When the

Fock matrix is diagonalized a new set of eigenvectors and








eigenvalues are produced. They are then used to reassign the
electrons in pairs to the molecular orbitals with the lowest energy
and to construct a new density matrix. These steps are repeated
until self-consistency is achieved [11]. Figure 2-6 shows the effect
of self consistency upon the radial part of a wavefunction. This
program utilizes the modifications made in the second
parameterization of CNDO. These modifications include the
incorporation of the "zero penetration effect" which equates the last
term in parenthesis in equation (38) to zero and the replacement of
the ionization potentials in the UlI term with the average of the
ionization potential and the electron affinity (i.e. -1/2 (lg + A )).


CND02/U

A relatively new CNDO algorithm was selected for this project.
Unlike the version written by Pople et al., [12,13] this program is
parameterized for the first 81 elements of the periodic table. This
is possible by the utilization of the concept of "fictitious atoms,"
whereby those elements which have their valence electrons
distributed over two or more subshells with different principal
quantum numbers, are treated as two or more atoms which are
centered at the same coordinate. Figure 2-7 illustrates this
principle.







(before SCF determination)


4n2 y2








Figure 2-6.


Effect of SCF calculation upon the electron distribution.


Although this program retains the concepts outlined in the
previous section, one of the major differences between this
program and the earlier version is in the formulation of the
coulomb repulsion matrix.





(F~kl 3d


Figure 2-7.


First Row Transition Element
Illustration of how a first row transition element is
treated in CNDO2/U.








From the last section it was stated that there is one matrix element
calculated per atom pair. However for a first row transition element
there are ns and (n-1) d valence electrons. It therefore would be
necessary to calculate the following r values:


F (n-1)d (n-1)d ; r(n-1)d ns ; Fns ns.

In addition to this modification in the formulation of the coulomb
integral matrix, there is also a modification in the calculation of
the atomic energies of transition type elements. Since the transition
element is considered to be two atoms it is necessary to calculate
two atomic energies for each atom. The equation used is given by

AE = s*ENEG(s) + p*ENEG(p) + (TE2 r(l,l)/2.) + d*ENEG(d). (40)

where AE equals the atomic energy, ENEG is the average of the
ionization potential and the electron affinity for the respective
subshell. TE equals the total number of electrons and s, p, and d
equal the number of s, p, and d electrons, respectively.













CHAPTER 3
THE EFFECT OF VARIATION OF MOLECULAR GEOMETRY OF A
TRANSITION METAL OXIDE CLUSTER ON THE VALENCE BAND DENSITY
OF STATES


Background


Dispersed particles or clusters, which usually have catalytic
properties on inert substrates such as carbon, silica, or aluminum
oxide, have been the focus of much investigation [15-26].
Investigations have focused primarily on their electronic structure-
experimentally, through the use of electron spectroscopy and
theoretically, through various molecular orbital algorithms. The
electronic structure of these deposited clusters can be investigated
by observing the shifts in binding energy of the main photoelectron
peaks in the relevant core regions and through acquisition of valence
band spectra. It has been reported in a study on the electronic
structure of catalytic metal clusters (i.e. Pd and Pt) that the valence
band undergoes a narrowing and a shift away from the Fermi level
relative to the bulk metal as the metal clusters become more highly
dispersed [27]. Unlike dispersed metals on inert substrates,
relatively little attention has been paid to the electronic structure
of dispersed metal oxides on inert substrates. As a result, the
electronic structure of dispersed and bulk like MnO on carbon foil
has been performed by Zhao and Young [28]. It was determined that



























Figure 3-1.


Comparison of spectra of highly dispersed and
continuous film of MnO on carbon foil.
a) The valence band spectrum of highly dispersed MnO on
carbon foil.
b) The valence band spectrum of a thick continuous film
of MnO on carbon foil.





40







a)







b)




I Ii


15 10 5 0 -5

B.E. (eV)









for highly dispersed MnO on carbon foil (a coverage of 0.22) the
valence band undergoes a narrowing and a shift in its binding energy
away from the Fermi level relative to bulk material, as can be seen
in Figure 3-1. In the case of supported metal particles, this behavior
led to investigations which sought to correlate XPS valence band
behavior with results from molecular orbital (M.O.) algorithms to
determine the minimum or threshold number of atoms required for a
cluster to exhibit properties of the bulk material. For example, R.C.
Baetzold et al. performed an investigation into the determination of
the particle size required for bulk metallic properties [29]. Extended
Huckel calculations were performed on clusters with face-centered
cubic (fcc) geometry of sizes ranging from 13 to 79 atoms. The
results from the calculations were used to construct valence band
density of state curves and the width of the d band was determined.
For the largest cluster size (i.e. 79) it was determined that the d
bandwidth was 86% of that for the bulk material and for a cluster of
13 atoms the d bandwidth was 50% of that of the bulk material.
Table 3-1 shows the results.


Table 3-1
Comparison of d bandwidths with cluster size


cluster Pd2 Pdl 3 Pd3l Pd55 Pd79 Bulk Pd

d band-
width 0.80 1.54 2.26 2.57 2.65 3.08








What is done can be summed .up by the following statement. For (M)x,
where X=1,2,3,4 *** and where M is some monomer unit, as X is
increased the electronic structure evolves to that of the bulk
material. In Baetzold's study the selection of one geometry (i.e. fcc)
for all cluster sizes is arbitrary. It seems reasonable that when a
substance is deposited either fractionally or partially on a substrate
that it will not form the same geometry for all possible values of X.
The goal of this research project is to see what effect the variation
of the molecular geometry for a given cluster size would have on the
valence band density of states (VBDOS). Could a "bulk like" VBDOS
curve be constructed by variation of the smallest possible cluster
size for MnO, namely (MnO)2 ?
As was mentioned briefly at the beginning of chapter 2, the
binding energy of the photoelectron is linked to eigenvalues derived
from molecular orbital theory by the rule of Koopman [7-8], which
can be represented by


-C (eigenvalue)= binding energy of the photoelectron. (41)


This rule is not entirely correct, however, because it is based on an
incorrect assumption-that the orbitals remain frozen orbitals
during photoemission. This is a "static" approximation. In actuality
the remaining electrons "relax" towards the site of photoemission
because of reduced screening of the nuclear charge. This relaxation
imparts a certain amount of kinetic energy to the ejected electron,
thus reducing its binding energy. If comparisons are being made
between clusters of different size, where the extent of relaxation is








different, this limitation of Koopman's rule could be a problem. In
addition, the rule of Koopman also neglects correlation energy,
which is due to electron repulsion. Since we are interested in the
relative eigenvalues for clusters where the number of atoms is held
constant, this limitation should not be a problem.


Modification of CNDO/2U Algorithm


In this work, the semiempirical molecular orbital method of
CNDO/2U [30] is utilized to determine the eigenvectors and
eigenvalues. This method treats the valence electrons as Slater
orbitals and used parameters which are fitted empirically [1]. This
new version of CNDO can be utilized on any element in the periodic
table whose atomic number is less than or equal to 81. One
fundamental difference between this method and the Pople method is
the way it treats elements whose valence electrons are distributed
over different subshells with different principal quantum numbers,
which is illustrated by Figure 2-7. The molecule TO for example,
where T is a transition element, would be treated as three atoms
with T accounting for two of them at the same coordinate. If this
treatment were carried over to the Lanthanides, where the valence
electrons are dispersed over three subshells, we would have three
atoms at the same coordinate (i.e. T(n-2)f, T(n-1)d, and Tn) [30].
Before the eigenvalues and eigenvectors of the various geometries
of (MnO)2 could be determined, it was necessary to check the
accuracy of the program by determining its ability to calculate
dissociation energies of various diatomic molecules. The author








performed such calculations, which are listed in Tables 3-2 and 3-3.
For those diatomic molecules which contain no transition elements,
most of the calculated dissociation energies are in good agreement
with experimental values, as seen in Table 3-2. When the
dissociation energies of diatomics which contained either one or
two transition elements are determined, there is very poor
agreement between the calculated results and experimental values,
as shown in Table 3-3. These results indicated that there is a
problem in the way transition elements are treated. It was decided
to modify those areas of the program which are a manifestation of
treating the transition element as two atoms centered at one
coordinate. One such area which needs to be modified is the
computation of the atomic energies.
In M.O. theory the atomic energy is related to the dissociation
energy by
Edissoc = Ebond = Etot Eatomic. (42)

Table 3-2
Bond Energies and Lengths of Selected Diatomic Molecules.


AB Bond Length Exp.a Dissociation Energy Exp.a
(A) (eV)
HF 1.00 0.92 -6.01 -5.90
LiH 1.54 1.60 -6.71 -2.50
IH 1.63 1.61 -4.47 -3.09
CO 1.22 1.13 -21.96 -11.09
SnO 2.25 1.84 -1.46 -5.46

a) Ref [30] -









Table 3-3
Bond Energies and Lengths of Selected Diatomic Molecules which
Contain one or more Transition Elements.

AB Bond Length Exp. Dissociation Energy Exp.a
(A) (eV)

Mn2 2.8 3.4b -286.18 -0.23
FeO 1.58 1.57 a -142.17 -4.20
FeS 1.90 -149.5 -3.31
MnBr 2.3 -108. -3.22
Fe2 2.7 -179.24 -1.06

a) Ref. [31] b) Ref. [32]


Since the transition element is being treated as two atoms it is
necessary to compute two atomic energies, as shown by

AE= s*ENEG(s) + p*ENEG(p) + (TE2 *F(l,l)/2) + d*ENEG(d). (43)

The ENEG terms are equal to the average of the ionization potential
and the electron affinity of the respective subshell. TE is the total
number of electrons and s,p, and d are the number of s,p, and d
electrons respectively. The r(l,l) term is the monocenter coulomb
repulsion for either the s or d subshell. The total atomic energy is
then computed by adding the "atomic energy" of the s and d shells
together. The program is modified to compute one atomic element
per transition atom and this is done by determining the probability








of a valence electron being either an s (i.e. s/TE) or a d (i.e. d/TE).
The equation utilized is

AE = s*ENEG(s) +p*ENEG(p) +((s/TE)*TE2 F(l,l)/2.) + ((d/TE)*TE2*
F(I,I)/2.) + d*ENEG(d). (44)

The effect of this modification on the diatomic molecules containing
transition elements is shown in Table 3-4. The reason that these
diatomics are chosen to test the accuracy of the program is that
they represent the two types of bonds that are encountered when the
eigenvectors and eigenvalues of the (MnO)2 cluster are being
determined (i.e. the T-T and T-O types where T is a transition
element).
Table 3-4
Results of atomic energy modification to CNDO/2U on selected
diatomics which contain one or more transition elements.


AB Bond Length(A) Dissociation Energy (eV) Exp.(eV)


FeO 1.58 40.9 -4.20
Mn2 2.80 1.0 -0.23
MnO 1.70 38.0 -3.70
Fe2 3.0 -4.52 -1.06
FeS 1.90 33.02 -3.31
MnS 2.00 30.9 -2.85


For molecules representing the T-T bond, (i.e. Mn2 and Fe2) there is
good agreement between data and calculated results. For molecules








representing the T-O type bond however, there is poor agreement.
This makes it necessary to modify the program so that it calculates
a lower total energy for T-0 and T-S bonds.
Another part of the algorithm which can be modified is that part
which computes the coulomb repulsion matrix. This matrix is a set
of values which represent the electrostatic repulsion between the
charge clouds occupied by the electrons in the system. Equation (28)
is the formula for the electrostatic repulsion between electrons (1)
and (2) distributed over orbitals i,j,k and I. When the approximations
of CNDO are applied to (28), equation (34) results. CNDO calculates
the average electrostatic repulsion between any electron on atom A
and any electron on atom B instead of the electrostatic repulsion
between orbitals. Therefore, one matrix element is calculated per
atom pair. For a T-O type molecule the following 3X3 coulomb
matrix is formulated.


0 4s 3d
0 Foo F04s F03d
4s FO4s F4s4s F3d4s
3d FO03d r4s3d F3d3d

and for a T-T type atom the following 4X4 matrix is formulated.

4s 3d 4s 3d
4s F4s4s F3d4s F4s4s F4s3d
3d F4s3d F3d3d F3d4s F3d3d
4s F4s4s F3d4s [4s4s F4s3d
3d r4s3d F3d3d F4s3d F3d3d








The relationship between' the electronic energy and the coulomb
integral matrix elements are seen by the equations derived from
CNDO approximations to SCF theory (i.e. equations 38 and 38a). The
term (ZBFAB-VAB), which represents the potential difference
between the core ( the nucleus and non-valence electrons) and the
valence electrons of atom B, is set to zero as a result of CNDO
approximations. A valence electron on atom A experiences no
potential difference between these components of atom B, thus the
possibility of its penetration into B is eliminated. Such a
penetration would lead to a net attraction yielding a lower bond and
dissociation energy between A and B. To modify the program so that
a greater net attraction between A and B is realized, the term-
QBFAB is modified. This term represents the effect of the potential
due to the total charge on atom B [11]. If FAB is increased, the
potential due to atom B (i.e. Mn or Fe) will be more negative. This
increase would have the same effect as increasing VAB which would
make the potential of the core of B greater than the valence
electrons of B. This should then cause a greater net attraction
between A and B to develop, which is what is desired. By looking at
the first matrix, it can be seen that FAB are represented by 1O3d
and rO4s, both of which are bicenter. The problem is to determine
by how much these elements should be increased. Possibilities exist
that the best results might be obtained by multiplying the FO4s and
f03d by the same or different amounts. By the process of trial and
error it has been determined that if each r value is multiplied by
1.1, the best fit between dissociation energy, ionization potential
and equilibrium bond distance results. After applying the above








corrections to the original program, the values shown in Table 3-5
result. Increasing the bicenter matrix elements of a T-O molecule
should have the effect of increasing the electron population in the
overlap between the oxygen and the d orbitals of the transition
element. This is substantiated by looking at the population matrix,
calculated from the equation
ocC
PgU = 2 ,c*gi c-i, (45)
i


where the c's are the coefficients of the atomic orbitals. This
matrix does indeed show an increased electron population in the
overlap between the oxygen and the d orbitals.

Table 3-5
Final values for the bond lengths, dissociation energies and
ionization potentials of selected diatomics after the atomic energy
and coulomb integral modifications were made to CNDO/2U.

Bond Ionization Dissociation
AB Length Exp. Potential Exp. Energy Exp.
(A) (eV) (eV)


FeO 1.40 1.57b -11.69 -8.71 a -6.77 -4.20

FeS 1.90 -5.02 -0.50 -3.70

Mn2 2.80 3.4e -7.08 -6.9c 1.00 -0.23

MnO 1.45 1.77b -8.06 -5.68 -3.70

Fe2 3.00 -16.09 -6.30e -4.52 -1.06

MnS 1.80 -11.53 -10.16 -2.85


C) Ref [34] d) Ref [35] e) Ref [32]


a) Ref [33] b) Ref [31]









Construction of VBDOS curves


After the modifications were made to the program it was then
possible to begin the acquisition of the eigenvalues and eigenvectors
of various geometries of the formula (MnO)2. In order for the
eigenvalues and eigenvectors of a given geometry to qualify for
comparison with XPS valence band spectra, it is necessary for that
geometry to pass the self consistency test-i.e. two successive
iterations of the total electronic energy must agree to within 0.01
eV. To pass this test it was necessary that the program calculated a
total electronic energy that was within 0.01eV of the previous
value. The determination of suitable geometries was like the
coulomb matrix modification, a trial and error process, but after a
long and arduous process, six suitable geometries were found, which
are illustrated by Figure 3-2.


Mn- 0O--- Mn-0 -
Linear Rectangular

0 \n

Mn Mn M Tetrahedral
Semicircular 1 r
0
0 n

Mn 0 Mn-

Cross Mn Angular Mn--- 0


Suitable geometries for cluster (MnO)2.


Figure 3-2.








After these geometries were determined, it was necessary to
construct valence band density of states (VBDOS) curves from the
eigenvalues and eigenvectors of each geometry. VBDOS curves are
constructed by centering a Gaussian distribution function about each
eigenvalue which has a FWHM of 0.85 eV (the natural line with for
AIKa( radiation is this value) and then summing them over some
specified energy range. The relative heights of the Gaussian
distribution functions are determined by the following formula.

Ht. of Gaussian = Z c2ij aj (46)
j

The cij 's are the coefficients of the atomic orbitals and the aj's are
the Scofield cross sections [36]. A VBDOS curve has been
constructed for each of the geometries shown in Figure 3-2. Figure
3-3 illustrates these VBDOS curves. Weighted distributions of these
geometries can be used to construct composites. These simulate the
effect of having active sites on the substrate surface which
stabilize different geometrical configurations of the clusters. The
weights simulate the relative fraction of each type of site on the
surface. One such composite, which can be seen by Figure 3-4,
shows a remarkable agreement with the lineshape obtained for very
thick MnO supported on carbon foil. Although there is no evidence
for "geometry' selective active sites on the supports normally used
for heterogeneous catalysts, there is also no evidence against such
sites. Based on Figure 3-4, the variation in the molecular geometry
for a given value of X does have an effect on the VBDOS. Valence band
broadening is not only due to an increase in the number of atoms in a





52

cluster, but can also be due to the formation of a distribution of
geometries of different stability on the surface. Thus a meaningful
interpretation of the experimental VBDOS curves of supported metal
oxide particles cannot be made without supplementary information
on the particle size distribution.




























c
C)

0)
U)
c
0

L-
0

U)

0


4-
U)


0


U)
.-













c
0C%

am
VU)





CM
cuo













...
0 0
(D -
(o 0
>




CO




uT-

































U 0
AD















I. .t".














0
0 *. O
















.o
"- "" 0 0-
i- ) (q 07













cV




(9


.0
>1-














L
L 4J






oEn
4i-- 0



E 40D
I-J

a

'7 C,1 at(9 "
0000 ?




c I V





9^ 00


4?
c (D










0





0<
















C.
u 8. cr-^.u 0"




















I-I


.0


(9
10 C9 in 10' 0i -










co . .07
(M -

















~~0

c E
v C8
Lnr^ ul 'n us U) 'n o








00
a ;

























Figure 3-4.


Valence band density of states of a calculated (MnO)2
composite compared to spectrum of a continuous film
of MnO.














)Calculated
Composite


-18 -1G -14 -12 -10 -8 -G -4


b) XPS
of


Spectra
bulk MnO


-14 -12 -b -6 -4 -2 0













CHAPTER 4
PHOTOEMISSION STUDIES OF VAPOR DEPOSITED AND SOLUTION
DEPOSITED MANGANESE OXIDES AND SOLUTION DEPOSITED IRON
OXIDES ON CARBON FOIL


Introduction


A large number of heterogeneous catalysts are composed of a
material (e.g. a metal like Pt or Pd) which has been dispersed upon
an inert support like silica, alumina, or carbon. These dispersed
substances can be characterized by x-ray photoelectron
spectroscopy. More specifically, XPS can be used to determine the
relative concentrations of the various constituents and the relative
particle size distributions of the supported material. The relative
concentrations of the various constituents on a surface are
determined by determining the relative peak areas of the
constituents concerned. This then allows a value for the number
atom ratio of one constituent atom to another to be computed. The
effect of differences in the relative particle size distributions of
the supported material can be qualitatively determined from shifts
in binding energy within a given region. Such effects may be
observed in both the core level regions and in the valence band
regions. Valence band distribution narrowing is one of the most
dramatic changes which can occur. Zhao and Young [28] prepared
carbon surfaces containing submonolayers of MnO, as confirmed by








the relative concentrations' of the constituents on the surface.
Changes in the electronic structure which accompany reduction in
the particle size distributions are determined for the highly
dispersed MnO by comparing its valence band region with that of the
bulk oxide. In that investigation, the oxide was prepared by vapor
deposition. The number atom ratios calculated from XPS data
indicated a low coverage ( represented by D) for the dispersed oxide
(the assumption is made that the lower the coverage value, the more
highly dispersed is the oxide). It is also shown that it is possible to
form a thick continuous film of the oxide on the carbon foil when a
number atom ratio (i.e. NMn/(NC+NMn)) of 1.0 is achieved at take off
angles between 0 and 50 degrees. The effect of changes in the
particle size distribution consisted of shifts in the position of the
maximum of core, Auger and valence level spectra and a narrowing
of the valence band level. This chapter will report results of similar
experiments on other dispersed oxides of manganese and on
dispersed ferric oxide. These characterizations are based on data
acquired from samples prepared by vapor deposition and solution
deposition. Because in solution deposition it might be possible for
the oxide particles to diffuse in from the edge of the carbon foil, it
is necessary to also perform quantitative analyses of samples
which have had 0 edges, 1 edge and 2 edges directly exposed to the
solution which is used in the solution deposition method in addition
to the normal sample which has 4 edges directly exposed.








Variable Angle XPS (VAXPS)

In the introduction of this chapter the term take off angle is
mentioned. The take off angle is the angle between the electron
analyzer and the sample, which is commonly denoted by the Greek
letter 0. The angle 0 is varied in almost any quantitative analysis
undertaken, because its variation causes a variation in the effective
mean electron escape depth, which is more commonly referred to as
the probe depth. The mean electron escape depth is the average
distance a photoelectron will travel before it undergoes an inelastic
collision, a collision whereby it looses energy from the initial
energy acquired from the photoemission process. Unfortunately
inelastic collision is the fate that awaits most photoelectrons
which are generated. This is what severely limits the depth that one
can investigate in XPS.
/,




-, -







Figure 4-1. Schematic showing the attenuation of the incident x-ray
radiation. The distance the photoelectron can travel
before it suffers inelastic collision is quite short
compared to the distance the x-ray can travel.








This is illustrated schematically in Figure 4-1. The distance the x-
rays can travel into the solid is much greater than the
photoelectrons can travel. The relationship between the mean and
the effective mean electron escape depth is illustrated in Figure 4-
2. Even though the mean electron escape depth is constant, the probe
depth, or the effective mean electron escape depth becomes smaller
as the take off angle becomes smaller until at a take off angle of 0
degrees, the photoelectrons generated are originating from the top
monolayers of atoms only. Conversely at a take off angle of 90
degrees, the spectra that are obtained are the most "bulklike". The
value of the effective mean electron escape depth depends upon the
substance that is being analyzed. For metals this depth can be as
small as 10 Angstroms. To change the take off angle in the KRATOS
XSAM 800, one simply rotates the sample probe.



To analyzer
X-Rays \ /



mean electron / effective mean electron
escape depth A8 -escape depth
(MEED) (EMEED)

EMEED = MEED*SIN 8

Figure 4-2. Diagram showing the relationship between the take off
angle and the effective mean electron escape depth.








Quantitative Analysis by XPS


XPS investigations often require that the relative concentrations
of the various components of a surface be determined. If one
averages over depth, then these relative concentrations can be
expressed as number atom ratios (i.e. Nx/Ny) which can be
calculated from the following equation.

Nx,i/Ny,j = (lx,i/ly,j) (oy,j/ax,i) (Xy(Ej)/Xx(Ei)) (F(Ej,Ea)/F(Ei,Ea))-
(T(Ej/Ea)/T(Ei,Ea)) (47)

The I's are the time normalized intensity ratios, the a's are the
asymmetry corrected photoionization cross sections, Ei and Ej are
the kinetic energies of photoelectrons i and j respectively and Ea is
the analyzer pass energy. The subscripts x and y are the specific
elements and subscripts i and j represent specific levels in x and y
respectively [37]. X(Ei) is the inelastic mean escape depth, F(Ei,Ea)
is the electron optical factor and T(Ei,Ea) is the analyzer
transmission function. Fortunately experimentation has given
results which allows equation 47 to be simplified. It has been shown
that the product of the electron optical factor, the analyzer
transmission function and the inelastic mean escape depth cancel
each other [38]. The simplified form of equation 47 is


Nx,i/Ny,i=(Ix,i/ly,i)(ay,i/ax,i)


(48)








If the elements x and y have not been recorded with identical
window widths, then the window width must be incorporated into
equation 48.

Nx,i/Ny,i = (Ix,i/lyi) (oy,i/ax,i) (Wx/Wy) (49)

The number atom ratio evaluated at 0=0 degrees is an estimate of
the coverage (0). The determination of the relative concentrations
of the various constituents of a sample is made relatively simple
with the DS800 software. After the spectra are acquired, the
operator constructs the desired window that needs to be quantified
and then simply types either "Q/A" or "Q/I" at the prompt, where
"Q/A" means quantify area and "Q/I" means quantify intensity. To
quantify area, "The peak area is calculated by summing the counts at
all energies within the appropriate window, multiplying by the
energy step between the channels and dividing by the total time
spent acquiring each channel (i.e. the dwell time)" [39]. The
quantification of peak intensity is determined by computing the
difference between the most intense and the least intense channels
within the spectral window, which is divided by the dwell time. The
dwell time is another name for time normalization that was
mentioned at the beginning of this section. Time normalization
ensures that the quantities obtained are not affected by the
operators choice of acquisition parameters. The atomic
concentration % is then calculated from equation (50).

[(xi/qi)/ Y (xi/qi)] X 100. (50)








The variable xi is the ratio .of the raw area/intensity of the ith peak
and qi is the corresponding quantification factor (i.e. related to a
which was discussed earlier). The quantification factor or a is a
term which is a manifestation of how sensitive the instrument is to
an electron in a particular orbital. The quantification factor is a
function of the size of the atomic orbital.
Not only is the relative concentration of elemental constituents
which comprise a surface desired, but also the relative
concentrations of different chemical species which are contributing
to a given spectral window (i.e. Ols, Cls). Analysis of a given
photoelectron peak is achieved by peak fitting a number of different
symmetrical line shape functions (either Gaussian or Lorentzian) to
the peak. With the DS 800 software it is possible to express a
distribution as a combination of a Gaussian and Lorentzian function.
The distribution can be made to have as much as 50% Lorentzian
character. To fit these distribution functions to a photoelectron
peak, it is first necessary to construct a synthetic window (a
different type of window than needed to determine the relative
atomic concentrations). The synthetic window is first constructed
by typing "syn" at the prompt. After the operator states the name of
the window (i.e. Clis, Ols etc.) the cursor appears and the window
width is determined by pressing the space bar at the desired
positions (in eV) at the beginning and the end of the window. After
the window is formed a table appears which requires the operator to
state what type(s) of functions) are to be fit, (i.e. either Gaussian
or Lorentzian or combinations thereof), the element IDs, the
positions of maximum intensity of the component distributions and








the beginning and ending of a given distribution. Some degree of
estimation and guesswork is required here and it takes practice for
the operator to become proficient. In addition the operator can
require the computer to fit a given distribution to within a given
FWHM. After this is done, the interactive synthesis option is
selected and the spectral window that the peak fit is being
performed upon appears in the upper right portion of the display that
appears. The background is subtracted out and the distributions that
the operator selects appear under the photoelectron peak. The degree
of fit is displayed, which at this point is usually very high. Next,
the autofit command is utilized by typing "au" at the prompt. The
computer fits the distributions selected to the peak, calculates the
final fit value and displays it. The lower the value of the fit, the
better it is. Figure 4-3 is an example of four distributions being fit
to the 01 s region of four year old carbon foil, for which the 01 s
contamination can not be completely eliminated.

Preparation of Samples


As is mentioned in the introduction section of this chapter,
vapor and solution deposition are utilized to prepare dispersed
manganese oxides on carbon foil, while the ferric oxide samples are
prepared by solution deposition only. To vapor deposit a manganese
oxide onto carbon foil, it is first necessary to vaporize the
manganese. Vaporization of the manganese is achieved by heating it
resistively in a tungsten filament basket. The vapor produced is
allowed to impinge upon a piece of carbon foil which is cut into a

























0 -

-C)
L..

C 0
o^




c0
(0 0
~o.



%e C

j) 0)
o ct )


~c
0) C


.-- c 70
a. c


:t-_
o CL







4-
S0)_
0 M.C
0 C-) 0)





OCZ
00







C)
E4






66





OJ

Co
'-Ii
k--
/ /

if If)
S'.-



c u '. T. LO
-- r O


OLD I I T al
/. O. "*- ,,o[ CO


o ? I
LL.







r
a ,. P) -.--' O






0-- a- c,. In . .
CK'


.LO ," J--) ,- .-



LL (n "- C#.
w- ID Iy P
ut












3) C: LO .,O U- . .
0 a -. ..


co



0~~~I "l 0 d,'


L 0 0 0 0 0
u-. ,,- m L .C
-J _n li m L C : ,1 z
C) c0 # -4 o m m
_j -n -1 r-4 mU cr <
ii. ~~ ~ Sn S- **i oc 'i
co Icu '-j.C c '-4in in I
2w i ni r-^ LL
0) 0 *-r
CC, .o. c *
o cui ~ r '-4 C') tf '4) 0
0l If) 3)i IJ ) 0 f 0 00
o; ** ***
1x1 I3 nN t-C **;** il> C') C') C') Cf
C'Ct i )J Ll 0 C S lb3 3
0)- LL- 0 r- 'A -< | < CT Ci








rectangle with dimensions of, approximately 1 cm X 1.2 cm. This is
done in a sample analysis chamber of a Hewlett Packard X-ray
photoelectron spectrometer at a base pressure of ~ 10-7 torr. Figure
4-4 illustrates that after the Mn is vaporized, it reacts with oxygen
to form either the Mn(ll) or Mn(lll) oxide, depending upon the
reaction conditions. These samples are outgassed by heating them
to 235 C for 20 minutes before recording spectra. If there is any
MnOOH on the surface, this procedure will convert it into Mn203.
Dispersed manganese dioxide on carbon foil is prepared by solution
deposition since is has been shown that MnO2 can be deposited by
means of the KMnO4 decomposition [40]. Absence of KMnO4 itself is
confirmed by the absence of K core level peaks in the survey scans.
The reaction for this decomposition is given by equation (51), where
the fate of the negative charge has not been established.

Mn(s) Mn(v) MnO/C
W filament Oxidation
basket (poor vacuum)

2500 C
atmosphere


Mn203/C

Figure 4-4. Schematic showing method of vapor deposition of
manganese oxides on carbon foil.

Equation (51a) symbolizes deposition onto the carbon foil.
MnO4- MnO2 + 02 (51)
MnO2 Mn0O2/C (51 a)
C foil








Solution deposition is accomplished by placing carbon foil
rectangles into permanganate solution (= 3.3 X 10-4 F) and allowing
the dioxide to deposit. The samples are kept in solution for various
lengths of times. Some were left in for 2 hours, some for 20 hours,
and the remainder for 100 hours. To prepare the samples which
contained either 0, 1, or 2 edges, a relatively large piece of carbon
foil ( 5cm X 5 cm) was placed in the permanganate solution for
100 hours. Figure 4-5 shows how the XPS samples with various
edges exposed to the permanganate solution were selected after the
100 hours of deposition time. The rectangles were cut from the
large rectangle with the use of a razor knife.


/ Double edge
Sample

No edge
sample







Single edge sample
Figure 4-5. Diagram showing how samples containing the number of
edges indicated were harvested after they were allowed
to have Mn02 deposit on them for 100 hours.


Solution deposition of ferric oxide onto carbon foil necessitated the
precipitation of the ferric ion out of solution before the carbon foil
could be added. The precipitation was accomplished by adding a 1M








NaOH solution dropwise to a. 0.1 N ferric nitrate solution. The NaOH
was added until there was no further change in the appearance of the
brown precipitate that was formed. The pH of the solution containing
the precipitate at this point was 14. The carbon foil was then placed
into the precipitate containing solution and the precipitate was
allowed to deposit for either 18 or 100 hours. After the time
allowed for the deposition to occur had expired the samples were
washed alternately with de-ionized water and acetone. The samples
resulting from manganese oxide deposition were also washed after
deposition. The acetone facilitated the removal of any organic on
the surface and aided in drying. Prior to letting either the Fe(lll) or
Mn(IV) oxide deposit onto the carbon foil, it is necessary to remove
contaminant oxygen from the surface of the foil. According to the
literature, this can be accomplished by heating the foil to 5310 C in
ultrapure nitrogen [41] or by heating it to 2100C in a vacuum [28].
Since the carbon foil is four years old, the oxygen peak could not
completely be removed. Quantitative analysis of the above samples
was performed after the acquisition of data by VAXPS. Regions in
which data are acquired are the 01s, Cls, Mn2p, Fe2p, and the
valence band (VB). It is also necessary to acquire data in the the
regions just mentioned for the carbon foil not being subject to
deposition of manganese dioxide. This allows the determination of
the quantity of contaminant oxygen on the surface and comparison
with carbon foil which has been subject to deposition. The valence
band region is scanned from 15-0 eV.








SResults


After the carbon foil rectangles are placed in the permanganate
solution for either 2, 20, or 100 hours, XPS data is acquired in the
regions mentioned in the previous section. The 01s region of the
manganese free carbon foil is compared with the 01 s regions of the
carbon foil samples which are subject to deposition to see if any
deposition had occurred. Figure 4-3 shows a peak fit of the 01 s

region of manganese free carbon foil acquired at a take off angle of
0 degrees. The manganese free carbon foil contains oxygens species
in four different chemical environments. Several of the oxygen
species have been identified in a paper written by Young [42]. The
additional species are probably due to the fact that the carbon foil
has aged. The carbon foil used by Young in the investigation to
identify inherent surface oxygen species was new. The carbon foil
used for the deposition of manganese dioxide is approximately 4
years old. Figure 4-6, which illustrates the Mn2p peaks of a sample
of carbon foil which has been allowed to soak in potassium
permanganate solution 100 hours, confirms that manganese
deposition has indeed occurred. Figure 4-7, which shows a peak fit
for the 01 s region at a 0 degree take off angle for a sample prepared
with 100 hours of deposition time, shows that there is an additional
peak at 529.0 eV. This value compares very favorably with the
literature value of 529.3 eV for the 01s peak of bulk Mn02 [43]. The
0/Mn ratio is 1.72, within experimental error of the expected ratio
2.0. Figure 4-8 illustrates a peak fit for the 01s region of the same
sample at a 85 degree take off angle. In this case, the 0/Mn ratio is























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1.90. By comparison of the- percent area values of the 529.0 eV
distribution of Figures 4-7 and 4-8, it can be seen that deposited
oxygen and therefore MnO2 is being incorporated into the layers of
the carbon foil (i.e. MnO2 increases with increasing take off angle).
This conclusion is substantiated by the number atom ratios NMn/NC
calculated at increasing values of the take off angle. As the angle is
increased, the amount of Mn increased, as shown in Table 4-1. This
is quite surprising since we expected to be able to form a continuous
layer of the oxide at the surface like it was possible to do for vapor
deposited MnO and Mn203. At 0=0 it is possible to form a continuous
film of the vapor deposited manganese oxide [28], as shown in
Table 4-2. It should be pointed out that the value of 1.00 is
determined not by NMn/NC but by NMn/(NMn+NC) in Table 4-2.




Table 4-1
Values of NMn/NC for solution deposited MnO2 on carbon foil.

e(degrees.) 2 hrs. 20 hrs. 100 hrs.


0 0.055 (0) 0.13 (0) 0.073(D)
15 0.13 0.20
35 0.26 0.83
55 0.046 0.22 1.24
85 0.041 0.18 1.07







Table 4-2
Coverage values for vapor deposited MnO and Mn203.


OXIDE


MnO 0.18
MnO 1.00 (no discernible Cl s)
Mn203 0.3
Mn203 0.65
Mn203 1.00 (no discernible Cl s)



Solution deposition of ferric oxide on carbon foil gave similar
quantitative results to that of the solution deposited manganese
dioxide. Figure 4-9, which illustrates the Fe2p peaks of a carbon
foil sample which was allowed to remain in the precipitated Fe
solution (see preparation of samples section) for 100 hours,
confirms that iron has indeed deposited onto the surface. In Figures
4-10 and 4-11, which are peaks fits of the 01is region of solution

deposited ferric oxide on carbon foil at take off angles of 0 and 85
degrees respectively, a peak can be seen at 529.1 eV at 0 degrees
and a peak at 529.2 eV at 85 degrees. This compares very favorably
with a literature value of 529.3 eV for the 01 s peak for the bulk
Fe203. The 0/Fe ratios for the sample analyzed at 0 and 85 degree
take off angles are 1.8 and 1.6 respectively, within experimental
error of the expected 1.5 for Fe203. There is incorporation of the
oxygen from the iron oxide into the layers of the surface of the
carbon, but the incorporation does not occur to the same extent as
for Mn02. This conclusion is made from the 100% area values in

Figures 4-10 and 4-11.























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At 0=0, it is 196991 and at .0=85 it is 354465. If the second value

for 100 % area is divided by the first a ratio of = 1.8 is obtained. The
same ratio for the MnO2 deposition yields a ratio 8.4, an
approximate 4 fold increase. The conclusion that ferric oxide is not
being incorporated to as great a degree into the layers of the carbon
foil as manganese dioxide can also be drawn from the area % of the
529 eV peak. At 85 degrees the 529 eV peak constitutes 52.9% of the
area under the curve for the sample prepared by the solution
deposition of MnO2 while it constitutes only 19.3% of the area under
the curve for the sample prepared by the solution deposition of
Fe203. The percentage of area contributed by the 529 eV peak is
greater at e=0 degrees than at 85 degrees for dispersed ferric oxide.
This further substantiates the differences in the degree of
incorporation between the two oxides. The number atom ratios also
indicate that less of the oxide is being incorporated into the carbon
foil. Table 4-3 gives the number atom ratios for the Fe and C atoms
as resulting from solution deposition.


Table 4-3
N Fe/NC values for samples prepared from the solution deposition of
Fe203 on carbon foil.

take off angle 18 hours 100 hours

0 0.057 0.044
10 0.12 0.095
25 0.098 0.089
55 0.075 0.092
85 0.063 0.083








The photoemission results clearly show that there is a difference
between the way that particles deposit from the vapor onto carbon
foil and the way that particles deposit from solution onto carbon
foil. The foil itself contains numerous gross defects, which are
evident as microscopic tears from SEM photomicrographs. For a
defect free foil, the surface monolayer would be expected to act as a
barrier to deposition material, thus all particles would be confined
to the top monolayer. It is obvious that particles can penetrate a
defect-laden barrier. The extent of penetration might be expected to
depend upon the particle deposition rate, the deposition time, and
the defect density. Our results on vapor deposited manganese oxide
particles show that the particles are confined mainly to the surface,
and thus indicate that defect penetration is a minor process. This is
expected because the particle dose (deposition rate multiplied by
deposition time) is low and the defect density is small, as can be
judged qualitatively from the fact that x-ray diffraction results
show that the foil is semicrystalline. This means that it has more
defects than a crystalline solid, and less defects than a
polycrystalline solid. Thus, the probability that a particle deposits
in a defect or that it deposits close enough to a defect to fall in
from a random walk is expected to be small. Besides the possibility
of a particle depositing through a defect in the surface, there is also
the possibility that a particle can leave the surface of the carbon
once it has been deposited. For the solution deposition of Mn02, at
least 4 scenarios can be envisaged, as follows:
1) Small particles of oxide produced by photodecomposition in the
solution phase deposit on the surface and penetrate through defects.








2) Small particles of oxide produced by photoemission in the
solution phase deposit on the surface and intercalate between layers
of carbon by penetrating along exposed edges. They then can leave or
"fall off" the carbon foil edges at a later time.
3) Permanganate anions intercalate the carbon foil and particles of
MnO2 are produced by in-situ decomposition, while small particles
produced by photodecomposition in solution phase deposit only on
the surface.
4) Some combination of all three.
Photoemission results can be used to investigate these scenarios.
Based on an earlier study of fresh carbon foil [42], the Ols peaks at
532.1 eV and 533.2 eV may be associated with graphite oxide, Cx+
(OH-)y (H20)2, where the 532.1 eV peak is due to OH- and the 533.2
eV peak is due to H20. For the four year old carbon foil, there is no
significant difference between the ratios of the areas of Ols peaks
at 529.8 eV and 530.9 eV to the area of the 0 s peak at 532.1 eV for
take off angles of 35 and 85 degrees, as shown in Figures 4-12 and
4-13. Thus, the subsurface has an almost homogeneous distribution
of carbon oxidation species (the relative amount of the peak at 533.2
eV increases slightly with the take off angle) and segregating
species in the depth explored. However after exposure of 4-year old
carbon foil to dilute, neutral permanganate for 100 hours, the
situation is that shown in Table 4-4. There are significant changes
(>> 5%) in the peaks at 533.2 eV and 529.7 eV. Similar results are
obtained in the case of the deposition of iron (111) as the hydrous
oxide, which can be seen in Table 4-5. The drastic reduction in the






























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533.2 eV peak is probably due to the dehydration of the surface
caused by the evaporating acetone wash. The increase in the peak at
529.7 eV cannot be directly correlated to the amount of the deposit.
There is a greater amount of deposited MnO2 than of deposited Fe203
after 100 hours. The ratio of NMn/NC to NFe/NC is 12.9 at a take off
angle of 85 degrees. The corresponding ratio of the change on Ols at
529.7 eV, column 4- column 3, is 1.7. Thus, the increase in the
species at 529.7 eV cannot be due to attack on carbon by MnO4- or
Fe+3, since it should be much larger in the case of MnO4- attack. If
we regard each pair of planes of carbon as a "two wall cuvette", then
they could entrain permanganate solution between them by capillary
action provided the interplane separation is large enough. One would
then expect to observe potassium peaks in the XPS spectra, but none
are observed. It seems unlikely that MnO4- would be selectively
drawn in, because of the charging problem. If the interplane
separation is the same as that of the graphite, then both K+ and
MnO4- are too large to be drawn in.


Table 4-4
Ols levels for carbon foil-- new [42], 4 year old (take off angle=85o)
and after deposition of MnO2 for 100 hours on the latter ( take off
angle=850)

Peak Relative % of Total Non Metal Oxygen
BE (eV) NEW 4-YR OLD DEPOSITED ASSIGNMENT

529.7 14.3 51.3 ?
530.9 24.4 26.9 ?
532.1 60.0 28.6 16.9 graphite oxide
533.2 40.0 31.8 4.9 bound water











Table 4-5
Ols levels for carbon foil-- new [42], 4 year old (take off angle=850)
and after deposition of Fe203 for 100 hours on the latter (take off
angle=850)

Peak Relative % of Total Non Metal Oxygen
BE (eV) NEW 4-YR OLD DEPOSITED ASSIGNMENT

529.9 14.3 36.5 ?
530.8 24.4 30.2 ?
532.1 60.0 28.6 33.3 graphite oxide
533.2 40.0 31.8 0 bound water



Thus scenario 3 is at best a minor process. Resolving the importance
of this scenario would allow the catalysis results to be better
addressed. Figure 4-5 illustrates how samples were prepared which
have either 0, 1, or 2 edges exposed to the solution during the
deposition process. It was stated that the samples were cut from
the large rectangle of carbon foil with a razor knife. It is possible
that the knife edge may have dislodged some of the manganese
dioxide particles in the area of the cut. This is probably not a
serious problem however since the x-ray beam is confined to the
center of the carbon foil. The results of the "edge" experiment are
shown in Table 4-6. The table indicates that an increase in the
number of edges does not cause an increase in the amount of
manganese oxide that is being incorporated in to the carbon foil. In
fact, the opposite effect seems to be occurring. If scenario 1 is the
major method for interlayer incorporation of MnO2, one would expect








the three samples to show the same distributions, because the
defects are uniformly distributed. Thus, the results do not support
the initial expectations for either scenario 1 or scenario 2. However
reflection shows that these results could be obtained for either
scenario 1 or scenario 2. Because the particles are more mobile at
edges, in the 0 edge region, a particle must perform a sequence of
directed "kicks" on a nearest neighbor in order to escape. However
particles near an edge can easily fall off into the dilute colloid
medium. If scenario 2 is occurring, then a decrease in the number of
particles which have intercalated into the surface should be seen if
the number of edges exposed to the permanganate solution is
increased. Likewise, if particles are being uniformly incorporated
into depths, they will be depleted more rapidly where 2 edges are
available for escape and least rapidly where 0 edges are available
for escape. Table 4-6 shows the largest number atom ratios for the
0 edge sample and the smallest number atoms ratios for the 2 edge
sample. Thus, these results cannot distinguish between scenario 1
and scenario 2; many more experiments will be needed before the
mechanism of particle incorporation can be established.
Besides being able to determine the relative concentrations of
various constituents on a surface, XPS can also be used to study the
electronic structure of particles on inert supports. The change in the
electronic structure of these particles can be monitored by
variations in the valence band density of states (VBDOS), which was
discussed in the previous chapter. One of the variations which
VBDOS undergoes when there is a change in the electronic structure




Full Text
CHAPTER 5
EFFECT OF DISPERSED MANGANESE OXIDES ON THE DECOMPOSITION OF
PERMANGANATE SOLUTIONS
Introduction
Heterogeneous catalysts have been the subject of much research
over the years. One of the largest users of this type of catalyst, the
petroleum industry, is devoting considerable effort in order to
improve catalyst performance and efficiency. At present the
fabrication of heterogeneous catalysts is relatively imprecise, thus
the field of heterogeneous catalysts has been referred to as a
technologically advanced field without a sound scientific foundation
[44], A heterogeneous catalyst is one which is in a different phase
than the reactants and products. The best example of such a catalyst
is that of a catalytic converter in an automobile. In this case,
substances in the gaseous phase (i.e. CO and unburned hydrocarbons)
react with a catalyst in the solid phase. As a result of research
conducted to improve performance, the catalytic substance is
frequently dispersed on an inert support, in the form of clusters. The
data acquired by XPS can be used to characterize clusters of
deposited materials on inert supports. The data can be interpreted to
obtain the number atom ratios of the catalytic substance to the
104


61
Quantitative Analysis bv XPS
XPS investigations often require that the relative concentrations
of the various components of a surface be determined. If one
averages over depth, then these relative concentrations can be
expressed as number atom ratios (i.e. Nx/Ny) which can be
calculated from the following equation.
Nx.i/Nyj = (lx.i/lyj) (ayj/oxt¡) (Xy(Ej)/Xx(Ej)) (F(Ej,Ea)/F(E¡,Ea))-
(T(Ej/Ea)/T(E¡,Ea)) (47)
The Ps are the time normalized intensity ratios, the a's are the
asymmetry corrected photoionization cross sections, Ej and Ej are
the kinetic energies of photoelectrons i and j respectively and Ea is
the analyzer pass energy. The subscripts x and y are the specific
elements and subscripts i and j represent specific levels in x and y
respectively [37], X(E¡) is the inelastic mean escape depth, F(E¡,Ea)
is the electron optical factor and T(E¡,Ea) is the analyzer
transmission function. Fortunately experimentation has given
results which allows equation 47 to be simplified. It has been shown
that the product of the electron optical factor, the analyzer
transmission function and the inelastic mean escape depth cancel
each other [38]. The simplified form of equation 47 is
Nx,i/NyJ = (lx,i/ly ,i)(ory ,i/ox,i)
(48)


125
Correlation of Rate Law Expressions with Experimental Data
One can investigate the fit of various rate law expressions to the
experimental data. Since the decomposition of neutral permanganate
in the absence of carbon supported manganese oxide particles is
autocatalytic with colloidally dispersed Mn02 particles catalyzing
the reaction, it is reasonable to assume that the decomposition
remains autocatalytic in the presence of carbon supported
manganese oxide particles. Unfortunately, such a fit cannot be made
directly, because the activity of permanganate is not known.
Nevertheless it is possible to simulate data from a second order
autocatalytic reaction and to explore the limiting behavior of such a
reaction. Equation (61) requires initial values for the concentrations
of A0 and B0. Arbitrary values of 1.00 M are chosen for A0 and 0.20 M
is chosen for B. Recalling that Ao-A=B-Bo and by the substitution of
the values chosen for A0 and B0 into equation 61, we have the
following the equation given by
(1/1.2)ln(5B/A) = kt.
By knowing t and k, one can solve for 5B/A which represents one
equation with two unknowns. If A0-A = B-B0, then 1.00-A=B-0.20.
There are now two equations with two unknowns, and A and B can be
uniquely determined. Knowing A and A0 for each value of time t, the
quantity |A-Ao|/Ao can be determined for each value of t. The
relationship between t and | A A 01 / A0 can be fit with high
correlation to the following linear functions


26
The one electron wavefunction <\>\ for a molecular orbital must be
expressed in some mathematical form. The manner in which this is
done is to express it as a linear combination of atomic orbitals
(LCAO). If <¡>¡ is the molecular orbital it can be expressed by
i = I Cjixj, (17)
where the xj's are the atomic orbitals and the cjj's are the
coefficients. The coefficients of the atomic orbitals are known as an
eigenvector. The atomic orbitals xji can be written as a function of
the following variables:
X(r,0,<>) =Rnl(r)Y|m(0,)- (18)
The variables r, 0, and (j> are expressed in terms of spherical polar
coordinates as illustrated by Figure 2-4. The Y|m(0,<¡>) part has
Figure 2-4. The relationship between spherical polar (r,0,(}>) and
cartesian coordinates (x,y,z).
It can further be broken down as exemplified by the equation given
by


14
to allow cooling water to pass through and the other end capped
with copper. The copper end resembles a roof with one side plated
with Al and the other side with Mg. To generate x-rays, the
emission stabilizer circuitry is first activated. This is a new circuit
design by KRATOS which is supposed to generate a more stable
emission of electrons from the filaments. After the emission
stabilizer is activated, the high voltage power supply is switched
on. Before this can occur, three safety interlocks must be satisfied.
First, the pressure of the cooling water to the anode must be
sufficient; second, the ion pump to the x-ray source must be on; and
third, the ion gauge must be switched on. If these interlocks are
satisfied, the power can be turned on. The desired voltage of the x-
ray radiation is dialed up. Usually a value of 15kV is selected. The
emission current is selected, and usually a value of 15mA is chosen.
At this point the x-rays can be generated either by computer
command or local command. When the Al anode is selected, the x-
rays have an energy of 1487 eV, and when the Mg anode is chosen,
the radiation is 1254 eV.
The sample analysis chamber (SAC) normally is kept at pressures
between 10"9 to 10-1"1 torr. To achieve this extremely low
pressure, it must be pumped in stages. First a roughing pump is used
to evacuate the chamber to approximately 0.5 torr. After this
pressure is obtained, a turbomolecular pump is used to bring the
vacuum down to the 10'3 torr region. The ion pump is switched on
and in conjunction with the turbomolecular pump evacuates the
chamber down to 10" torr. The valve between the SAC and the
turbomolecular pump is closed and the ion pump brings the vacuum


CHAPTER 2
BACKGROUND OF THEORETICAL RESEARCH UNDERTAKEN
Overview of Molecular Orbital Theory
Fundamental Principles
One aspect of the research that is undertaken here involves the
effect of variation of the molecular geometry of clusters of the
formula (MnO)2 on the XPS valence band density of states (VBDOS).
To show this effect, results of molecular orbital theory are
compared with XPS valence band spectra. This comparison is
possible as a result of the theory of Koopman [7-8], which states
that the negative of an eigenvalue or molecular orbital energy (-8) is
equal to the binding energy (B.E.) of the photoelectron as given by
-e = B.E.
By making comparisons between eigenvalues and XPS valence band
data, information can be deduced about the electronic structure of
discontinuous clusters of deposited material on the surface of a
substrate. Using the postulates of quantum mechanics, the
eigenvalues can be obtained from the wavefunction of a system, as
discussed briefly below.
17


18
The particle, detected by XPS, can be regarded as a wave, with
the wavelength given by the de Broglie relation given by
mv = p = h/(X)
or X=h/p, (6)
where p is the particle momentum and h is Planck's constant [6].
This wave behavior of the electron can be characterized by a wave
function ^(im) which contains all the information possible about it
[9]. The Schrodinger equation, which allows eigenvalues to be
extracted from the wavefunction, can be derived from the de Broglie
relationship and the classical time-independent wave equation. It is
given by
ih/47i2(3/at) 'F(r,t) = -(h2/8:t2m) A^r.t) + (7)
where Ais the Laplacian operator 32/3x2 + 32/3y2 + 32/3z2. This
equation describes the motion of a particle when it is under the
influence of a potential V(r,t). The Laplacian operator and the
potential acting together on *F(r,t) form the Hamiltonian operator,
which represents the total energy of the system. The wavefunction
vF(r,t) must meet certain conditions, however, in order for the
equation to be valid. These conditions derive from the postulate of
quantum mechanics which states that a system of particles must be
described by a square-integrable function. Thus '{'(r.t) = ¥ (qi,q2,Q3,-
wi, W2, W3, , t), where the qs are the space coordinates, the
w's are the spin coordinates, and t is the time coordinate. V/*VF is the
probability that the space spin coordinates lie in the volume element


25
"self consistent field" or SCF. The reason for this importance is seen
by looking at the last term in the equation for the Hamiltonian
operator (14), which is the interelectronic repulsion operator.
Because electrons repel each other, the electron density is more
diffuse than it would otherwise be. Electron (2) "sees" electron (1)
as a smeared out, time averaged cloud. Electron (2) "sees" electron
(1) as a smeared out, time averaged cloud. Electron (2) is thus
screening the positive nucleus from electron (1). Since the nucleus
is being screened, electron (1) will occupy a less constricted orbital
than it otherwise would. If electron (1) is in a 1s orbital, its orbital
as a result of this screening is represented by
ls(l)= V£3/rc exp(-£n). (electron (1)) (16)
A numerical value for which is related to the screened nuclear
charge seen by electron (1), can be determined. Likewise electron (2)
is being screened by electron (1) in its expanded orbital A value
for can therefore be determined for electron (2). will be
different from £ because the shielding of the nucleus by electron (1)
is different from the previous step. Each change in £ for electron (1)
necessitates a change in This process is continued until the two
values (i.e. £ and £') converge. When this happens electrons (1) and (2)
are being screened by the same amount. The potential due to the
nucleus and charge cloud of each electron causes the orbital for each
electron to be self consistent. The electrons move in a self
consistent field [8].


68
Solution deposition is accomplished by placing carbon foil
rectangles into permanganate solution (= 3.3 X 10'4 F) and allowing
the dioxide to deposit. The samples are kept in solution for various
lengths of times. Some were left in for 2 hours, some for 20 hours,
and the remainder for 100 hours. To prepare the samples which
contained either 0, 1, or 2 edges, a relatively large piece of carbon
foil ( = 5cm X 5 cm) was placed in the permanganate solution for
100 hours. Figure 4-5 shows how the XPS samples with various
edges exposed to the permanganate solution were selected after the
100 hours of deposition time. The rectangles were cut from the
large rectangle with the use of a razor knife.
Figure 4-5. Diagram showing how samples containing the number of
edges indicated were harvested after they were allowed
to have Mn02 deposit on them for 100 hours.
Solution deposition of ferric oxide onto carbon foil necessitated the
precipitation of the ferric ion out of solution before the carbon foil
could be added. The precipitation was accomplished by adding a 1M


Intensi ty (c ounts)
3rd CCF HEATED FOR £ MO. lOOHR MN02 DEP. THETA=35 DEGREES.
Run: 3M10O4 Rey: 4 (MN2P ) Scan: 1 Base: 16816 Max Cts/s: 4£1
-o
to


44
performed such calculations, which are listed in Tables 3-2 and 3-3.
For those diatomic molecules which contain no transition elements,
most of the calculated dissociation energies are in good agreement
with experimental values, as seen in Table 3-2. When the
dissociation energies of diatomics which contained either one or
two transition elements are determined, there is very poor
agreement between the calculated results and experimental values,
as shown in Table 3-3. These results indicated that there is a
problem in the way transition elements are treated. It was decided
to modify those areas of the program which are a manifestation of
treating the transition element as two atoms centered at one
coordinate. One such area which needs to be modified is the
computation of the atomic energies.
In M.O. theory the atomic energy is related to the dissociation
energy by
Edissoc = Ebond = Etot Eatomic- (42)
Table 3-2
Bond Energies and Lengths of Selected Diatomic Molecules.
AB
Bond Length
(A)
Exp.a
Dissociation Energy
(eV)
Exp.a
HF
1.00
0.92
-6.01
-5.90
LiH
1.54
1.60
-6.71
-2.50
IH
1.63
1.61
-4.47
-3.09
CO
1.22
1.13
-21.96
-11.09
SnO
2.25
1.84
-1.46
-5.46
a) Ref [30]


Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
CHARACTERIZATION AND CATALYTIC ACTIVITY OF DISPERSED
TRANSITION METAL OXIDE CLUSTERS ON CARBON SUBSTRATES
By
JACK G. DAVIS, JR.
December 1988
Chairperson: Vaneica Y. Young
Major Department: Chemistry
After modification of a CND02/U algorithm, a valence band
density of states curve (VBDOS) is constructed from the resulting
eigenvectors and eigenvalues for a distribution of MnO dimer
structures. The resulting curve shows a remarkable similarity to the
X-ray photoelectron spectroscopy (XPS) spectrum of a thick
continuous film of MnO.
In order to investigate the properties of small particles using
XPS, they must be isolated on supports. Different methods of
preparing dispersed oxides on carbon foil supports are investigated.
In particular, vapor and solution deposition are used to fabricate
various transition metal oxides on carbon foil. Vapor deposition is
used to disperse MnO and Mn203 on the carbon substrate and solution
deposition is used to disperse Mn02 and Fe23 on the substrate. Data
v


TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ii
ABSTRACT v
CHAPTERS
1 INTRODUCTION 1
Fundamental Principles of X-Ray Photoelectron
Spectroscopy 1
Instrumentation 3
2 BACKGROUND OF THEORETICAL RESEARCH UNDERTAKEN .17
Overview of Molecular Orbital Theory 17
Approximations to Molecular Orbital Theory 31
3 THE EFFECT OF VARIATION OF MOLECULAR GEOMETRY
OF A TRANSITION METAL OXIDE CLUSTER ON THE
VALENCE BAND DENSITY OF STATES 38
Background 38
Modification of CND02/U Algorithm 43
Construction of VBDOS curves 50
4 PHOTOEMISSION STUDIES OF VAPOR DEPOSITED AND
SOLUTION DEPOSITED MANGANESE OXIDES AND
SOLUTION DEPOSITED IRON OXIDES ON CARBON FOIL 57
Introduction 57
Variable Angle XPS (VAXPS) 59
Quantitative Analysis by XPS 61
Preparation of Samples 64
Results 70
in


Figure 4-14.
XPS spectra of dispersed and bulk Mn23.
a) Highly dispersed oxide (coverage =0.3);
b) Less highly dispersed oxide (coverage =0.65);
c) Bulk Mn203.


Figure 4-3. Peak fit of the Os photoelectron peak of carbon foil
not subject to deposition by MnC>2 (clean carbon foil).
The take off angle is 0 degrees.


119
Figure 5-6. Illustration of vapor deposited oxide particles on one
side of carbon foil.
Thus, the effective coverage is less than the measured coverage (i.e.
d>eff <0). By taking these two factors into account, it is possible to
formulate an equation which is normalized for the catalytic effect
due to the oxide alone. The normalized equation is given by
Y = |Aabs| /(Oeff C0). (62)
|Aabs| is the magnitude of the absorbance change due to the oxide
alone, Co is the initial concentration of the permanganate solution,
and Oeff has been defined above. Plots of Y vs. t (time) are shown in
Figures 5-7 and 5-8. It has been determined that the data for MnO on
carbon foil and Mn02 on carbon foil with a coverage of 0.073 can be
fit with a high correlation to an equation of the form
Y=a In (t+1) +b
(63)


4
with high energy electrons. When these electrons impinge upon the
target they knock out its electrons, which creates vacancies. The
photons are generated as a result of the higher energy electrons of
the target filling the vacancies created by the ejection of the lower
energy electrons. This process creates photons of various energies
which then pass through either a Be or an Al window. This acts to
partially filter the bremsstrahlung or x-ray continuum from the
desired Ka rays. Even after filtration, however, only about 50% of
the photons are of the desired energy. The contribution to the
photoelectron spectrum by the bremsstrahlung is not important
because it is distributed over 2 KeV while the Ka rays are
concentrated in a peak of 1eV FWHM [1]. In addition to the Ka 1,2
line, other lines are present due the to difference in energy between
the L|| and L||| levels. This difference is important because Ka 3^
gives satellites in the spectra. With monochromatization it is
possible to reduce the width of Al Ka 12 radiation to as little as 0.2
eV [2]. X-ray radiation can be monochromatized by allowing it to
impinge upon a crystal which will cause it to be dispersed. After
dispersion, radiation of a particular energy can be selected by means
of a slit. This method is known as slit filtering. Another method
involves the matching the dispersion of the crystal with that of the
spectrometer. In this technique the X-rays are dispersed by the
crystal before they reach the sample. Their dispersion will cause
the resulting photoelectrons to come out at slightly different
energies, depending on their position along the target. This
dispersion is compensated for by the spectrometer so all electrons
will be ejected as if they came from atomic orbitals having the


62
If the elements x and y have not been recorded with identical
window widths, then the window width must be incorporated into
equation 48.
Nx.i/Ny.i = (Ixj/ly.i) (oy,i/ox,i) (Wx/Wy) (49)
The number atom ratio evaluated at 0=0 degrees is an estimate of
the coverage (O). The determination of the relative concentrations
of the various constituents of a sample is made relatively simple
with the DS800 software. After the spectra are acquired, the
operator constructs the desired window that needs to be quantified
and then simply types either "Q/A" or "Q/l" at the prompt, where
"Q/A" means quantify area and "Q/l" means quantify intensity. To
quantify area, "The peak area is calculated by summing the counts at
all energies within the appropriate window, multiplying by the
energy step between the channels and dividing by the total time
spent acquiring each channel (i.e. the dwell time)" [39]. The
quantification of peak intensity is determined by computing the
difference between the most intense and the least intense channels
within the spectral window, which is divided by the dwell time. The
dwell time is another name for time normalization that was
mentioned at the beginning of this section. Time normalization
ensures that the quantities obtained are not affected by the
operators choice of acquisition parameters. The atomic
concentration % is then calculated from equation (50).
[(xj/qj)/ I (xj/qi)] X 100.
(50)


86
The photoemission results clearly show that there is a difference
between the way that particles deposit from the vapor onto carbon
foil and the way that particles deposit from solution onto carbon
foil. The foil itself contains numerous gross defects, which are
evident as microscopic tears from SEM photomicrographs. For a
defect free foil, the surface monolayer would be expected to act as a
barrier to deposition material, thus all particles would be confined
to the top monolayer. It is obvious that particles can penetrate a
defect-laden barrier. The extent of penetration might be expected to
depend upon the particle deposition rate, the deposition time, and
the defect density. Our results on vapor deposited manganese oxide
particles show that the particles are confined mainly to the surface,
and thus indicate that defect penetration is a minor process. This is
expected because the particle dose (deposition rate multiplied by
deposition time) is low and the defect density is small, as can be
judged qualitatively from the fact that x-ray diffraction results
show that the foil is semicrystalline. This means that it has more
defects than a crystalline solid, and less defects than a
polycrystalline solid. Thus, the probability that a particle deposits
in a defect or that it deposits close enough to a defect to fall in
from a random walk is expected to be small. Besides the possibility
of a particle depositing through a defect in the surface, there is also
the possibility that a particle can leave the surface of the carbon
once it has been deposited. For the solution deposition of MnC>2, at
least 4 scenarios can be envisaged, as follows:
1) Small particles of oxide produced by photodecomposition in the
solution phase deposit on the surface and penetrate through defects.


This dissertation was submitted to the Graduate Faculty of the
Department of Chemistry in the College of Liberal Arts and Sciences
and to the Graduate School and was accepted as partial fulfillment
of the requirements for the degree of Doctor of Philosophy.
December, 1988
Dean, Graduate School


Figure 5-8. Normalized change in absorbance magnitude (see text)
versus time for colloidally deposited Mn02- The origin
is a point for each.
(o) 100 hour deposit; () 2 hour deposit; (A) 20 hour
deposit.


108
particular time would be the negative of the slope of the curve. For
the nth order reaction of a single component we have the following
-dc/dt=kcn (55)
after integration for n=1
ln(co/c) = kt (56)
or c=Coe'kt (57)
The data should then fit a plot of log c vs. t in order for it to be a
reaction which is first order overall.
log c
Figure 5-1. Linear plot for a first-order reaction.
For a second order reaction, n=2 and the integrated form of the rate
equation is
1/c 1/Co = kt.
(58)


118
of absorbance versus time are constructed, which can be seen in
Figures 5-3 to 5-5.
Results
Before the raw data in Figures 5-3 to 5-5 can be interpreted, it
needs to be normalized so the increase in the rate of decomposition
due to the oxide alone can be realized. Two factors for normalization
must be considered. The first factor is the differing concentrations
of the permanganate solutions. The vapor deposited samples and the
solution deposited MnC>2 samples which were prepared four years
ago were allowed to decompose a 2.0 X 10'4 F permanganate
solution while the freshly prepared MnC>2 samples are allowed to
decompose a 3.3 X 10"4 F solution. The second factor which is
factored into the normalized equation is the differing areas of
coverage of the carbon foil with the oxide particles due to the
differences in vapor and solution deposition. With solution
deposition the oxide particles are covered on both sides while for
vapor deposition, only a circular area of one side is covered. This can
be seen by Figure 5-6. Because of this difference, the effective
coverage is determined. Since in solution deposition both sides are
being covered, the effective coverage is equal to the measured
coverage. But for samples prepared by vapor deposition, the
measured coverage must be multiplied by the area of the circle and
divided by two times the area of one side of the carbon rectangle.


127
On the basis of the simulation results, the conclusion is made that
the rate of reaction is greater in the presence of dispersed MnO
particles than dispersed Mn23 particles. Also the rate of reaction
for carbon supported dispersed Mn2C>3 particles is greater than for
thick continuous films of Mn23 on carbon and for bulk Mn203. It is
interesting that the curves for continuous film and bulk Mn23 are
coincident. This should be the case since thick film is expected to
exhibit bulk behavior based on its electronic structure. The rates of
reaction for Mn02 are probably too high. This may be due to the
intercalated particles contributing to the catalytic activity, which
are not accounted for in Oeff. Presently experiments are being
performed on other layered and unlayered solid supports to help
clarify this situation. Figure 5-9 shows a proposed mechanism for
the autodecomposition of neutral permanganate [48]. The role of the
dispersed Mn2C>3 can be seen in steps 4 & 5. The Mn(lll) allows the
cycle to go from step 2 to 5 without having to go through step 4. As
a result of this, MnC>2 can build up faster. Since the concentration of
H+ is low in neutral solution, it is advantageous that step 4 be
avoided.


t CLEAN CARBON FOIL. OIS REGION. THETA=0 DEGREES
Run: 2CCF05 Reg: 1
Scan: 1 Chans: 157
Start- eU: 535.50
End eU: 527.65
Fit-: 1.7
1OO: I n tens i ty: 579.
100: Area 39042.
Line
Elrot.
Energy
I n t.
FWHM
Area
lor 10
ols
533.5
31.0
1.6
15.2
gauss
ols
532.5
52.9
1.6
27.5
gauss
ols
531.6
61 .6
1.9
35.9
gauss
ols
530.0
34.3
2.0
21.5
534


Run: lFEl Re-3: 3
Scan: 1 Chans: 153
Start- eU: 534.60
End eU: 526.95
Fit-:
1 .6
100 V
Intens
i t.y:
100*.
Area
Line
El rat..
Ener;
Ejy
GAUSS
OIS
531
.9
GAUSS
01S
530
.7
GAUSS
OIS
529
1
GAUSS
OIS
529
.1
3042.
196991.
Int. FUHM Area
42.0 1.9 26.1
47.0 1.6 24.
57.1 1.5 28.
41.2 1.5 20.
f'- o OJ
00
to


48
The relationship between' the electronic energy and the coulomb
integral matrix elements are seen by the equations derived from
CNDO approximations to SCF theory (i.e. equations 38 and 38a). The
term (ZbTab-Vab). which represents the potential difference
between the core ( the nucleus and non-valence electrons) and the
valence electrons of atom B, is set to zero as a result of CNDO
approximations. A valence electron on atom A experiences no
potential difference between these components of atom B, thus the
possibility of its penetration into B is eliminated. Such a
penetration would lead to a net attraction yielding a lower bond and
dissociation energy between A and B. To modify the program so that
a greater net attraction between A and B is realized, the term-
QbTab is modified. This term represents the effect of the potential
due to the total charge on atom B [11]. If Tab is increased, the
potential due to atom B (i.e. Mn or Fe) will be more negative. This
increase would have the same effect as increasing Vab which would
make the potential of the core of B greater than the valence
electrons of B. This should then cause a greater net attraction
between A and B to develop, which is what is desired. By looking at
the first matrix, it can be seen that Tab are represented by To 3d
and ro4s, both of which are bicenter. The problem is to determine
by how much these elements should be increased. Possibilities exist
that the best results might be obtained by multiplying the T04s and
r03d by the same or different amounts. By the process of trial and
error it has been determined that if each r value is multiplied by
1.1, the best fit between dissociation energy, ionization potential
and equilibrium bond distance results. After applying the above


different, this limitation of Koopmans rule could be a problem. In
addition, the rule of Koopman also neglects correlation energy,
which is due to electron repulsion. Since we are interested in the
relative eigenvalues for clusters where the number of atoms is held
constant, this limitation should not be a problem.
Modification of CNDO/2U Algorithm
In this work, the semiempirical molecular orbital method of
CNDO/2U [30] is utilized to determine the eigenvectors and
eigenvalues. This method treats the valence electrons as Slater
orbitals and used parameters which are fitted empirically [1]. This
new version of CNDO can be utilized on any element in the periodic
table whose atomic number is less than or equal to 81. One
fundamental difference between this method and the Pople method is
the way it treats elements whose valence electrons are distributed
over different subshells with different principal quantum numbers,
which is illustrated by Figure 2-7. The molecule TO for example,
where T is a transition element, would be treated as three atoms
with T accounting for two of them at the same coordinate. If this
treatment were carried over to the Lanthanides, where the valence
electrons are dispersed over three subshells, we would have three
atoms at the same coordinate (i.e. T(n_2)f, T(n-1)d. and Tn) [30].
Before the eigenvalues and eigenvectors of the various geometries
of (MnO)2 could be determined, it was necessary to check the
accuracy of the program by determining its ability to calculate
dissociation energies of various diatomic molecules. The author


CHAPTER 3
THE EFFECT OF VARIATION OF MOLECULAR GEOMETRY OF A
TRANSITION METAL OXIDE CLUSTER ON THE VALENCE BAND DENSITY
OF STATES
Background
Dispersed particles or clusters, which usually have catalytic
properties on inert substrates such as carbon, silica, or aluminum
oxide, have been the focus of much investigation [15-26].
Investigations have focused primarily on their electronic structure-
experimentally, through the use of electron spectroscopy and
theoretically, through various molecular orbital algorithms. The
electronic structure of these deposited clusters can be investigated
by observing the shifts in binding energy of the main photoelectron
peaks in the relevant core regions and through acquisition of valence
band spectra. It has been reported in a study on the electronic
structure of catalytic metal clusters (i.e. Pd and Pt) that the valence
band undergoes a narrowing and a shift away from the Fermi level
relative to the bulk metal as the metal clusters become more highly
dispersed [27]. Unlike dispersed metals on inert substrates,
relatively little attention has been paid to the electronic structure
of dispersed metal oxides on inert substrates. As a result, the
electronic structure of dispersed and bulk like MnO on carbon foil
has been performed by Zhao and Young [28]. It was determined that
38


131
shown that the dispersed Mn02 has the greatest effect on the
decomposition. This would be expected since the Mn02 catalyzes the
reaction. However the effect of dispersed Mn02 may be
overestimated. The reason for this may be because the particles
incorporated below the surface are contributing to the
decomposition. These particles are not considered in the coverage
value. The dispersed MnO has the second greatest and then the
dispersed Mn(lll) oxide has the third greatest effect. The continuous
film and bulk of the Mn(lll) oxide had the least effect. An explanation
as to how the MnO affects the reaction is not clear at this point. An
explanation is given for why the Mn(lll) oxide affects the reaction
however. Its presence may allow the bypassing of several steps in a
mechanism proposed by Duke [48]. The bypassing of these steps
would eliminate the need for hydrogen ion, which is very low in a
neutral solution.
Future work in the area should center on investigating the effect,
if any, of the incorporation of the manganese dioxide particles into
the carbon substrate upon the autocatalytic decomposition of
permanganate. At present there is experimentation underway which
is involved with the deposition of Mn02 on mica and glass. Mica is a
layered and glass is an unlayered substrate. Knowing the effect of
these samples upon the autocatalytic decomposition would enable
conclusions to be drawn as to whether the incorporated manganese
dioxide particles are responsible for the rate of the permanganate
reaction being too high. Future work should also be focused on the
quantification of the catalytic activity of dispersed ferric oxide on


CHAPTER 1
INTRODUCTION
Fundamental Principles of X-Rav Photoelectron Spectroscopy
The analytical methodology of X-Ray Photoelectron Spectroscopy
(XPS) is an effective means for the chemical analysis of surfaces. In
XPS, a solid is bombarded with X-Ray radiation, typically of energies
of either 1487 or 1254 eV. Photoemission of electrons from the
surface region of the solid occurs. The ejected photoelectrons are
dispersed according to their kinetic energy (if an electrostatic
analyzer is used) and then counted. The intensity of the signal is a
function of the number of counts at a given kinetic energy.
Conservation of energy requires that
hv= B.E. + K.E. + 0Spect, 0 )
where hv is the energy of the incident X-Ray radiation, B.E. is the
binding energy and K.E. is the kinetic energy of the photoelectron and
0spect is the spectrometer work function. The value of 0spect. W¡H
vary from instrument to instrument, thus each instrument must be
calibrated for this quantity. From the measured kinetic energy of the
photoelectron its binding energy can be calculated by
B.E. = hv K.E. 0spect. (2)
1


94
the three samples to show the same distributions, because the
defects are uniformly distributed. Thus, the results do not support
the initial expectations for either scenario 1 or scenario 2. However
reflection shows that these results could be obtained for either
scenario 1 or scenario 2. Because the particles are more mobile at
edges, in the 0 edge region, a particle must perform a sequence of
directed "kicks" on a nearest neighbor in order to escape. However
particles near an edge can easily fall off into the dilute colloid
medium. If scenario 2 is occurring, then a decrease in the number of
particles which have intercalated into the surface should be seen if
the number of edges exposed to the permanganate solution is
increased. Likewise, if particles are being uniformly incorporated
into depths, they will be depleted more rapidly where 2 edges are
available for escape and least rapidly where 0 edges are available
for escape. Table 4-6 shows the largest number atom ratios for the
0 edge sample and the smallest number atoms ratios for the 2 edge
sample. Thus, these results cannot distinguish between scenario 1
and scenario 2; many more experiments will be needed before the
mechanism of particle incorporation can be established.
Besides being able to determine the relative concentrations of
various constituents on a surface, XPS can also be used to study the
electronic structure of particles on inert supports. The change in the
electronic structure of these particles can be monitored by
variations in the valence band density of states (VBDOS), which was
discussed in the previous chapter. One of the variations which
VBDOS undergoes when there is a change in the electronic structure


134
These values resulted in a mean binding energy of 4.26 eV with a
a standard deviation of 0.18 eV. The mean FWHM is 5.78 eV with a
standard deviation of 0.30 eV.


Ill
these deposits are unchanged even after four months in a drybox
filled with ultrapure nitrogen. It has been shown that MnO is quite
stable to air exposure at room temperature for short periods of time
[45,50,52],
Table 5-1
Coverage () values for vapor deposited MnO and Mn203 and
solution deposited Mn02 on carbon foil.
Oxide
0
length of time for
solution deposition
MnO
0.18
MnO
1.00 (no discernible Ci s peak)
Mn203
0.23
Mn203
1.00 (no discernible Ci s peak)
Mn02
0.055
2 hours
Mn02
0.133
20 hours
Mn02
0.073
100 hours
In addition there are results for samples of dispersed Mn02 on
carbon foil which were prepared and studied four years ago, but for
which the coverages were not determined. The effects of all of the
samples listed in Table 5-1 upon the decomposition of permanganate
solution are determined by placing them into a permanganate
solution and measuring the absorbance of permanganate at 525 nm at
12 hour intervals for a total time of 48 hours. From this data plots


101
B.E. (eV)


58
the relative concentrations- of the constituents on the surface.
Changes in the electronic structure which accompany reduction in
the particle size distributions are determined for the highly
dispersed MnO by comparing its valence band region with that of the
bulk oxide. In that investigation, the oxide was prepared by vapor
deposition. The number atom ratios calculated from XPS data
indicated a low coverage ( represented by (the assumption is made that the lower the coverage value, the more
highly dispersed is the oxide). It is also shown that it is possible to
form a thick continuous film of the oxide on the carbon foil when a
number atom ratio (i.e. N|\/|n/(Nc + NMn)) of 1.0 is achieved at take off
angles between 0 and 50 degrees. The effect of changes in the
particle size distribution consisted of shifts in the position of the
maximum of core, Auger and valence level spectra and a narrowing
of the valence band level. This chapter will report results of similar
experiments on other dispersed oxides of manganese and on
dispersed ferric oxide. These characterizations are based on data
acquired from samples prepared by vapor deposition and solution
deposition. Because in solution deposition it might be possible for
the oxide particles to diffuse in from the edge of the carbon foil, it
is necessary to also perform quantitative analyses of samples
which have had 0 edges, 1 edge and 2 edges directly exposed to the
solution which is used in the solution deposition method in addition
to the normal sample which has 4 edges directly exposed.


31
operator, which is used to solve for the new MOs (i.e.'). These are
then used to construct a new F' and so on until no significant change
is detected. The solutions are said to be self-consistent.
Approximations to Molecular.Qrbitai Theory
Basic Principles of Complete Neglect of Differential Overlap (CNDQ)
The SCF principles that were outlined above involve very lengthy
algorithms (some methods have more than 80,000 lines of code) and
as a result, require a considerable amount of computer memory and
CPU time in order to execute. As a result, approximations have been
applied to SCF principles. Thus considerably shorter codes (typically
between 1200-1600 lines) requiring less computer memory are
obtained. One of the best known examples of approximate molecular
orbital theory is complete neglect of differential overlap (CNDO)
written by John A. Pople and associates in 1965 [12-13]. Such an
approximate method is also referred to as semiempirical because
the eigenvectors and eigenvalues no longer result solely from the
principles of quantum mechanics. Experimental data is used in the
formulation of the Fock matrix.
The first approximation in CNDO which is applied to SCF theory
applies to the formulation of the overlap integral matrix. This
matrix is composed of values which show the degree of overlap
between the various atomic orbitals in the molecule. The
approximation consists of replacing the overlap matrix by a unit


24
assumed to be in the same state after measurement. Therefore there
is no way of distinguishing electron (1) at position r-j, from electron
(2) at position r2. If we want to know r, we can only average
together n and r2- Since we cannot distinguish electron (1) from
electron (2), the wavefunction 'F can not be written as simply the
product of one electron functions <}> of the form
V = 4>l(l)2(2)<|>3(3)... (15)
Since electrons are fermions, which are particles with half integral
spin, the wavefunctions are required to be antisymmetric with
respect to electron exchange. This behavior is accounted for if the
wavefunctions are written in the form of a Slater determinant [6],
For example, for a two electron system, the wavefunction would be
given by the following equation:
1 ^(1) Ml)
Â¥ =
^2 *j(2) 4>2(2)
The general form for the Slater determinant is
4>1(l)4>2(1) *n(1)
1(2)<^2(2) 4>n(2)
^(nH^v) <|>n(n)
In molecular quantum mechanics it is very important to calculate
eigenvectors and eigenvalues which represent electrons moving in a
1
V =
/ n!


CHAPTER 4
PHOTOEMISSION STUDIES OF VAPOR DEPOSITED AND SOLUTION
DEPOSITED MANGANESE OXIDES AND SOLUTION DEPOSITED IRON
OXIDES ON CARBON FOIL
Introduction
A large number of heterogeneous catalysts are composed of a
material (e.g. a metal like Pt or Pd) which has been dispersed upon
an inert support like silica, alumina, or carbon. These dispersed
substances can be characterized by x-ray photoelectron
spectroscopy. More specifically, XPS can be used to determine the
relative concentrations of the various constituents and the relative
particle size distributions of the supported material. The relative
concentrations of the various constituents on a surface are
determined by determining the relative peak areas of the
constituents concerned. This then allows a value for the number
atom ratio of one constituent atom to another to be computed. The
effect of differences in the relative particle size distributions of
the supported material can be qualitatively determined from shifts
in binding energy within a given region. Such effects may be
observed in both the core level regions and in the valence band
regions. Valence band distribution narrowing is one of the most
dramatic changes which can occur. Zhao and Young [28] prepared
carbon surfaces containing submonolayers of MnO, as confirmed by
57


69
NaOH solution dropwise to a 0.1 N ferric nitrate solution. The NaOH
was added until there was no further change in the appearance of the
brown precipitate that was formed. The pH of the solution containing
the precipitate at this point was 14. The carbon foil was then placed
into the precipitate containing solution and the precipitate was
allowed to deposit for either 18 or 100 hours. After the time
allowed for the deposition to occur had expired the samples were
washed alternately with de-ionized water and acetone. The samples
resulting from manganese oxide deposition were also washed after
deposition. The acetone facilitated the removal of any organics on
the surface and aided in drying. Prior to letting either the Fe(lll) or
Mn(IV) oxide deposit onto the carbon foil, it is necessary to remove
contaminant oxygen from the surface of the foil. According to the
literature, this can be accomplished by heating the foil to 531 C in
ultrapure nitrogen [41] or by heating it to 210C in a vacuum [28].
Since the carbon foil is four years old, the oxygen peak could not
completely be removed. Quantitative analysis of the above samples
was performed after the acquisition of data by VAXPS. Regions in
which data are acquired are the Os. Cis. Mn2p, Fe2p, and the
valence band (VB). It is also necessary to acquire data in the the
regions just mentioned for the carbon foil not being subject to
deposition of manganese dioxide. This allows the determination of
the quantity of contaminant oxygen on the surface and comparison
with carbon foil which has been subject to deposition. The valence
band region is scanned from 15-0 eV.


105
supporting substance (i.e. NMn/Nc discussed in the previous chapter)
at the surface by the acquisition of data at a take off angle of 0=0
and at various depths below the surface (0>O). XPS can also be used
to determine the particle size distribution. These two pieces of
information can be correlated with the rate of the reaction the
catalyst is enhancing. It is possible then to determine if the rate of
the catalytic reaction is being affected due to the catalyst
dispersion. In this chapter the results obtained when the
decomposition of permanganate is carried out in the presence of
dispersed MnO, Mn23 and Mn02 on carbon foil is discussed. It is
necessary that the reaction be carried out in neutral solution
because strongly alkaline or acidic solutions affect the rate of
decomposition [45-46], Light also affects the rate of decomposition
of permanganate [47]. While MnC>2 has been shown to catalyze the
decomposition of permanganate [46], neither Mn23 or MnO have been
shown to catalyze its decomposition. However, Mn(lll) in the solid
is proposed as an intermediate in the propagation steps for the
decomposition of manganate [48] and Mn+2 has been shown to react
with permanganate in 3M HCLO4 solution [49], It seems reasonable
that both MnO and Mn203 can affect the decomposition of Mn04~
even though they cannot be regarded as true catalysts. Fortunately,
the kinetics of this decomposition are slow enough so as to allow
spectrophotometric monitoring [47,50], The electronic structure
data reported in the last chapter will then be correlated with the
catalytic activity (i.e. the rate of decomposition of permanganate
solution) to determine the effect of dispersion on the rate of the
decomposition reaction.


8
EbinF is the Fermi level referenced binding energy of the electron in
the sample. Thus, binding energies will be measured correctly only
when the Fermi level of the sample is pinned to the Fermi level of
the spectrometer. This is not possible for insulators, and the
problem is further aggravated by sample charging which results
from the photoemission process. The work function of the
spectrometer is determined by calibrating it with a known standard,
for example, the binding energy of the Au4f electron, which has a
literature value of 83.8 eV. Auxiliary referencing must be employed
for insulators. Most common are the gold decoration technique or
referencing to the C-|s contamination peak.
There are three main types of analyzers which perform these
functions. The two most important are the retarding grid and
dispersion types. The retarding grid analyzer forces the electron to
traverse a potential difference between two grids. This analyzer has
a poor resolution and is not employed in any commercial x-ray
photoelectron spectrometer. The dispersive type analyzer, which is
most commonly used today, separates photoelectrons either
according to their momentum or energy by making them traverse
either a magnetic or electrostatic field respectively. The earliest
dispersion analyzers were of the magnetic type. In this type
analyzer, the photoelectrons are sorted according to their
momentum. The equation which relates the magnetic field, with the
path and momentum of the photoelectron is given by
B(p0) = mo/ep0.
(4)


27
Y|m(0,<>) = ImW^m () (19)
To be sure that the wavefunction will be unchanged if 0 or is
replaced by (0+2rc) or (4>+2;i)the spherical harmonics depend upon the
angular-momentum quantum numbers I and m, which arise in the
solution of differential equations involving angular coordinates 0
and <}>. The radial part of the atomic orbital Rnl(r) is a function of
exponential decay function (exp) and can take either the Slater-type
[10] form
rn"1 exp(-^r) (20)
or the Gaussian type form
rn_1 exp(-£r2). (21)
The Slater type orbital is used in the research undertaken in this
dissertation. Slater functions behave better in the region of r=0 and
do not fall off as sharply as do the Gaussian type orbitals [11].
The orbital exponent £ is a function of how "spread out" the orbital
is. The formula for £ is given by
£ = (Z-s)/n*, where n* is the effective principal number,
s is the screening constant and Z is the atomic number. The greater
the screening by the other electrons, the smaller will be the value of
C and the more diffuse the orbital will be. The effect of the value of
C on the orbital is shown by Figure 2-5.


acquired by XPS from the samples of both methods indicate that two
completely different surfaces result. Vapor deposition yields a
surface in which the particles are confined to the surface. Solution
deposition yields a surface whereby the particles have been
incorporated into the surface. The electronic structure of these
particles are investigated using valence band photoemission.
When the dispersed Mn oxides on carbon foil are placed in
permanganate solution, it is found that the dispersed MnO has a
greater effect on the autocatalytic decomposition of permanganate
than does dispersed Mn203. It is also found that dispersed Mn23 has
a greater effect on this reaction than either the bulk or continuous
film of the Mn(lll) oxide. Dispersed MnC>2 on carbon foil are judged to
have too high an effect on the reaction, possibly because of the
particles which are incorporated into the surface.


Figure 4-9. Fe2p photoelectron peaks of a sample of carbon foil
which was allowed to have ferric oxide deposit on it
for 100 hours.


30
that results from the evaluation of the two electron Hamiltonian is
the exchange integral denoted by K. This integral gives the
interaction between an electron "distribution" and another electron
in the same distribution [8], The exchange integral is given by
Kjj = ¡ ¥¡*(1) vFj*(2) (1/rpq) 'Fj(l) ¥¡(2) dxi dx2- (29)
By collecting terms the formula for the total electronic energy is
given by
n n n n
E = 2 X H¡¡ + Xj¡¡ til (2Jjj Kjj) (30)
i i i j(*i)
and the orbital energies are given by
n
£ = H¡j + X{ 2J¡j Kjj}. (31)
j
The derivation of the Fock operator is very complex and it is not
necessary for it to be presented here. If interested in its derivation
consult reference 8 appendix 7. By utilization of the previously
mentioned terms, the Fock operator is given by

F = [ Hcre + X(2Jj (1) Kj(1))]. (32)
(1) i
which leads to the following equation in the eigenvector form.
RJ>i = ei (33)
Self consistency is achieved by making an initial guess at the
molecular orbitals

*CLEAN CARBON FOIL. OIS REGION. THETA=S5 DEGREES
Run: ECCFIO Reg: £
Scan: 1 Chans: 160
Start- eU: 535.55
End eU: 527.60
Fit: £.8
100* I n t ens i t y: 5SS.
100:-; Area 42973.
Line
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Energy
Int.
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Area
LOR 10
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£ .6
14 .3
Binding Energy


96
metals Pt and Pd have an electronic configuration of d9s1 when
they are supported by other atoms. However the configuration
changes to d9-6s-4 per atom for the bulk metal. The correlation
between increased d electron population and the shift in the binding
energy towards the Fermi level makes sense, since the electrons in
the d atomic orbitals require less energy to undergo ionization. The
reason for increased electron population in the d orbitals when an
atom is part of the bulk material can be explained by
renormalization of the Wigner-Seitz cell [27]. To achieve charge
neutrality within this cell, the atomic wavefunction is truncated at
the radius of the cell and the Wigner-Seitz sphere is renormalized.
This renormalization places more change outside the cell and thus
causes more energy to be required to compress it. Since in transition
metals ns orbitals are more diffuse than (n+1)d orbitals, most of the
s electron population will reside outside the radius of the cell.
When the atom undergoes the transition from atom to bulk, the
compression of the atoms will require less energy if the electrons
shift into the d atomic orbitals. This shifting lessens the amount of
charge external to the Wigner-Seitz cell, thus making its
compression easier. This shifting of electrons into the d atomic
orbitals from the s atomic orbitals may be of importance in
understanding catalytic reactions which show increased rates with
decreasing coverage because it is believed that d electron vacancy
is related to catalytic activity. Thus the dispersed material by the
virtue of having less electrons in the d orbitals should have greater
catalytic activity. An example is Ni deposition from solution. The


99
In conclusion, quantitative analysis of dispersed manganese
oxides which were prepared by vapor deposition (i.e. Mn23 and MnO)
gave number atom ratios which indicated that the oxide particles
stayed in the vicinity of the surface. This statement can be made
because of the high coverage values at a take off angle of 0 degrees.
Not only are the particles confined to the surface, but they are small
enough to cause a change in the appearance in the valence band
density of states and in addition shifts in binding energies of core
level photoelectron peaks relative to the bulk oxide. Solution
deposition gives completely different results. Number atom ratios
show that the oxide particles diffuse into the layers of the carbon
foil as time of deposition is increased. The particles which are
solution deposited are larger than those which are vapor deposited.
This may be due to the particle being able to grow in size in solution
before it becomes lodged onto the surface of the carbon foil. This is
especially true for solution deposited ferric oxide.


Figure 3-3. Valence band density of states for self-consistent
conformations of (MnO)2.


Figure 4-8. Peak fit of the Os photoelectron peak for a sample of
carbon foil which was prepared by allowing Mn02 to
deposit on it for 100 hours. The take off angle is 85
degrees.
I


46
of a valence electron being either an s (i.e. s/TE) or a d (i.e. d/TE).
The equation utilized is
AE = s*ENEG(s) +p*ENEG(p) +((s/TE)*TE2 r(l,l)/2.) + ((d/TE)*TE2*
r(l,l)/2.) + d*ENEG(d). (44)
The effect of this modification on the diatomic molecules containing
transition elements is shown in Table 3-4. The reason that these
diatomics are chosen to test the accuracy of the program is that
they represent the two types of bonds that are encountered when the
eigenvectors and eigenvalues of the (MnO)2 cluster are being
determined (i.e. the T-T and T-0 types where T is a transition
element).
Table 3-4
Results of atomic energy modification to CNDO/2U on selected
diatomics which contain one or more transition elements.
AB
Bond Length(A)
Dissociation Energy (eV)
Exp.(eV)
FeO
1.58
40.9
-4.20
Mn2
2.80
1.0
-0.23
MnO
1.70
38.0
-3.70
Fe2
3.0
-4.52
-1.06
FeS
1.90
33.02
-3.31
MnS
2.00
30.9
-2.85
For molecules representing the T-T bond, (i.e. Mn2 and Fe2) there is
good agreement between data and calculated results. For molecules


37
From the last section it was stated that there is one matrix element
calculated per atom pair. However for a first row transition element
there are ns and (n-1) d valence electrons. It therefore would be
necessary to calculate the following r values:
r (n-1)d (n-1)d I T(n-l)d ns I Tns ns.
In addition to this modification in the formulation of the coulomb
integral matrix, there is also a modification in the calculation of
the atomic energies of transition type elements. Since the transition
element is considered to be two atoms it is necessary to calculate
two atomic energies for each atom. The equation used is given by
AE = s*ENEG(s) + p*ENEG(p) + (TE2 r(l,l)/2.) + d*ENEG(d). (40)
where AE equals the atomic energy, ENEG is the average of the
ionization potential and the electron affinity for the respective
subshell. TE equals the total number of electrons and s, p, and d
equal the number of s, p, and d electrons, respectively.


Figure 5-4. Absorbance versus time data for colloidal Mn02
deposited from a 2.0 X 10"4 F potassium permanganate
solution.
(o) permanganate solution; () permanganate solution +
100 hour deposit; (+) permanganate solution + 20 hour
deposit; (A) permanganate + carbon foil;
(X) permanganate + 4 hour deposit; (A) permanganate
+ 2 hour deposit.


Figure 4-12. Peak fit of Os photoelectron peak of carbon foil.
The peak was acquired at a take off angle of 35
degrees.


plates, the kinetic energy of the photoelectron, and the radius of its
orbit in the analyzer.
11
Figure 1-5. Schematic illustration of electron analyzer with
retardation section.
V=E/e(R2/Rl-Rl/R2) (5)
This equation states that when a particular voltage is being applied
between the plates, only photoelectrons of a particular kinetic
energy will be able to completely traverse space between the plates
and reach the detector. To measure the kinetic energies of all
photoelectrons which are generated, the voltage is continuously
varied over some specified range, usually with the aid of a computer
which has been interfaced with the system. To reduce or lessen the
tolerances of many of the mechanical components of the
spectrometer, the photoelectron passes through a retardation
section prior to its entry into the analyzer. If the kinetic energy of
the electron is reduced from Ekin to some final Eg, the relative


In-O


I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy. r t ,
^ M / V>TQ /Q-\-L,
Vaneica Y. Young, Chairperson
Associate Professor of Chemistr
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.
J
.
Anna Brajter/j
Associate Prc
Toth
ifessor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy. ^ j ^ r ^
Christopher D. Batich
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as dissertation for the degree
of Doctor of Philosophy. (O
' irO:
Associate Professor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy. (\ Q
Japfies D. Winefordrier
Graduate Research Professor of
Chemistry


32
matrix whereby all elements are zero except the diagonal elements
which are 1. In the normalization of Roothaan's equations X(FfiD-
eS^t))C-ui = 0 [14]. By ignoring differential overlap, S(j.-o =0 for In
other words, the atomic orbitals are treated as if they were
orthogonal and as a result, the Roothaan equations reduce to
SFp\)C\)j = £jCjj.¡ where is the Fock operator, C-uj is the
eigenvector or coefficients to the same atomic orbital as the Fock
operator and the £¡'s are the eigenvalues or molecular orbital
energies. This approximation becomes more severe as the
internuclear distance decreases, however, because it causes larger
and larger electron populations to be ignored. The second
approximation results in a simplification of equation (28), which
computes the matrix elements of the electrostatic coulomb
repulsion between charge clouds. The approximation neglects all
differential overlaps in two electrons integrals. Differential overlap
occurs when ¥¡*(1)'Fj(1 )*0, where probability density is coming
from electron (1) over orbitals i and j. Such electron densities are
exceedingly numerous and also exceedingly small. Ignoring
differential overlap means than equation (28) vanishes unless i=k
and j=l. This has the obvious benefit of reducing the number of
integrals that need to be evaluated. The third approximation, which
results from the second, is to reduce the number of coulomb
repulsions to one value per atom pair. Differential overlap can be
monoatomic, where 'FjH'k is on the same atom or diatomic where
T'jT'kis on different atoms. For the monoatomic case neglect of
differential overlap causes invariance of rotation to be negated. This
means that rotation of an atom with respect to another atom will


1-CLEAN C FOIL MHERE MNOS NAS DEPOSITED FOR 100HR
Run: 3M1Q06 Reg: £
Scan: 1 Chans: 14S
Start- eU: 534.35
End eU: 527.00
Fit.: 1.0
100: Intensity: 8632.
100?: Area 360064.
Line
Elnt.
Energy
I n t.
FNHM
Area
gauss
ols
533.2
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2.3
gauss
ols
532.1
13.0
1.2
7.9
gauss
ols
530.9
21.5
1.2
12.6
gauss
ols
523.6
33.7
1.4
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gauss
ols
529.0
74.1
1.4
52.9
534
TO Oj
01S REG. THETA=S5 DEGREES.
-4
On


Figure 5-5. Absorbance versus time data for colloidal Mn02
deposited from a 3.3 X 10'4 F potassium permanganate
solution.
(o) permanganate solution; (A) permanganate + carbon
foil; () permanganate + 20 hour deposit;
(+) permanganate + 2 hour deposit; (X) permanganate +
100 hour deposit.


7
with a particular kinetic energy can be counted by the detector
system it must be separated from photoelectrons which have kinetic
energies different from itself. The function of the electron analyzer
is to perform this separation. The spectrum of photoelectron kinetic
energies relative to the sample is not identical to the spectrum of
photoelectron kinetic energies relative to the electron analyzer,
because the sample and the spectrometer share a common ground, as
seen by Figure 1-3. However, they are in one-to-one correspondence,
since they differ by a constant factor, as shown by the following
equations:
Ekin = E'kin + (0sam-spect)
hv = Ebin^ + E'kin + 0sam
hv = EbinF + Ekin + Aspect.
Figure 1-3. Diagram showing principles for the calculation of
binding energies.


34
where Pab is the bonding parameter, which is characteristic of a
particular atom. As the overlap increases, the bonding capacity of
the overlap will increase [11]. With all these approximations, the
Fock matrix elements can be computed and are given by
Fpp = + ( PAA 1/2 Ppp) TAA + X (PBB Tab VAB) and (36)
B(*A)
Fpu = PABS^ 1/2 P^ TAB- (37)
Equation (36) can be rearranged into
F\i\i = U(j.(j. + (PAA 1/2 P^) TAA + X [-Qb fab + (Zb fab VAB)]
B(*A)
(38)
and the total energy can then be derived. This is shown by
E Total = (1/2) X Ppo(HpD + F,^) + XXzaZbRAB'1 (38a)
4V A To achieve self-consistency an initial guess is made of the
molecular orbital coefficients. The diagonal elements of the Fock
matrix (i.e. F^jj.) come from experimental values for the ionization
potentials ( i.e. U^jj. in equation (38)). The off diagonal elements (i.e.
F|iv) are replaced by pABS^u. The electrons are then assigned to
M.O.s with the lowest energy (i.e. lowest eigenvalues). The density
matrix, which is given by
occ
P(i\)=X c^jc-uj, (39)
i
is calculated from the coefficients of the occupied atomic orbitals.
This matrix is used to formulate a new Fock matrix F^. When the
Fock matrix is diagonalized a new set of eigenvectors and


CLEAN C FOIL WHERE MH02 WAS DEPOSITED FOR 100HR. OIS REG. THETA=0 DEGREES
Run
: 3M1001
Reg:
2
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: 1
Chans:
141
Start
eU:
534.S5
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527.S5
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£.4
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576.
100%
Area
42
S67.
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ea
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533.0
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45.5
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IS
.1
gauss
ols
531.4
54.7
1.5
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gauss
ols
530.1
40.0
1.8
£0
.0
gauss
o1s
529.0
44.9
1.3
15
.8


Figure 5-3. Absorbance versus time data for MnO and Mn23
samples.
(o) permanganate solution; () permanganate solution
+ carbon foil; (+) permanganate + dispersed MnO on
carbon foil; (X) permanganate solution + dispersed
Mn203 on carbon foil; (A) permanganate solution + thick
Mn23 on carbon foil.


6
Crystal
Figure 1-2.--continued
c) Schematic showing the fine focusing method of
monochromatization.
It also removes all of the high energy brehmsstrahlung radiation,
which is responsible for the decomposition of organic samples and
some inorganic salts. The one disadvantage is that there is a large
intensity loss for those instruments which employ a large sample
area like the retarding grid instruments [2], Figure 1-2 illustrates
the above methods of monochromatization.
To avoid collisions between the X-rays and photoelectrons with
the surrounding gas molecules, it is necessary to contain the source
and sample in a high vacuum sample analysis chamber (SAC). In our
instrument typically pressures as low as 10-9 torr are achieved.
With some degree of effort, namely by placing liquid nitrogen in the
cold trap of the SAC, pressures as low as 5 X 10'1"' torr are
possible. The next major component of an X-Ray Photoelectron
Spectrometer is the electron or energy analyzer. Photoelectrons are
generated with a very broad spectrum of energies. Before an electron


1
Figure 4-10. Peak fit of the Os photoelectron peak for a sample of
carbon foil which is prepared by allowing Fe2C>3 to
deposit on it for 100 hours. The take off angle is 0
degrees.


97
reaction proceeds spontaneously when small Pt clusters are used
and then becomes completely quenched at higher Pt coverages [27].
Variation in the electronic structure of highly dispersed MnO on
carbon foil can be seen when its VBDOS is compared to that of a
thick continuous film of the oxide, which can be seen in Figure 3-1.
The important thing to notice is that the VBDOS for the dispersed
Mn(ll) oxide is narrower and the binding energy of the centroid
region has shifted away from the Fermi level. If indeed the theory
discussed in the preceding paragraph is correct, then there is an
increased s electron population in the Mn of the dispersed oxide
particles as compared to the bulk oxide. The variation in the
electronic structure of highly dispersed Mn203 on carbon foil is
similar to that of MnO when the VBDOS of the dispersed Mn(lll) oxide
is compared with its bulk oxide. This variation can be seen by
looking at Figure 4-14. Note the spectra for two dispersed samples
with coverages of 0.3 and 0.65. Since the VBDOS of the sample with
a coverage of 0.3 is narrower than the VBDOS of the sample with a
coverage of 0.65, there is apparently a difference in the electronic
structure of these two samples also. Since the VBDOS is narrower
for the samples with a coverage of 0.3, there is probably a larger s
electron population in its Mn atoms, like in the highly dispersed MnO.
For dispersed Mn02 on carbon foil, which unlike the previous oxides
was prepared by solution deposition, dissimilar results were
obtained. For dispersed Mn02, there is not as great a shift in binding
energy and not as great a change in the FWHM in its VBDOS relative
to the bulk oxide VBDOS. These smaller changes can be seen in Table
4-7 and Figure 4-15. From these results, the particles are more


representing the T-0 type bond however, there is poor agreement.
This makes it necessary to modify the program so that it calculates
a lower total energy for T-0 and T-S bonds.
Another part of the algorithm which can be modified is that part
which computes the coulomb repulsion matrix. This matrix is a set
of values which represent the electrostatic repulsion between the
charge clouds occupied by the electrons in the system. Equation (28)
is the formula for the electrostatic repulsion between electrons (1)
and (2) distributed over orbitals i,j,k and I. When the approximations
of CNDO are applied to (28), equation (34) results. CNDO calculates
the average electrostatic repulsion between any electron on atom A
and any electron on atom B instead of the electrostatic repulsion
between orbitals.
Therefore,
one matrix
element is calculated per
atom pair. For
a T-0 type
* molecule
the following 3X3 coulomb
matrix is formulated.
0
4s
3d
0
TOO
ro4s
r03d
4s
T04s
T4s4s
T3d4s
3d
T03d
T4s3d
T3d3d
and for a T-T type atom the
following 4X4 matrix is formulated.
4s
3d
4s
3d
4s
T4s4s
T3d4s
T4s4s
T4s3d
3d
T4s3d
T3d3d
T3d4s
T3d3d
4s
T4s4s
T3d4s
T4s4s
T4s3d
3d
T4s3d
T3d3d
T4s3d
T3d3d


50
Construction of VBDOS curves
After the modifications were made to the program it was then
possible to begin the acquisition of the eigenvalues and eigenvectors
of various geometries of the formula (MnO)2- In order for the
eigenvalues and eigenvectors of a given geometry to qualify for
comparison with XPS valence band spectra, it is necessary for that
geometry to pass the self consistency test-i.e. two successive
iterations of the total electronic energy must agree to within 0.01
eV. To pass this test it was necessary that the program calculated a
total electronic energy that was within 0.01eV of the previous
value. The determination of suitable geometries was like the
coulomb matrix modification, a trial and error process, but after a
long and arduous process, six suitable geometries were found, which
are illustrated by Figure 3-2.
Mn 0 Mn 0
Linear
Semicircular
Cross tin
Rectangular
Figure 3-2. Suitable geometries for cluster (MnO)2-


BIOGRAPHICAL SKETCH
Jack Davis was born on June 21, 1950, in Kansas City, Missouri.
He was raised in nearby Independence where he received his high
school diploma in 1968 from William Chrisman High School.
After graduation Jack attended the University of Missouri-
Columbia and graduated from there in 1972 with a Bachelor of
Science degree in chemistry. Upon graduation he accepted
employment with the Speas Company, where he worked as a quality
control chemist for a period of five years. In 1979 he began his
tenure as a graduate student in the Chemistry Department of the
University of Missouri-Kansas City. He worked for Dr. Jerry R. Dias
there and in 1981 received a Master of Science in chemistry. In 1982
he moved to College Station Texas so he could attend Texas A&M
University. While there he partially completed the requirements for
the Ph.D. degree in analytical chemistry. In 1984 he transferred to
the University of Florida to complete the requirements for the
degree.
139


12
resolution required from the analyzer is reduced from AEkin/Ekin to
AEkin/Eo- If, for example, a spectrometer is required to achieve a
resolution of 0.1 eV for 1000eV electrons or 0.01% as the result of
retardation, it would be required to achieve a resolution of 0.1 ev for
100eV electrons. Retardation does reduce the intensity of the signal,
however, so a trade-off between intensity and resolution results.
After the photoelectrons have been dispersed according to their
kinetic energies, they must be detected and counted. Almost all
detectors in XPS utilize continuous-dynode electron multipliers of
the "channeltron" type [3-5]. These devices consist of glass tubes
which have been doped with lead and then treated in such a way so
as to leave the surface coated with a semiconducting material with
a very high secondary electron emissive power [3]. A voltage of a
few kV is placed between the ends of these tubes and electron
multiplications of the order 106-108 are achieved by repeated wall
collisions as electrons travel down the inside of the tube [6]. As the
voltage between the plates of the analyzer is swept, the electron
counts at different kinetic energies is usually stored with the aid of
a computer. Computer control is advantageous because it is
desirable to make repeated scans over a spectral region to average
out instrument drifts and to eliminate certain types of noise [6]. In
many cases repeated scans are mandatory. Weak signals can result
due to a small amount of the analyte or if the take-off angle (angle
between the sample and the analyzer about which more will be
covered in a later chapter) is at or near zero. The output from the
electron multiplier can be linked directly to a plotter or printer for
a single continuous sweep. The data system also allows one to


ACKNOWLEDGMENTS
I would like to express my appreciation to Dr. Vaneica Young for
her guidance and very helpful suggestions during the course of my
research project. I would also like to thank members of my
research committee who were also of help.
Paul McCaslin, Linda Volk, Mike Clay, and Peter ten Berge all
made my stay at the University of Florida much more enjoyable by
their friendship and advice.
11


13
perform peak fits whereby -spectral data can be resolved into
Gaussian or Lorentzian distributions. For example the 0-|s spectra
can be resolved into a given number of these distributions which can
then be compared to literature values. By doing so, various chemical
species on the surface which contain oxygen can be deduced. Besides
performing peak fits, it is possible to deconvolute XPS spectra so
as to mathematically remove instrumental linewidth contributions.
This term is not to be confused with peak fit.
Instrument Employed
The instrument utilized for this work is the KRATOS XSAM 800.
This instrument has a dual anode (either Mg or Al can be selected) x-
ray source, a sample analysis chamber which can be pumped on by
either a roughing, turbomolecular, ion, or titanium sublimation type
pump, a hemispherical electron analyzer which includes a
retardation section to reduce the kinetic energy of the
photoelectrons before entering the analyzer, a detector consisting of
a electron multiplier and a data system (A Digital Micro PDP-11
with 256 K bytes of RAM) to control the scanning of the
photoelectrons and to collect and store the data. Peak fits are also
possible at the convenience of the operator.
The X-ray source consists of a filament assembly which is
essentially a tube with tungsten filaments which have been coated
with thorium on either side. The thorium has a lower work function
than the tungsten which makes the emission of electrons more
efficient. The anode is a hollow metal rod with one end open so as


41
for highly dispersed MnO on carbon foil (a coverage of 0.22) the
valence band undergoes a narrowing and a shift in its binding energy
away from the Fermi level relative to bulk material, as can be seen
in Figure 3-1. In the case of supported metal particles, this behavior
led to investigations which sought to correlate XPS valence band
behavior with results from molecular orbital (M.O.) algorithms to
determine the minimum or threshold number of atoms required for a
cluster to exhibit properties of the bulk material. For example, R.C.
Baetzold et al. performed an investigation into the determination of
the particle size required for bulk metallic properties [29]. Extended
Huckel calculations were performed on clusters with face-centered
cubic (fee) geometry of sizes ranging from 13 to 79 atoms. The
results from the calculations were used to construct valence band
density of state curves and the width of the d band was determined.
For the largest cluster size (i.e. 79) it was determined that the d
bandwidth was 86% of that for the bulk material and for a cluster of
13 atoms the d bandwidth was 50% of that of the bulk material.
Table 3-1 shows the results.
Table 3-1
Comparison of d bandwidths with cluster size
cluster
Pd2
Pdi3
Pd31
Pd55
Pd79
d band-
width
0.80
1.54
2.26
2.57
2.65
3.08


60
This is illustrated schematically in Figure 4-1. The distance the x-
rays can travel into the solid is much greater than the
photoelectrons can travel. The relationship between the mean and
the effective mean electron escape depth is illustrated in Figure 4-
2. Even though the mean electron escape depth is constant, the probe
depth, or the effective mean electron escape depth becomes smaller
as the take off angle becomes smaller until at a take off angle of 0
degrees, the photoelectrons generated are originating from the top
monolayers of atoms only. Conversely at a take off angle of 90
degrees, the spectra that are obtained are the most "bulklike". The
value of the effective mean electron escape depth depends upon the
substance that is being analyzed. For metals this depth can be as
small as 10 Angstroms. To change the take off angle in the KRATOS
XSAM 800, one simply rotates the sample probe.
EMEED = MEED*SIN0
Figure 4-2. Diagram showing the relationship between the take off
angle and the effective mean electron escape depth.


10
One disadvantage of this type analyzer is that of cost. A magnetic
analyzer comparable to an electrostatic one would cost
approximately ten times as much. Another disadvantage of the
magnetic analyzer instruments is their sensitivity to stray
magnetic fields. If a resolution of 0.01% is desired the stray field
must be reduced to 0.1 mG over a very large volume. To achieve this
reduction of stray magnetism, very large compensating coils must
be used. This makes the instrument as a whole very space consuming.
Also, the stray fields must be monitored continuously [2].
Besides magnetic dispersive analyzers, there are also
electrostatic type analyzers, which are more commonly used today
because they cost less to construct and are less cumbersome. Their
principle disadvantage is that they are unsuitable for studies
involving high energy photoelectrons. If one is analyzing electrons
with an eV greater than 2000, relativistic effects become
noticeable. The optics for dealing with these effects are better
understood for magnetic than for electrostatic analyzers. In an
electrostatic analyzer, the photoelectron is dispersed according to
its kinetic energy along a predescribed path. This is done by forcing
the photoelectron to traverse an electrostatic field instead of a
magnetic one. Such a field is achieved by placing a potential between
two plates. The geometry of these plates determines the type of
electrostatic analyzer. Several of the possible geometries of the
plates are hemispherical and cylindrical. In our instrument
hemispherical plates are employed. If we look at Figure 1-5 we can
see a schematic diagram of a hemispherical electron analyzer.
Equation (5) shows the relationship between the voltage between the


93
Table 4-5
Os levels for carbon foil-- new [42], 4 year old (take off angle=85)
and after deposition of Fe2C>3 for 100 hours on the latter (take off
angle=85)
Peak Relative % of Total Non Metal Oxygen
BE (eV) NEW 4-YR OLD DEPOSITED ASSIGNMENT
529.9
14.3
36.5
?
530.8
24.4
30.2
?
532.1
60.0
28.6
33.3
graphite oxide
533.2
40.0
31.8
0
bound water
Thus scenario 3 is at best a minor process. Resolving the importance
of this scenario would allow the catalysis results to be better
addressed. Figure 4-5 illustrates how samples were prepared which
have either 0, 1, or 2 edges exposed to the solution during the
deposition process. It was stated that the samples were cut from
the large rectangle of carbon foil with a razor knife. It is possible
that the knife edge may have dislodged some of the manganese
dioxide particles in the area of the cut. This is probably not a
serious problem however since the x-ray beam is confined to the
center of the carbon foil. The results of the "edge" experiment are
shown in Table 4-6. The table indicates that an increase in the
number of edges does not cause an increase in the amount of
manganese oxide that is being incorporated in to the carbon foil. In
fact, the opposite effect seems to be occurring. If scenario 1 is the
major method for interlayer incorporation of MnC>2, one would expect


109
From the above equation, a plot of 1/c vs. t should be linear, with a
positive slope.
Figure 5-2. Linear plot for a second order reaction.
Data for a second order reaction should fit a plot as seen in Figure
5-2. The decomposition of permanganate solutions, which is the
focus of this chapter, is an example of an autocatalytic reaction,
where the rate of the reaction is affected by the amount of the
manganese dioxide that is being produced. The decomposition of
permanganate is represented by the following equation
MnC>4- = MnC>2 + 02 + e". (59)
It is not known where the electron is resident in equation (59)
however [45], Generically, an autodecomposition reaction can be
represented by the equation
A= B +
where A is the reactant and B is a product which catalyzes the
reaction. The rate expression for such a reaction is given by


From the binding energies of photoelectrons, chemical information
can be deduced about the surface.
2
Figure 1-1. Schematic Representing Basic XPS Principles.
X-Ray bombardment of a surface can produce another type of
electron other than a photoelectron. Upon the photoemission of an
electron, a vacancy will develop after ejection. An electron with
lower binding energy from another subshell can move in and fill the
vacancy. This movement results in the dissipation of energy which
can cause a third electron, known as an Auger electron, to be
ejected. Auger electrons are denoted by three upper case letters. The
first letter represents the subshell containing the electron which is
ionized by the incident X-Ray radiation, the second represents the
subshell containing the electron which fills the vacancy, and the
third the subshell from which the Auger electron is ejected. The
signal intensity or peak height is affected by parameters which do
not affect the binding energies. One such parameter is the
differential cross section for photoionization [1], which is given by


Table 4-2
Coverage values for vapor deposited MnO and Mn2C>3.
78
OXIDE
O
MnO
0.18
MnO
1.00
(no discernible Cis)
Mn203
0.3
Mn203
0.65
Mn203
1.00
(no discernible Ci s)
Solution deposition of ferric oxide on carbon foil gave similar
quantitative results to that of the solution deposited manganese
dioxide. Figure 4-9, which illustrates the Fe2p peaks of a carbon
foil sample which was allowed to remain in the precipitated Fe
solution (see preparation of samples section) for 100 hours,
confirms that iron has indeed deposited onto the surface. In Figures
4-10 and 4-11, which are peaks fits of the Oi s region of solution
deposited ferric oxide on carbon foil at take off angles of 0 and 85
degrees respectively, a peak can be seen at 529.1 eV at 0 degrees
and a peak at 529.2 eV at 85 degrees. This compares very favorably
with a literature value of 529.3 eV for the Oi s peak for the bulk
Fe23. The O/Fe ratios for the sample analyzed at 0 and 85 degree
take off angles are 1.8 and 1.6 respectively, within experimental
error of the expected 1.5 for Fe23. There is incorporation of the
oxygen from the iron oxide into the layers of the surface of the
carbon, but the incorporation does not occur to the same extent as
for MnC>2. This conclusion is made from the 100% area values in
Figures 4-10 and 4-11.


95
is a change in its width (FWHM). Changes in the FWHM can be
attributed to three sources [27].
Table 4-6
NMn/Nc values for solution deposited Mn02 on carbon foil with
either 0,1, or 2 edges having been exposed to permanganate solution.
(All samples were result of 100 hours of
deposition time).
0
0 edges
1 edge
2 edges
0
0.15
0.079
0.12
35
0.32
0.17
0.18
55
0.33
0.18
85
0.29
0.21
0.13
1) An increase in the spin-orbit interactions from the
renormalization of the d-electron wave functions in going from a
free atom to a metal.
2) The splitting of atomic d levels by the crystal field into a
doublet.
3) The mixing of the atomic levels throughout the Brillouin zone.
Items 2 and 3 are considered to be almost totally responsible for the
increase of the FWHM with the increase in particle size. The two
factors should also operate to increase the FWHM of nonmetals. Not
only can changes in the electronic structure change the FWHM, but it
can also change the value of the binding energy of the centroid
region of the VBDOS (ed). This shift is brought about in metals by an
increase in the d atomic orbital population when the supported atom
undergoes transformation to the bulk material. For example, the


77
1.90. By comparison of the percent area values of the 529.0 eV
distribution of Figures 4-7 and 4-8, it can be seen that deposited
oxygen and therefore MnC>2 is being incorporated into the layers of
the carbon foil (i.e. MnC>2 increases with increasing take off angle).
This conclusion is substantiated by the number atom ratios NMn/NQ
calculated at increasing values of the take off angle. As the angle is
increased, the amount of Mn increased, as shown in Table 4-1. This
is quite surprising since we expected to be able to form a continuous
layer of the oxide at the surface like it was possible to do for vapor
deposited MnO and Mn2C>3. At 0=0 it is possible to form a continuous
film of the vapor deposited manganese oxide [28], as shown in
Table 4-2. It should be pointed out that the value of 1.00 is
determined not by NMn/NQ but by NMn/(NMn+Nc) in Table 4-2.
Table 4-1
Values of NMn/Nc for solution deposited MnC>2 on carbon foil.
0(degrees.)
2 hrs.
20 hrs.
100 hrs.
0
0.055 (O)
0.13 (O)
0.073(0)
15
0.13
0.20
35
0.26
0.83
55
0.046
0.22
1.24
85
0.041
0.18
1.07


5
same energy [1], Still another means to reduce the inherent line
width of the radiation is the fine focusing method, which uses a
rotating anode to concentrate the beam before it impinges upon the
crystal. Its advantages are that it gives more photons after
emergence from the monochromator and does not put any
restrictions on the sample. Monochromatization removes those lines
responsible for source satellites in the spectra.
a)
b)
Crystal
Sample
Crystal
Figure 1-2. Schematics showing different types of
monochromatization.
a) Slit Filtering
b) Dispersion Compensation


number, a problem arises as to which value k should be. Since the
absolute square |Â¥|2 is proportional to the probability density for
finding an electron,
21
/N
v=o
T
WW
Higher E
Lower E
(a)
Figure 2-2. Illustration showing relationship between wave
curvature and energy.
(a) When the potential energy V=0, the higher energy
has more curvature (more wiggly). (b) As V increases
the wavefunction becomes less wiggly [8].
then the probability of finding a particle between x=-o and x=<~
must be 1. The following equation is given by
k*k J vF*(x)vF(x)dx =1. (10)
If selection of the k multiplier is made such that (10) is satisfied,
then the wave function VF' = kY is normalized. If two different


40
B.E. ( e V )


di (=dii, di2, ) at time t, if ¥ is normalized. To be acceptable the
function must be single valued, nowhere infinite, continuous, with a
piecewise continuous first derivative [8] as seen in Figure 2-1.
19
M
b) Not Continuous
M
c) Has Infinite
Value
x
Figure 2-1.
Illustrations of unacceptable and acceptable
wavefunctions.


137
31. Huber, T.; Herzberg, G. Molecular Structure and Molecular Spectra
(Van Nostrand Reinhold & Co., New York, London 1979).
32. Baumann, C.; Van Zee, R.; Bhat, S.; Weltner, Jr., W.; J. Chem. Phys.
1983, 78, 190.
33. Hildenbrand, D. Chem. Phys. Lett. 1975, 34, 352.
34. Ervin, K.; Loh, S.; Aristov, N.; Armentrout, P. J. Chem. Phys. 1983,
3593.
35. Rohlfing, E.; Cox, D.; Kaldor, A. J. Chem. Phys. 1984, 81, 3846.
36. Scofield, J. J. Electron Spectrosc. Relat. Phenom. 1976, 8, 129.
37. Young, V.; McCaslin, P. Anal. Chem. 1985, 57, 880.
38. Kelly, M.; Scharpen, L. Surface Science Laboratories, Palo Alto,
CA, private communication.
39. Reference Manual for DS 800 Software (KRATOS Analytical,
Ramsey, New Jersey 1987).
40. Shabalina, O.; Ryzhen'kov, A.; Egorov, Y.; Stotskii, V.; Popov,V.; .
Kotel'nikov, A. Deposited Document SPSTL 422 khp-D8 1980:
CA 96: 208570a.
41. Helsop, R.; Jones, P. Inorganic Chemistry (Elsevier Scientific
Publishing Company, New York 1976).
42. Young, V. Carbon 1982, 20, 35.
43. Rao, C.; Sarma, D.; Vasudevan, S.; Hedge, M. Proc. R. Soc. Lond.
1979, A 367, 239.
44. Young, V. Preparation and Characterization of Surface Dispersed
Metal Oxides (Proposal submitted to the Petroleum Research
Fund, 1984).
45. Zimmerman, G. J. Chem. Phys. 1955, 23, 825.


136
13. Pople, J,; Segal, G. J. Chem. Phys. 1966, 44, 3289.
14. Roothaan, C. J. Rev. Mod. Phys. 1962, 36, 33.
15. Ross, P.; Kinoshita, K.; Stonehart, P. J. Catal. 1974, 32, 163.
16. Steiner, P.; Hochst, H.; Huffner, S. J. Phys. F7 1977, L105.
17. Tibbetts, G.; Egelhoff, Jr., W. Phys. Rev. Letters 1978, 41, 188.
18. Liang, K.; Salaneck,W.; Aksay, I. Solid State Commun. 1976, 19,
329.
19. Takasu, Y.; Unwin, R.; Tesche, B.; Bradshaw, A. Surface Sci.
1978, 77, 219.
20. Egelhoff, Jr., W.; Tibbetts, G. Phys. Rev. B 1979, B19, 5028.
21. Roulet, H.; Mariot, R.; Dufour, G.; Hague, C. J. Phys. F10 1980,
1025.
22. Oberli, L.; Monot, R.; Mathieu, H.; Landolt, D.; Buttet, J. Surface
Sci. 1981, 106, 301.
23. Cheung, T. Surface Sci. 1983, 127, L129.
24. Baetzold, R.; Mason, M.; Hamilton, J. J. Chem. Phys. 1980, 72, 366.
25. Baetzold, R. Surface Sci. 1981, 106, 243.
26. Young, V.; Gibbs, R.; Winograd, N. J. Chem. Phys. 1979, 70, 5714.
27. Mason, M.; Gerenser, L.; Lee, S. Phys. Rev. Letters 1977, 39, 288.
28. Young, V.; Zhao, L. Chem. Phys. Lett. 1983, 102, 455.
29. Baetzold, R.; Mason, M.; Hamilton, J. J. Chem. Phys. 1980, 72,
366.
30. Baba-Ahmed, A.; Gayoso, J. Theoret. Chim. Acta. (Berl.) 1983, 62
507.


Intensity (counts)
10GHR MN02 DEPOST I ON ON CCF. UALENCE BAND REG. THETA=10 DEG.
Run: 3MN4 Regs 1 (UB ) Scan: 1 Bases 1980 Max Cts's:
Run: BULK6 Regs 1 (UB ) Scans 1 Bases -9 Scales 1.2381
Binding Energy (eU)
103


and the data for Mn23 on carbon foil, bulk Mn203, and Mn02 with
coverages of 0.055 and 0.133 on carbon foil can be fit with high
correlation to a linear equation of the form
120
Y=at+b. (64)
Table 5-2 shows the values for a,b, and the degree of correlation
when equations 63 and 64 are fitted to experimental data. The solid
lines in Figures 5-7 and 5-8 correspond to the best fits.
Table 5-2
Fit Parameters for Experimental Data.
Sample
a
Equation 63
b CORR
a
Equations 64
b CORR
Dispersed MnO
33.2
-1.65
0.992
Dispersed Mn23
43.4
-16.6
0.913
3.89
5.32
0.991
Thick Mn23
11.2
-2.63
0.965
0.94
4.68
0.976
Bulk Mn23
11.4
-3.32
0.947
0.98
3.44
0.987
Mn02 (O=.055)
114
-49.5
0.878
10.5
2.20
0.977
Mn02 (O=.073)
117
-19.1
0.981
9.33
66.8
0.951
Mn02 ($=.133)
3.70
-42.0
0.998


Figure 5-7. Normalized change in absorbance magnitude (see text)
versus time for MnO and Mn23 samples. The original is
a point for each.
(o) dispersed Mn23 on carbon foil; () dispersed MnO on
carbon foil; (A) thick Mn23 on carbon foil; (+) bulk
Mn203.


CHARACTERIZATION AND CATALYTIC ACTIVITY OF DISPERSED
TRANSITION METAL OXIDE PARTICLES ON CARBON SUBSTRATES
By
JACKG. DAVIS, JR.
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988
u :OF F LIBRARIES


Absorbance
0 550
0500 -
0.450 -
24 36
time (hours)
48
113


85
At 0=0, it is 196991 and at 0=85 it is 354465. If the second value
for 100 % area is divided by the first a ratio of = 1.8 is obtained. The
same ratio for the MnC>2 deposition yields a ratio = 8.4, an
approximate 4 fold increase. The conclusion that ferric oxide is not
being incorporated to as great a degree into the layers of the carbon
foil as manganese dioxide can also be drawn from the area % of the
529 eV peak. At 85 degrees the 529 eV peak constitutes 52.9% of the
area under the curve for the sample prepared by the solution
deposition of Mn02 while it constitutes only 19.3% of the area under
the curve for the sample prepared by the solution deposition of
Fe23. The percentage of area contributed by the 529 eV peak is
greater at 0=0 degrees than at 85 degrees for dispersed ferric oxide.
This further substantiates the differences in the degree of
incorporation between the two oxides. The number atom ratios also
indicate that less of the oxide is being incorporated into the carbon
foil. Table 4-3 gives the number atom ratios for the Fe and C atoms
as resulting from solution deposition.
Table 4-3
NFe/Nc values for samples prepared from the solution deposition of
Fe23 on carbon foil.
take off angle
18 hours
100 hours
0
0.057
0.044
10
0.12
0.095
25
0.098
0.089
55
0.075
0.092
85
0.063
0.083


Figure 3-1. Comparison of spectra of highly dispersed and
continuous film of MnO on carbon foil.
a) The valence band spectrum of highly dispersed MnO on
carbon foil.
b) The valence band spectrum of a thick continuous film
of MnO on carbon foil.


87
2) Small particles of oxide produced by photoemission in the
solution phase deposit on the surface and intercalate between layers
of carbon by penetrating along exposed edges. They then can leave or
"fall off" the carbon foil edges at a later time.
3) Permanganate anions intercalate the carbon foil and particles of
Mn02 are produced by in-situ decomposition, while small particles
produced by photodecomposition in solution phase deposit only on
the surface.
4) Some combination of all three.
Photoemission results can be used to investigate these scenarios.
Based on an earlier study of fresh carbon foil [42], the Os peaks at
532.1 eV and 533.2 eV may be associated with graphite oxide, Cx+
(OH')y (H20)2, where the 532.1 eV peak is due to OH' and the 533.2
eV peak is due to H2O. For the four year old carbon foil, there is no
significant difference between the ratios of the areas of O1 s peaks
at 529.8 eV and 530.9 eV to the area of the Os peak at 532.1 eV for
take off angles of 35 and 85 degrees, as shown in Figures 4-12 and
4-13. Thus, the subsurface has an almost homogeneous distribution
of carbon oxidation species (the relative amount of the peak at 533.2
eV increases slightly with the take off angle) and segregating
species in the depth explored. However after exposure of 4-year old
carbon foil to dilute, neutral permanganate for 100 hours, the
situation is that shown in Table 4-4. There are significant changes
( 5%) in the peaks at 533.2 eV and 529.7 eV. Similar results are
obtained in the case of the deposition of iron (III) as the hydrous
oxide, which can be seen in Table 4-5. The drastic reduction in the


22
eigenfunctions 'Fa, *Fb are integrated over x, they must give zero as
a result, as shown by equation (11)
J T'a'Fb dx =0. a*b (11)
Such wavefunctions are orthogonal. If wavefunctions are normalized
and orthogonal, they are said to be orthonormal.
A second postulate states that when a dynamical variable of an
operator is measured, that the measurement is one of the
eigenvalues of that operator. If a large number of identical systems
have the same function 'F then the average number of measurements
on the variable M is given by
Mav = XF*MVF dx. (if 'P is normalized) (12)
By linking the postulates together, and knowing the Hamiltonian
operator represents the total energy of the system, the average
value for the energy of a large number of identical systems can be
obtained. This is given by equations (13) and (13a).
E = ivF*HvFdx (if NF is normalized) (13)
The bra-ket form of (13) is
E = . (13a)
In molecular orbital calculations, the energy of the system is
minimized according to equation (13). Before this can be done
however, it is necessary to formulate the Hamiltonian operator for
the system and the form of the wavefunction VF. To formulate the


126
[A-AqI/Aq = a In (t+1) +b (65)
when k is large and
|A-A0|/A0 = at + b (66)
when k is small.
The values for a, b, and the degree of correlation for a given rate
constant k are shown in Table 5-3. Thus in fact, the empirical fits to
the experimental data can be regarded as limiting forms of a 2nc*
order autocatalytic reaction.
Table 5-3
Example of 2nc) order Autocatalytic Simulation for various Rate
Constants on Time Intervals Corresponding to Those Used
Experimentally.
A0 = 1.00 M; B0 = 0.20 M
Equation 65* Equation 66*
Rate Constant(hr1) a b CORR a b CORR
1/6
0.271
-0.005
0.990
0.020
0.241
0.874
1/12
0.236
-0.085
0.927
0.021
0.046
0.983
1/24
0.138
-0.070
0.858
0.013
-0.021
0.998
*Y=|A-A0|/Aq


Figure 4-15. XPS spectra of valence band region of MnC>2-
Spectrum with higher binding energy is that for
dispersed MnC>2 on carbon foil. The other spectrum
is for bulk Mn02.


70
Results
After the carbon foil rectangles are placed in the permanganate
solution for either 2, 20, or 100 hours, XPS data is acquired in the
regions mentioned in the previous section. The Oi s region of the
manganese free carbon foil is compared with the 0-|s regions of the
carbon foil samples which are subject to deposition to see if any
deposition had occurred. Figure 4-3 shows a peak fit of the Oi s
region of manganese free carbon foil acquired at a take off angle of
0 degrees. The manganese free carbon foil contains oxygens species
in four different chemical environments. Several of the oxygen
species have been identified in a paper written by Young [42]. The
additional species are probably due to the fact that the carbon foil
has aged. The carbon foil used by Young in the investigation to
identify inherent surface oxygen species was new. The carbon foil
used for the deposition of manganese dioxide is approximately 4
years old. Figure 4-6, which illustrates the Mn2p peaks of a sample
of carbon foil which has been allowed to soak in potassium
permanganate solution 100 hours, confirms that manganese
deposition has indeed occurred. Figure 4-7, which shows a peak fit
for the Ois region at a 0 degree take off angle for a sample prepared
with 100 hours of deposition time, shows that there is an additional
peak at 529.0 eV. This value compares very favorably with the
literature value of 529.3 eV for the 0-|s peak of bulk Mn02 [43]. The
O/Mn ratio is 1.72, within experimental error of the expected ratio
2.0. Figure 4-8 illustrates a peak fit for the Ois region of the same
sample at a 85 degree take off angle. In this case, the O/Mn ratio is


REFERENCES
1. Carlson, T. Photoelectron and Auger Spectroscopy (Plenum Press,
New York, London 1978).
2. Fellner-Felldegg, H.; Gelius, U.; Wannberg, A.; Nilsson, G.;
Basilier, E. Siegbahn, K. J. Electron Spectrosc. 1974, 5, 643.
3. Wannberg, B.; Gelius, U.; Siegbahn, K., Uppsala University,
Institute of Physics Report No. 818 (1973).
4. Wiley, W.; Hendee, C. I.R.E. Trans. Nucl. Sci. 1972, NS-9, 103.
5. Brundle, C.; Baker, A. (editors) Electron Spectroscopy: Theory,
Techniques and Applications ( Academic Press, London, New York,
San Francisco 1978).
6. Ballard, R. Photoelectron Spectroscopy and Molecular Orbital
Theory (John Wiley & Sons, New York 1978).
7. Koopmans, T. Physica 1934, 1, 104.
8. Lowe, J. Quantum Chemistry (Academic Press, New York, London
1978).
9. Claude, C.; Bernard, D.; Frank, L. Quantum Mechanics Vols. 1&2.
(John Wiley & Sons New York, London 1977).
10. Slater, J. Phys, Rev. 1959, 34, 1293.
11. Pople, J.; Beveridge, D.; Approximate Molecular Orbital Theory
(McGraw-Hill Book Company, New York, London 1970).
12. Pople, J.; Segal, G. J. Chem. Phys. 1965, 43, S136.
135


98
"bulklike" than the particles prepared by vapor deposition. This
dissimilarity between particles prepared by solution deposition and
vapor deposition is no doubt due to the vast difference between the
two methods of deposition as opposed to the differences between
the MnO, Mn23, and MnC>2 oxides. In vapor deposition the Mn probably
becomes highly dispersed when vaporized and impinges upon the foil
in a highly dispersed fashion. In solution deposition, the Mn02 may
grow in solution before it becomes lodged to the carbon foil surface.
It would be of interest to compare the catalytic activity of the
dispersed oxide with its bulk counterpart to see if the presumed
decreased d electron population found in Mn of the more dispersed
oxides can affect the rate of a catalytic reaction. This is in fact the
topic of the next chapter.
Table 4-7
FWHM and binding energy values for dispersed and bulk Mn2<33 and
MnC>2
Oxide
FWHM (eV)*
B.E.(eV)*
Mn203 (coverage=0.3)
6.2
4.3
Mn23 (coverage=0.65)
6.6
3.0
Bulk Mn23
6.9
2.5
Mn02 (coverage=0.07)
6.3
4.5
Bulk Mn02
6.3
4.2
see Appendix


16
stored, it can be viewed by choosing the off line processing option.
After this option is chosen the data file name is typed in and the
data appears in the form of spectra. The y-axis represents the
intensity of the signal (number of photoelectron counts for a given
kinetic energy) and the x-axis can represent either the binding or
kinetic energy of the photoelectrons. It is also possible to perform
depth profiling, which is done in conjunction with the ion gun. The
ion gun creates argon ions which are directed as a beam to the
sample. The beam strips away successive layers of the sample and
the composition of each layer is determined. One of the
disadvantages of this technique is that it destroys the sample. If one
is using the sample in a catalytic experiment it might be preferable
to use the sample after it has been analyzed. Also, matrix effect
data is not attainable. Very rarely is the analyte going to be
unaffected by the matrix in which it resides. Depth profiling works
from the premise that all of the molecules are going to be sputtered
at an equal rate, which is not the case. For example, in my work with
dispersed manganese dioxide on carbon substrates, one factor which
causes the molecules to be sputtered at different rates is the
difference in the weights between the manganese and carbon atoms.


106
Kinetics of Reactions
In this research project the relative amounts of catalytic
reactivity for various samples of dispersed manganese oxides on
carbon foil are reported. Catalytic activity affects the rate of
reaction, which is defined as the "rate of change of concentration of
a substance involved in the reaction with a minus or plus sign
attached, depending on whether the substance is a reactant or a
product" [51]. If we examine the equation given by
aA +bB = gG +hH (52)
the rate of reaction can be defined by any of the following
-d[A]/dt, -d[B]/dt, +d[G]/dt, or +d[H]/dt.
From the above relationships it can be seen that the rate of reaction
is affected by the concentration of the components of the reaction.
Usually, it is affected only by the concentration of the reactants. If
the concentration of the products does affect the reaction rate, then
the reaction is referred to as autocatalytic. If an equation is formed
which shows the relationship between the rate of reaction and the
concentration of a component, then that equation is a rate
expression. The reaction of hydrogen and iodine to produce hydrogen
iodine is given by
H2 + l2 = 2 HI.
(53)


6 7
rectangle with dimensions of approximately 1 cm X 1.2 cm. This is
done in a sample analysis chamber of a Hewlett Packard X-ray
photoelectron spectrometer at a base pressure of ~ 10'7 torr. Figure
4-4 illustrates that after the Mn is vaporized, it reacts with oxygen
to form either the Mn(ll) or Mn(lll) oxide, depending upon the
reaction conditions. These samples are outgassed by heating them
to 235 C for 20 minutes before recording spectra. If there is any
MnOOH on the surface, this procedure will convert it into Mn23.
Dispersed manganese dioxide on carbon foil is prepared by solution
deposition since is has been shown that Mn02 can be deposited by
means of the KMn04 decomposition [40]. Absence of KMn04 itself is
confirmed by the absence of K core level peaks in the survey scans.
The reaction for this decomposition is given by equation (51), where
the fate of the negative charge has not been established.
Mn(s)
W filament
basket
Mn(v)-
Oxidation
(poor vacuum)
MnO/C
250 C
atmosphere
M1123/c
Figure 4-4. Schematic showing method of vapor deposition of
manganese oxides on carbon foil.
Equation (51a) symbolizes deposition onto the carbon foil.
Mn04 MnC>2 + O2
Mn02 MnC>2/C
C foil
(51)
(51a)


Intensity (counts)


b) XPS Spectra
of bulk MnO
-12
-10^8
" 6 -4
eV


Figure 4-13. Peak fit of 0-|S photoelectron peak of carbon foil.
The peak was acquired at a take off angle of 85
degrees.


23
Hamiltonian operator, one must account for the total energy of the
system. Terms must be formulated for the kinetic energy of the
electrons, the potential between the electron and the nucleus and
the electrostatic repulsion between electrons. Formulation of these
terms results in an equation given by
n N n n-1 n
H = -(1/2) E A¡2 E E ( Zn/|>¡) + E E 1/rij. (14)
¡=1 n=1 ¡=1 ¡=1 j=i+1
The letters i and j are indices for the n electrons and jj. is an index
for the N nuclei. In principle wavefunctions can be symmetric or
antisymmetric. An antisymmetric wavefunction has equal amounts
of area represented by (+) and (-) regions. Symmetric wavefunctions
do not. This principle can be seen in Figure 2-3.
Figure 2-3. Figure showing principle of antisymmetric and
symmetric wavefunctions.
a) antisymmetric; b) symmetric
The Heisenberg uncertainty principle states that the ability to "see"
electrons in an atom would perturb it so strongly that it could not be


Absorbance
115


63
The variable x¡ is the ratio of the raw area/intensity of the ith peak
and q¡ is the corresponding quantification factor (i.e. related to a
which was discussed earlier). The quantification factor or a is a
term which is a manifestation of how sensitive the instrument is to
an electron in a particular orbital. The quantification factor is a
function of the size of the atomic orbital.
Not only is the relative concentration of elemental constituents
which comprise a surface desired, but also the relative
concentrations of different chemical species which are contributing
to a given spectral window (i.e. Ois, C-|S)- Analysis of a given
photoelectron peak is achieved by peak fitting a number of different
symmetrical line shape functions (either Gaussian or Lorentzian) to
the peak. With the DS 800 software it is possible to express a
distribution as a combination of a Gaussian and Lorentzian function.
The distribution can be made to have as much as 50% Lorentzian
character. To fit these distribution functions to a photoelectron
peak, it is first necessary to construct a synthetic window (a
different type of window than needed to determine the relative
atomic concentrations). The synthetic window is first constructed
by typing "syn" at the prompt. After the operator states the name of
the window (i.e. Cis, Oi s etc.) the cursor appears and the window
width is determined by pressing the space bar at the desired
positions (in eV) at the beginning and the end of the window. After
the window is formed a table appears which requires the operator to
state what type(s) of function(s) are to be fit, (i.e. either Gaussian
or Lorentzian or combinations thereof), the element IDs, the
positions of maximum intensity of the component distributions and


52
cluster, but can also be due to the formation of a distribution of
geometries of different stability on the surface. Thus a meaningful
interpretation of the experimental VBDOS curves of supported metal
oxide particles cannot be made without supplementary information
on the particle size distribution.


51
After these geometries were determined, it was necessary to
construct valence band density of states (VBDOS) curves from the
eigenvalues and eigenvectors of each geometry. VBDOS curves are
constructed by centering a Gaussian distribution function about each
eigenvalue which has a FWHM of 0.85 eV (the natural line with for
AlKa radiation is this value) and then summing them over some
specified energy range. The relative heights of the Gaussian
distribution functions are determined by the following formula.
Ht. of Gaussian = X c2jj oj (46)
j
The c¡j 's are the coefficients of the atomic orbitals and the aj's are
the Scofield cross sections [36]. A VBDOS curve has been
constructed for each of the geometries shown in Figure 3-2. Figure
3-3 illustrates these VBDOS curves. Weighted distributions of these
geometries can be used to construct composites. These simulate the
effect of having active sites on the substrate surface which
stabilize different geometrical configurations of the clusters. The
weights simulate the relative fraction of each type of site on the
surface. One such composite, which can be seen by Figure 3-4,
shows a remarkable agreement with the lineshape obtained for very
thick MnO supported on carbon foil. Although there is no evidence
for "geometry* selective active sites on the supports normally used
for heterogeneous catalysts, there is also no evidence against such
sites. Based on Figure 3-4, the variation in the molecular geometry
for a given value of X does have an effect on the VBDOS. Valence band
broadening is not only due to an increase in the number of atoms in a


110
-dA/dt=k[A][B]. (60)
If Aq and B0 equal the initial concentrations of A and B, then A0-A =
B Bo or B = A0 + B0 A. If equation (60) is integrated the following
rate expression results.
1/(A0 +B0)ln (A0B/B0A)= kt (61)
Experimental
As was mentioned in the previous chapter, vapor deposition was
used to prepare dispersed MnO and Mn23 on carbon foil and solution
deposition was used to prepare dispersed MnC>2 on carbon foil. The
carbon foil which was used as a support of these oxides was from
Goodfellow metals and is assayed at 99.8% C. The foil is cut into
rectangles with dimensions of 1 cm X 1.2 cm. There is oxygen
contamination on the surface of this foil, which can be almost
completely removed by heating to 210 C in vacuum [28]. Some of
the carbon foil that was used was four years old; not as much of its
oxygen could be removed by heating. The method of vapor and
solution deposition was discussed in the previous chapter and will
not be repeated here. The coverages (O) (i.e. NMn/Nc at 0=0) of the
oxides were determined by variable angle XPS. The names of the
oxides and their coverages for the samples used in this investigation
are listed in Table 5-1. A value of O =1 means a continuous film of
the oxide is present. This value is obtained only when no discernible
C-|s peak is present for 0 0. No discernible Ci s peak was
observed for a take off angle of 50 degrees. The composition of


128
1. Mn04'
-Mn04
hv
2. Mn04*' + Mn04
radiationless relaxation
Mn04'2 + Mn02 + 02(g)
-Mn04
3. Mn04' + Mn02
-Mn02 Mn04
-2
4. Mn02 Mn04 '2 + 2 H +
-Mn04" + Mn(lll) (ppt.)
5. 2 Mn(lll) + Mn04
-2
3 Mn02
6. Mn02 (active)
-Mn02 (inactive)
Figure 5-9. Proposed mechanism for the autodecomposition of
neutral permanganate [48].


138
46. Narita, E.; Hashimoto, T;. Yoshida, S.; Okabe, T. Bull. Chem. Soc.
Jpn. 1982, 55, 963.
47. Kachan, A.; Sherstoboeva, M.; Zhur. Neorg. Khim. 1958, 3, 1089.
48. Duke, F. J Phys. Chem. 1952, 56, 882.
49. Adamson, A.; J. Phys. & Colloid Chem. 1951, 55, 293.
50. logansen A.; Grushina, N. Khim. Fiz. 1982, 1, 121.
51. Frost, A.; Pearson, R. Kinetics and Mechanism (John Wiley & Sons
Inc., New York, London 1961).
52. Oku, M.; Hirokawa, K. J. Electron Spectrosc. Relat. Phenom. 1975,
7, 465.


CHARACTERIZATION AND CATALYTIC ACTIVITY OF DISPERSED
TRANSITION METAL OXIDE PARTICLES ON CARBON SUBSTRATES
By
JACKG. DAVIS, JR.
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1988
u :OF F LIBRARIES

ACKNOWLEDGMENTS
I would like to express my appreciation to Dr. Vaneica Young for
her guidance and very helpful suggestions during the course of my
research project. I would also like to thank members of my
research committee who were also of help.
Paul McCaslin, Linda Volk, Mike Clay, and Peter ten Berge all
made my stay at the University of Florida much more enjoyable by
their friendship and advice.
11

TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ii
ABSTRACT v
CHAPTERS
1 INTRODUCTION 1
Fundamental Principles of X-Ray Photoelectron
Spectroscopy 1
Instrumentation 3
2 BACKGROUND OF THEORETICAL RESEARCH UNDERTAKEN .17
Overview of Molecular Orbital Theory 17
Approximations to Molecular Orbital Theory 31
3 THE EFFECT OF VARIATION OF MOLECULAR GEOMETRY
OF A TRANSITION METAL OXIDE CLUSTER ON THE
VALENCE BAND DENSITY OF STATES 38
Background 38
Modification of CND02/U Algorithm 43
Construction of VBDOS curves 50
4 PHOTOEMISSION STUDIES OF VAPOR DEPOSITED AND
SOLUTION DEPOSITED MANGANESE OXIDES AND
SOLUTION DEPOSITED IRON OXIDES ON CARBON FOIL 57
Introduction 57
Variable Angle XPS (VAXPS) 59
Quantitative Analysis by XPS 61
Preparation of Samples 64
Results 70
in

CHAPTERS
5 EFFECT OF DISPERSED MANGANESE OXIDES ON THE
DECOMPOSITION OF PERMANGANATE SOLUTIONS 104
Introduction 104
Kinetics of Reactions 106
Experimental 110
Results 118
Correlation of Rate Law Expressions
with Experimental Data 125
6 CONCLUSIONS AND FUTURE WORK 129
APPENDIX
STATISTICAL ANALYSIS OF XPS VALENCE BAND DATA 133
REFERENCES 135
BIOGRAPHICAL SKETCH 139

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
CHARACTERIZATION AND CATALYTIC ACTIVITY OF DISPERSED
TRANSITION METAL OXIDE CLUSTERS ON CARBON SUBSTRATES
By
JACK G. DAVIS, JR.
December 1988
Chairperson: Vaneica Y. Young
Major Department: Chemistry
After modification of a CND02/U algorithm, a valence band
density of states curve (VBDOS) is constructed from the resulting
eigenvectors and eigenvalues for a distribution of MnO dimer
structures. The resulting curve shows a remarkable similarity to the
X-ray photoelectron spectroscopy (XPS) spectrum of a thick
continuous film of MnO.
In order to investigate the properties of small particles using
XPS, they must be isolated on supports. Different methods of
preparing dispersed oxides on carbon foil supports are investigated.
In particular, vapor and solution deposition are used to fabricate
various transition metal oxides on carbon foil. Vapor deposition is
used to disperse MnO and Mn203 on the carbon substrate and solution
deposition is used to disperse Mn02 and Fe23 on the substrate. Data
v

acquired by XPS from the samples of both methods indicate that two
completely different surfaces result. Vapor deposition yields a
surface in which the particles are confined to the surface. Solution
deposition yields a surface whereby the particles have been
incorporated into the surface. The electronic structure of these
particles are investigated using valence band photoemission.
When the dispersed Mn oxides on carbon foil are placed in
permanganate solution, it is found that the dispersed MnO has a
greater effect on the autocatalytic decomposition of permanganate
than does dispersed Mn203. It is also found that dispersed Mn23 has
a greater effect on this reaction than either the bulk or continuous
film of the Mn(lll) oxide. Dispersed MnC>2 on carbon foil are judged to
have too high an effect on the reaction, possibly because of the
particles which are incorporated into the surface.

CHAPTER 1
INTRODUCTION
Fundamental Principles of X-Rav Photoelectron Spectroscopy
The analytical methodology of X-Ray Photoelectron Spectroscopy
(XPS) is an effective means for the chemical analysis of surfaces. In
XPS, a solid is bombarded with X-Ray radiation, typically of energies
of either 1487 or 1254 eV. Photoemission of electrons from the
surface region of the solid occurs. The ejected photoelectrons are
dispersed according to their kinetic energy (if an electrostatic
analyzer is used) and then counted. The intensity of the signal is a
function of the number of counts at a given kinetic energy.
Conservation of energy requires that
hv= B.E. + K.E. + 0Spect, 0 )
where hv is the energy of the incident X-Ray radiation, B.E. is the
binding energy and K.E. is the kinetic energy of the photoelectron and
0spect is the spectrometer work function. The value of 0spect. W¡H
vary from instrument to instrument, thus each instrument must be
calibrated for this quantity. From the measured kinetic energy of the
photoelectron its binding energy can be calculated by
B.E. = hv K.E. 0spect. (2)
1

From the binding energies of photoelectrons, chemical information
can be deduced about the surface.
2
Figure 1-1. Schematic Representing Basic XPS Principles.
X-Ray bombardment of a surface can produce another type of
electron other than a photoelectron. Upon the photoemission of an
electron, a vacancy will develop after ejection. An electron with
lower binding energy from another subshell can move in and fill the
vacancy. This movement results in the dissipation of energy which
can cause a third electron, known as an Auger electron, to be
ejected. Auger electrons are denoted by three upper case letters. The
first letter represents the subshell containing the electron which is
ionized by the incident X-Ray radiation, the second represents the
subshell containing the electron which fills the vacancy, and the
third the subshell from which the Auger electron is ejected. The
signal intensity or peak height is affected by parameters which do
not affect the binding energies. One such parameter is the
differential cross section for photoionization [1], which is given by

3
da(e)/dft= oj(e)/4 [1 + BP2(cos(0)]. (3)
It is seen that the intensity is a function of the total cross section
for photoionization, which is the probability of observing an
electron of a given energy for ionization, and the angle 0 between
the incident photon beam and the direction of ejection of the
photoelectron. The 3 term is known as the asymmetry parameter
and is a term which is characteristic of a given molecular orbital.
The value of I3 indicates what the preferred direction of the
photoelectrons will be with respect to the incident photon beam. If
3=+2 as is the case for a spherically symmetric distribution of
charge (an atomic s orbital), then the phbtoelectrons will be
preferentially ejected at angles of 90 to the photon beam [1]. For
orbitals having angular momentum (i.e. p, d or f), 3 values will be
less than +2, which will cause the photoelectron to be preferentially
ejected at different angles. If the intensity is plotted against 0 for
many different values of 3 it is found that there is a "magic angle"
of 54.7 where the intensity is independent of 0. When
spectrometers are operated at this magic angle, total cross sections
can be used directly in quantitative analysis.
Instrumentation
General Principles
An X-ray photoelectron spectrometer is composed of a x-ray
source, a sample analysis chamber (SAC), an electron or energy
analyzer, and a detector system, which is usually interfaced with a
computer. X-rays are generated by bombarding a material (target)

4
with high energy electrons. When these electrons impinge upon the
target they knock out its electrons, which creates vacancies. The
photons are generated as a result of the higher energy electrons of
the target filling the vacancies created by the ejection of the lower
energy electrons. This process creates photons of various energies
which then pass through either a Be or an Al window. This acts to
partially filter the bremsstrahlung or x-ray continuum from the
desired Ka rays. Even after filtration, however, only about 50% of
the photons are of the desired energy. The contribution to the
photoelectron spectrum by the bremsstrahlung is not important
because it is distributed over 2 KeV while the Ka rays are
concentrated in a peak of 1eV FWHM [1]. In addition to the Ka 1,2
line, other lines are present due the to difference in energy between
the L|| and L||| levels. This difference is important because Ka 3^
gives satellites in the spectra. With monochromatization it is
possible to reduce the width of Al Ka 12 radiation to as little as 0.2
eV [2]. X-ray radiation can be monochromatized by allowing it to
impinge upon a crystal which will cause it to be dispersed. After
dispersion, radiation of a particular energy can be selected by means
of a slit. This method is known as slit filtering. Another method
involves the matching the dispersion of the crystal with that of the
spectrometer. In this technique the X-rays are dispersed by the
crystal before they reach the sample. Their dispersion will cause
the resulting photoelectrons to come out at slightly different
energies, depending on their position along the target. This
dispersion is compensated for by the spectrometer so all electrons
will be ejected as if they came from atomic orbitals having the

5
same energy [1], Still another means to reduce the inherent line
width of the radiation is the fine focusing method, which uses a
rotating anode to concentrate the beam before it impinges upon the
crystal. Its advantages are that it gives more photons after
emergence from the monochromator and does not put any
restrictions on the sample. Monochromatization removes those lines
responsible for source satellites in the spectra.
a)
b)
Crystal
Sample
Crystal
Figure 1-2. Schematics showing different types of
monochromatization.
a) Slit Filtering
b) Dispersion Compensation

6
Crystal
Figure 1-2.--continued
c) Schematic showing the fine focusing method of
monochromatization.
It also removes all of the high energy brehmsstrahlung radiation,
which is responsible for the decomposition of organic samples and
some inorganic salts. The one disadvantage is that there is a large
intensity loss for those instruments which employ a large sample
area like the retarding grid instruments [2], Figure 1-2 illustrates
the above methods of monochromatization.
To avoid collisions between the X-rays and photoelectrons with
the surrounding gas molecules, it is necessary to contain the source
and sample in a high vacuum sample analysis chamber (SAC). In our
instrument typically pressures as low as 10-9 torr are achieved.
With some degree of effort, namely by placing liquid nitrogen in the
cold trap of the SAC, pressures as low as 5 X 10'1"' torr are
possible. The next major component of an X-Ray Photoelectron
Spectrometer is the electron or energy analyzer. Photoelectrons are
generated with a very broad spectrum of energies. Before an electron

7
with a particular kinetic energy can be counted by the detector
system it must be separated from photoelectrons which have kinetic
energies different from itself. The function of the electron analyzer
is to perform this separation. The spectrum of photoelectron kinetic
energies relative to the sample is not identical to the spectrum of
photoelectron kinetic energies relative to the electron analyzer,
because the sample and the spectrometer share a common ground, as
seen by Figure 1-3. However, they are in one-to-one correspondence,
since they differ by a constant factor, as shown by the following
equations:
Ekin = E'kin + (0sam-spect)
hv = Ebin^ + E'kin + 0sam
hv = EbinF + Ekin + Aspect.
Figure 1-3. Diagram showing principles for the calculation of
binding energies.

8
EbinF is the Fermi level referenced binding energy of the electron in
the sample. Thus, binding energies will be measured correctly only
when the Fermi level of the sample is pinned to the Fermi level of
the spectrometer. This is not possible for insulators, and the
problem is further aggravated by sample charging which results
from the photoemission process. The work function of the
spectrometer is determined by calibrating it with a known standard,
for example, the binding energy of the Au4f electron, which has a
literature value of 83.8 eV. Auxiliary referencing must be employed
for insulators. Most common are the gold decoration technique or
referencing to the C-|s contamination peak.
There are three main types of analyzers which perform these
functions. The two most important are the retarding grid and
dispersion types. The retarding grid analyzer forces the electron to
traverse a potential difference between two grids. This analyzer has
a poor resolution and is not employed in any commercial x-ray
photoelectron spectrometer. The dispersive type analyzer, which is
most commonly used today, separates photoelectrons either
according to their momentum or energy by making them traverse
either a magnetic or electrostatic field respectively. The earliest
dispersion analyzers were of the magnetic type. In this type
analyzer, the photoelectrons are sorted according to their
momentum. The equation which relates the magnetic field, with the
path and momentum of the photoelectron is given by
B(p0) = mo/ep0.
(4)

9
The magnetic field is B, m and x> are the mass and velocity of the
electron and p0 is the radius of the orbit of the electron. Double
focusing can be understood by looking at Figure 1-4. If the
photoelectron enters the analyzer; at an angle 0 to po (the optic
circle), in the xy plane or at an angle ji with respect to the z-axis,
then it will return to the optic circle after it has traversed an angle
of 7W2 or 255 degrees. In other words, the analyzer has the ability
to redirect the deviation of the photoelectron whether it deviates in
or out of the plane of p0. The major advantage of the magnetic
dispersion analyzers is that a greater field can be supplied for the
study of high energy (>5000eV) photoelectrons. At this energy
relativistic effects become significant and the optics needed to
study such electrons are better understood for magnetic
instruments^ ]. -
Figure 1-4. Principle of Magnetic Double Focusing Electron Analyzer.

10
One disadvantage of this type analyzer is that of cost. A magnetic
analyzer comparable to an electrostatic one would cost
approximately ten times as much. Another disadvantage of the
magnetic analyzer instruments is their sensitivity to stray
magnetic fields. If a resolution of 0.01% is desired the stray field
must be reduced to 0.1 mG over a very large volume. To achieve this
reduction of stray magnetism, very large compensating coils must
be used. This makes the instrument as a whole very space consuming.
Also, the stray fields must be monitored continuously [2].
Besides magnetic dispersive analyzers, there are also
electrostatic type analyzers, which are more commonly used today
because they cost less to construct and are less cumbersome. Their
principle disadvantage is that they are unsuitable for studies
involving high energy photoelectrons. If one is analyzing electrons
with an eV greater than 2000, relativistic effects become
noticeable. The optics for dealing with these effects are better
understood for magnetic than for electrostatic analyzers. In an
electrostatic analyzer, the photoelectron is dispersed according to
its kinetic energy along a predescribed path. This is done by forcing
the photoelectron to traverse an electrostatic field instead of a
magnetic one. Such a field is achieved by placing a potential between
two plates. The geometry of these plates determines the type of
electrostatic analyzer. Several of the possible geometries of the
plates are hemispherical and cylindrical. In our instrument
hemispherical plates are employed. If we look at Figure 1-5 we can
see a schematic diagram of a hemispherical electron analyzer.
Equation (5) shows the relationship between the voltage between the

plates, the kinetic energy of the photoelectron, and the radius of its
orbit in the analyzer.
11
Figure 1-5. Schematic illustration of electron analyzer with
retardation section.
V=E/e(R2/Rl-Rl/R2) (5)
This equation states that when a particular voltage is being applied
between the plates, only photoelectrons of a particular kinetic
energy will be able to completely traverse space between the plates
and reach the detector. To measure the kinetic energies of all
photoelectrons which are generated, the voltage is continuously
varied over some specified range, usually with the aid of a computer
which has been interfaced with the system. To reduce or lessen the
tolerances of many of the mechanical components of the
spectrometer, the photoelectron passes through a retardation
section prior to its entry into the analyzer. If the kinetic energy of
the electron is reduced from Ekin to some final Eg, the relative

12
resolution required from the analyzer is reduced from AEkin/Ekin to
AEkin/Eo- If, for example, a spectrometer is required to achieve a
resolution of 0.1 eV for 1000eV electrons or 0.01% as the result of
retardation, it would be required to achieve a resolution of 0.1 ev for
100eV electrons. Retardation does reduce the intensity of the signal,
however, so a trade-off between intensity and resolution results.
After the photoelectrons have been dispersed according to their
kinetic energies, they must be detected and counted. Almost all
detectors in XPS utilize continuous-dynode electron multipliers of
the "channeltron" type [3-5]. These devices consist of glass tubes
which have been doped with lead and then treated in such a way so
as to leave the surface coated with a semiconducting material with
a very high secondary electron emissive power [3]. A voltage of a
few kV is placed between the ends of these tubes and electron
multiplications of the order 106-108 are achieved by repeated wall
collisions as electrons travel down the inside of the tube [6]. As the
voltage between the plates of the analyzer is swept, the electron
counts at different kinetic energies is usually stored with the aid of
a computer. Computer control is advantageous because it is
desirable to make repeated scans over a spectral region to average
out instrument drifts and to eliminate certain types of noise [6]. In
many cases repeated scans are mandatory. Weak signals can result
due to a small amount of the analyte or if the take-off angle (angle
between the sample and the analyzer about which more will be
covered in a later chapter) is at or near zero. The output from the
electron multiplier can be linked directly to a plotter or printer for
a single continuous sweep. The data system also allows one to

13
perform peak fits whereby -spectral data can be resolved into
Gaussian or Lorentzian distributions. For example the 0-|s spectra
can be resolved into a given number of these distributions which can
then be compared to literature values. By doing so, various chemical
species on the surface which contain oxygen can be deduced. Besides
performing peak fits, it is possible to deconvolute XPS spectra so
as to mathematically remove instrumental linewidth contributions.
This term is not to be confused with peak fit.
Instrument Employed
The instrument utilized for this work is the KRATOS XSAM 800.
This instrument has a dual anode (either Mg or Al can be selected) x-
ray source, a sample analysis chamber which can be pumped on by
either a roughing, turbomolecular, ion, or titanium sublimation type
pump, a hemispherical electron analyzer which includes a
retardation section to reduce the kinetic energy of the
photoelectrons before entering the analyzer, a detector consisting of
a electron multiplier and a data system (A Digital Micro PDP-11
with 256 K bytes of RAM) to control the scanning of the
photoelectrons and to collect and store the data. Peak fits are also
possible at the convenience of the operator.
The X-ray source consists of a filament assembly which is
essentially a tube with tungsten filaments which have been coated
with thorium on either side. The thorium has a lower work function
than the tungsten which makes the emission of electrons more
efficient. The anode is a hollow metal rod with one end open so as

14
to allow cooling water to pass through and the other end capped
with copper. The copper end resembles a roof with one side plated
with Al and the other side with Mg. To generate x-rays, the
emission stabilizer circuitry is first activated. This is a new circuit
design by KRATOS which is supposed to generate a more stable
emission of electrons from the filaments. After the emission
stabilizer is activated, the high voltage power supply is switched
on. Before this can occur, three safety interlocks must be satisfied.
First, the pressure of the cooling water to the anode must be
sufficient; second, the ion pump to the x-ray source must be on; and
third, the ion gauge must be switched on. If these interlocks are
satisfied, the power can be turned on. The desired voltage of the x-
ray radiation is dialed up. Usually a value of 15kV is selected. The
emission current is selected, and usually a value of 15mA is chosen.
At this point the x-rays can be generated either by computer
command or local command. When the Al anode is selected, the x-
rays have an energy of 1487 eV, and when the Mg anode is chosen,
the radiation is 1254 eV.
The sample analysis chamber (SAC) normally is kept at pressures
between 10"9 to 10-1"1 torr. To achieve this extremely low
pressure, it must be pumped in stages. First a roughing pump is used
to evacuate the chamber to approximately 0.5 torr. After this
pressure is obtained, a turbomolecular pump is used to bring the
vacuum down to the 10'3 torr region. The ion pump is switched on
and in conjunction with the turbomolecular pump evacuates the
chamber down to 10" torr. The valve between the SAC and the
turbomolecular pump is closed and the ion pump brings the vacuum

15
down to the operating range of 10*9 torr. The specifications of the
machine state that it is capable of reaching a pressure as low as
5X10*"*1 torr. To reach this pressure, however, it is necessary to add
liquid nitrogen to the cold trap in the SAC. This procedure is very
time consuming and is usually not necessary. To improve the
efficiency of the ion pump, it may be used in conjunction with a
titanium sublimation pump.
After the SAC has been pumped down to the 10*9 torr range and
the X-ray source has been activated, data can be acquired. This can
be done with or without computer control. Almost always computer
control is the option chosen. As stated previously the computer is a
Digital Micro PDP-11 with the RT-11 operating system and 256K
bytes of RAM. DS800, the software written by KRATOS, allows the
user to acquire and process data off line. To acquire data, one simply
chooses that option from the master menu which first appears after
the system is booted. After the data acquisition menu appears one
selects the region(s) which is (are) to be scanned, the number of
sweeps to be performed in that region and the time allowed for each
sweep. In addition, the operator has the choice of excitation source
(either Al or Mg), low or high magnification, low or high resolution,
and analyzer mode (either FRR or FAT). After the parameters have
been selected, data acquisition can begin. One chooses the run option
and assigns a file name to that run. The file name can be anything
with six or fewer characters. One parameter that the computer
cannot control on our instrument is the angle between the analyzer
and the sample (sometimes referred to as the take off angle). This
has to be adjusted manually. After the data has been collected and

16
stored, it can be viewed by choosing the off line processing option.
After this option is chosen the data file name is typed in and the
data appears in the form of spectra. The y-axis represents the
intensity of the signal (number of photoelectron counts for a given
kinetic energy) and the x-axis can represent either the binding or
kinetic energy of the photoelectrons. It is also possible to perform
depth profiling, which is done in conjunction with the ion gun. The
ion gun creates argon ions which are directed as a beam to the
sample. The beam strips away successive layers of the sample and
the composition of each layer is determined. One of the
disadvantages of this technique is that it destroys the sample. If one
is using the sample in a catalytic experiment it might be preferable
to use the sample after it has been analyzed. Also, matrix effect
data is not attainable. Very rarely is the analyte going to be
unaffected by the matrix in which it resides. Depth profiling works
from the premise that all of the molecules are going to be sputtered
at an equal rate, which is not the case. For example, in my work with
dispersed manganese dioxide on carbon substrates, one factor which
causes the molecules to be sputtered at different rates is the
difference in the weights between the manganese and carbon atoms.

CHAPTER 2
BACKGROUND OF THEORETICAL RESEARCH UNDERTAKEN
Overview of Molecular Orbital Theory
Fundamental Principles
One aspect of the research that is undertaken here involves the
effect of variation of the molecular geometry of clusters of the
formula (MnO)2 on the XPS valence band density of states (VBDOS).
To show this effect, results of molecular orbital theory are
compared with XPS valence band spectra. This comparison is
possible as a result of the theory of Koopman [7-8], which states
that the negative of an eigenvalue or molecular orbital energy (-8) is
equal to the binding energy (B.E.) of the photoelectron as given by
-e = B.E.
By making comparisons between eigenvalues and XPS valence band
data, information can be deduced about the electronic structure of
discontinuous clusters of deposited material on the surface of a
substrate. Using the postulates of quantum mechanics, the
eigenvalues can be obtained from the wavefunction of a system, as
discussed briefly below.
17

18
The particle, detected by XPS, can be regarded as a wave, with
the wavelength given by the de Broglie relation given by
mv = p = h/(X)
or X=h/p, (6)
where p is the particle momentum and h is Planck's constant [6].
This wave behavior of the electron can be characterized by a wave
function ^(im) which contains all the information possible about it
[9]. The Schrodinger equation, which allows eigenvalues to be
extracted from the wavefunction, can be derived from the de Broglie
relationship and the classical time-independent wave equation. It is
given by
ih/47i2(3/at) 'F(r,t) = -(h2/8:t2m) A^r.t) + (7)
where Ais the Laplacian operator 32/3x2 + 32/3y2 + 32/3z2. This
equation describes the motion of a particle when it is under the
influence of a potential V(r,t). The Laplacian operator and the
potential acting together on *F(r,t) form the Hamiltonian operator,
which represents the total energy of the system. The wavefunction
vF(r,t) must meet certain conditions, however, in order for the
equation to be valid. These conditions derive from the postulate of
quantum mechanics which states that a system of particles must be
described by a square-integrable function. Thus '{'(r.t) = ¥ (qi,q2,Q3,-
wi, W2, W3, , t), where the qs are the space coordinates, the
w's are the spin coordinates, and t is the time coordinate. V/*VF is the
probability that the space spin coordinates lie in the volume element

di (=dii, di2, ) at time t, if ¥ is normalized. To be acceptable the
function must be single valued, nowhere infinite, continuous, with a
piecewise continuous first derivative [8] as seen in Figure 2-1.
19
M
b) Not Continuous
M
c) Has Infinite
Value
x
Figure 2-1.
Illustrations of unacceptable and acceptable
wavefunctions.

20
The more familiar form of the Schrodinger equation (7) is
H'f' = E^, (8)
where H is the Hamiltonian operator and E is the energy. Equation (8)
is an example of a class of equations called eigenvalue equations as
shown by
Opf-cf, (9)
where Op is an operator, f is a function called an eigenfunction and c
is a constant called an eigenvalue. Therefore ¥ is an eigenfunction.
In equation (7) V is the potential energy, and the second derivatives
of the wavefunction ¥ are related to the kinetic energy. This is so
because the second derivative of T* with respect to a given direction
of measure is the rate of change of slope (i.e. the curvature) of ¥ in
that direction. A wave function with more curvature will yield a
greater kinetic energy. This is in agreement with the de Broglie
relationship which states that a wave with a shorter wavelength
will have a greater kinetic energy. Since we have a constant E, the
wave must have more curvature in regions where the potential
energy is low and visa versa [8]. The wavefunctions which are
associated with a particle are related to its momentum by equation
(6). In addition, the wavefunctions are eigenfunctions of the
Schrodinger equation (8) and must meet the conditions which are
illustrated in Figure 2-2. Also, the absolute square of the
wavefunctions (i.e. I'FI2) is proportional to the probability density
for finding a particle. If H' is an eigenfunction of equation (8), then
k*F is also an eigenfunction, where k is a constant. Since k can be any

number, a problem arises as to which value k should be. Since the
absolute square |Â¥|2 is proportional to the probability density for
finding an electron,
21
/N
v=o
T
WW
Higher E
Lower E
(a)
Figure 2-2. Illustration showing relationship between wave
curvature and energy.
(a) When the potential energy V=0, the higher energy
has more curvature (more wiggly). (b) As V increases
the wavefunction becomes less wiggly [8].
then the probability of finding a particle between x=-o and x=<~
must be 1. The following equation is given by
k*k J vF*(x)vF(x)dx =1. (10)
If selection of the k multiplier is made such that (10) is satisfied,
then the wave function VF' = kY is normalized. If two different

22
eigenfunctions 'Fa, *Fb are integrated over x, they must give zero as
a result, as shown by equation (11)
J T'a'Fb dx =0. a*b (11)
Such wavefunctions are orthogonal. If wavefunctions are normalized
and orthogonal, they are said to be orthonormal.
A second postulate states that when a dynamical variable of an
operator is measured, that the measurement is one of the
eigenvalues of that operator. If a large number of identical systems
have the same function 'F then the average number of measurements
on the variable M is given by
Mav = XF*MVF dx. (if 'P is normalized) (12)
By linking the postulates together, and knowing the Hamiltonian
operator represents the total energy of the system, the average
value for the energy of a large number of identical systems can be
obtained. This is given by equations (13) and (13a).
E = ivF*HvFdx (if NF is normalized) (13)
The bra-ket form of (13) is
E = . (13a)
In molecular orbital calculations, the energy of the system is
minimized according to equation (13). Before this can be done
however, it is necessary to formulate the Hamiltonian operator for
the system and the form of the wavefunction VF. To formulate the

23
Hamiltonian operator, one must account for the total energy of the
system. Terms must be formulated for the kinetic energy of the
electrons, the potential between the electron and the nucleus and
the electrostatic repulsion between electrons. Formulation of these
terms results in an equation given by
n N n n-1 n
H = -(1/2) E A¡2 E E ( Zn/|>¡) + E E 1/rij. (14)
¡=1 n=1 ¡=1 ¡=1 j=i+1
The letters i and j are indices for the n electrons and jj. is an index
for the N nuclei. In principle wavefunctions can be symmetric or
antisymmetric. An antisymmetric wavefunction has equal amounts
of area represented by (+) and (-) regions. Symmetric wavefunctions
do not. This principle can be seen in Figure 2-3.
Figure 2-3. Figure showing principle of antisymmetric and
symmetric wavefunctions.
a) antisymmetric; b) symmetric
The Heisenberg uncertainty principle states that the ability to "see"
electrons in an atom would perturb it so strongly that it could not be

24
assumed to be in the same state after measurement. Therefore there
is no way of distinguishing electron (1) at position r-j, from electron
(2) at position r2. If we want to know r, we can only average
together n and r2- Since we cannot distinguish electron (1) from
electron (2), the wavefunction 'F can not be written as simply the
product of one electron functions <}> of the form
V = 4>l(l)2(2)<|>3(3)... (15)
Since electrons are fermions, which are particles with half integral
spin, the wavefunctions are required to be antisymmetric with
respect to electron exchange. This behavior is accounted for if the
wavefunctions are written in the form of a Slater determinant [6],
For example, for a two electron system, the wavefunction would be
given by the following equation:
1 ^(1) Ml)
Â¥ =
^2 *j(2) 4>2(2)
The general form for the Slater determinant is
4>1(l)4>2(1) *n(1)
1(2)<^2(2) 4>n(2)
^(nH^v) <|>n(n)
In molecular quantum mechanics it is very important to calculate
eigenvectors and eigenvalues which represent electrons moving in a
1
V =
/ n!

25
"self consistent field" or SCF. The reason for this importance is seen
by looking at the last term in the equation for the Hamiltonian
operator (14), which is the interelectronic repulsion operator.
Because electrons repel each other, the electron density is more
diffuse than it would otherwise be. Electron (2) "sees" electron (1)
as a smeared out, time averaged cloud. Electron (2) "sees" electron
(1) as a smeared out, time averaged cloud. Electron (2) is thus
screening the positive nucleus from electron (1). Since the nucleus
is being screened, electron (1) will occupy a less constricted orbital
than it otherwise would. If electron (1) is in a 1s orbital, its orbital
as a result of this screening is represented by
ls(l)= V£3/rc exp(-£n). (electron (1)) (16)
A numerical value for which is related to the screened nuclear
charge seen by electron (1), can be determined. Likewise electron (2)
is being screened by electron (1) in its expanded orbital A value
for can therefore be determined for electron (2). will be
different from £ because the shielding of the nucleus by electron (1)
is different from the previous step. Each change in £ for electron (1)
necessitates a change in This process is continued until the two
values (i.e. £ and £') converge. When this happens electrons (1) and (2)
are being screened by the same amount. The potential due to the
nucleus and charge cloud of each electron causes the orbital for each
electron to be self consistent. The electrons move in a self
consistent field [8].

26
The one electron wavefunction <\>\ for a molecular orbital must be
expressed in some mathematical form. The manner in which this is
done is to express it as a linear combination of atomic orbitals
(LCAO). If <¡>¡ is the molecular orbital it can be expressed by
i = I Cjixj, (17)
where the xj's are the atomic orbitals and the cjj's are the
coefficients. The coefficients of the atomic orbitals are known as an
eigenvector. The atomic orbitals xji can be written as a function of
the following variables:
X(r,0,<>) =Rnl(r)Y|m(0,)- (18)
The variables r, 0, and (j> are expressed in terms of spherical polar
coordinates as illustrated by Figure 2-4. The Y|m(0,<¡>) part has
Figure 2-4. The relationship between spherical polar (r,0,(}>) and
cartesian coordinates (x,y,z).
It can further be broken down as exemplified by the equation given
by

27
Y|m(0,<>) = ImW^m () (19)
To be sure that the wavefunction will be unchanged if 0 or is
replaced by (0+2rc) or (4>+2;i)the spherical harmonics depend upon the
angular-momentum quantum numbers I and m, which arise in the
solution of differential equations involving angular coordinates 0
and <}>. The radial part of the atomic orbital Rnl(r) is a function of
exponential decay function (exp) and can take either the Slater-type
[10] form
rn"1 exp(-^r) (20)
or the Gaussian type form
rn_1 exp(-£r2). (21)
The Slater type orbital is used in the research undertaken in this
dissertation. Slater functions behave better in the region of r=0 and
do not fall off as sharply as do the Gaussian type orbitals [11].
The orbital exponent £ is a function of how "spread out" the orbital
is. The formula for £ is given by
£ = (Z-s)/n*, where n* is the effective principal number,
s is the screening constant and Z is the atomic number. The greater
the screening by the other electrons, the smaller will be the value of
C and the more diffuse the orbital will be. The effect of the value of
C on the orbital is shown by Figure 2-5.

28
Figure 2-5. Schematic showing the effect of the Slater exponent
on the radial portion of an atomic orbital.
Self-Consistent Field Theory
As was mentioned in the previous section, it is necessary to
determine eigenvalues and eigenvectors which are the result of
electrons moving in a self-consistent field. From equation (13), the
energy is obtained by allowing the Hamiltonian operator H to operate
on the probability density VF*VF. H can be broken down into a one
electron part H-| and a two electron part H2 as illustrated by
H = Hi + H2. (22)
The one electron part is a function of the kinetic energy of the ith
electron and the potential between that electron and the nucleus. If
summed over all electrons we have
Hi =E Hcore (p)> (23)
P
Hcore (p) (-1/2) Ap2 £ ZArpA-1.
A
where
(24)

29
The two electron part of equation (22) is H2 = 22 rpq-1. (25)
p Equation (13a) is given by
E = c''l H \x¥>,
where E = c'i'l H-j |VF> + . (26)
The wavefunction ¥ must be written as a Slater determinant so that
electron exchange can be incorporated into it. Allowing a
permutation operator P to act on the wavefunction is the equivalent
to writing the wavefunction as a Slater determinant. The
expectation value of the one electron operator is
Hj, = / 'Fj(l) Hcore ^¡(1) dxl. (27)
The two electron Hamiltonian is a function of the two electron
operator 1/rpg (equation 25). This operator gives the electrostatic
coulomb repulsion energy between two charge clouds [8]. A matrix
element of this electrostatic coulomb repulsion is defined as
Jij = JJ xFi*(1)xFj*(2) (1/rpq) ^k(1)^l(2) dxidx2- (28)
The value of this integral represents the repulsion between electron
(1) on orbitals 'Fj and 4^ and electron (2) on orbital 4^ and 4/|. Since
the charge clouds are everywhere negative, their product causes J to
be everywhere positive. The entire matrix would represent the
electrostatic repulsions between all orbitals in the molecule
including differential overlap where 4'j*(1)4'k(1)- Another integral

30
that results from the evaluation of the two electron Hamiltonian is
the exchange integral denoted by K. This integral gives the
interaction between an electron "distribution" and another electron
in the same distribution [8], The exchange integral is given by
Kjj = ¡ ¥¡*(1) vFj*(2) (1/rpq) 'Fj(l) ¥¡(2) dxi dx2- (29)
By collecting terms the formula for the total electronic energy is
given by
n n n n
E = 2 X H¡¡ + Xj¡¡ til (2Jjj Kjj) (30)
i i i j(*i)
and the orbital energies are given by
n
£ = H¡j + X{ 2J¡j Kjj}. (31)
j
The derivation of the Fock operator is very complex and it is not
necessary for it to be presented here. If interested in its derivation
consult reference 8 appendix 7. By utilization of the previously
mentioned terms, the Fock operator is given by

F = [ Hcre + X(2Jj (1) Kj(1))]. (32)
(1) i
which leads to the following equation in the eigenvector form.
RJ>i = ei (33)
Self consistency is achieved by making an initial guess at the
molecular orbitals
31
operator, which is used to solve for the new MOs (i.e.'). These are
then used to construct a new F' and so on until no significant change
is detected. The solutions are said to be self-consistent.
Approximations to Molecular.Qrbitai Theory
Basic Principles of Complete Neglect of Differential Overlap (CNDQ)
The SCF principles that were outlined above involve very lengthy
algorithms (some methods have more than 80,000 lines of code) and
as a result, require a considerable amount of computer memory and
CPU time in order to execute. As a result, approximations have been
applied to SCF principles. Thus considerably shorter codes (typically
between 1200-1600 lines) requiring less computer memory are
obtained. One of the best known examples of approximate molecular
orbital theory is complete neglect of differential overlap (CNDO)
written by John A. Pople and associates in 1965 [12-13]. Such an
approximate method is also referred to as semiempirical because
the eigenvectors and eigenvalues no longer result solely from the
principles of quantum mechanics. Experimental data is used in the
formulation of the Fock matrix.
The first approximation in CNDO which is applied to SCF theory
applies to the formulation of the overlap integral matrix. This
matrix is composed of values which show the degree of overlap
between the various atomic orbitals in the molecule. The
approximation consists of replacing the overlap matrix by a unit

32
matrix whereby all elements are zero except the diagonal elements
which are 1. In the normalization of Roothaan's equations X(FfiD-
eS^t))C-ui = 0 [14]. By ignoring differential overlap, S(j.-o =0 for In
other words, the atomic orbitals are treated as if they were
orthogonal and as a result, the Roothaan equations reduce to
SFp\)C\)j = £jCjj.¡ where is the Fock operator, C-uj is the
eigenvector or coefficients to the same atomic orbital as the Fock
operator and the £¡'s are the eigenvalues or molecular orbital
energies. This approximation becomes more severe as the
internuclear distance decreases, however, because it causes larger
and larger electron populations to be ignored. The second
approximation results in a simplification of equation (28), which
computes the matrix elements of the electrostatic coulomb
repulsion between charge clouds. The approximation neglects all
differential overlaps in two electrons integrals. Differential overlap
occurs when ¥¡*(1)'Fj(1 )*0, where probability density is coming
from electron (1) over orbitals i and j. Such electron densities are
exceedingly numerous and also exceedingly small. Ignoring
differential overlap means than equation (28) vanishes unless i=k
and j=l. This has the obvious benefit of reducing the number of
integrals that need to be evaluated. The third approximation, which
results from the second, is to reduce the number of coulomb
repulsions to one value per atom pair. Differential overlap can be
monoatomic, where 'FjH'k is on the same atom or diatomic where
T'jT'kis on different atoms. For the monoatomic case neglect of
differential overlap causes invariance of rotation to be negated. This
means that rotation of an atom with respect to another atom will

3 3
result in a different set of eigenvalues and eigenvectors. To restore
invariance, there is an additional approximation made. The remaining
two electrons integrals will not be dependent upon the nature of the
atomic orbitals, but on the atoms to which and ''k belong [11].
This can be shown as
(ii|kk) = Tab for all i on atom A and for all k on atom B.
TAB is the average electrostatic repulsion between any electron on
atom A and any on atom B [11], The value of TAB is given by
TAB = SS sa2(1) (1/ri2) sb2(2) dxidt2- (34)
As equation (34) shows all orbitals are taken to be of the "s" type.
The fourth approximation is to neglect differential overlap in the
interaction integrals involving the cores of other atoms where
(¡IVb|k) = Vab if i=k. If i*k the integral vanishes.
Vab is the interaction between any electron on atom A with the
core of atom B. Therefore, any differential overlap between two
atomic orbitals on atom A will be ignored in the calculation of this
interaction.
The last approximation made in CNDO is to allow off diagonal
matrix elements in the Hamiltonian to be proportional to the
overlap integrals. This is shown by
Hik = pABSik,
(35)

34
where Pab is the bonding parameter, which is characteristic of a
particular atom. As the overlap increases, the bonding capacity of
the overlap will increase [11]. With all these approximations, the
Fock matrix elements can be computed and are given by
Fpp = + ( PAA 1/2 Ppp) TAA + X (PBB Tab VAB) and (36)
B(*A)
Fpu = PABS^ 1/2 P^ TAB- (37)
Equation (36) can be rearranged into
F\i\i = U(j.(j. + (PAA 1/2 P^) TAA + X [-Qb fab + (Zb fab VAB)]
B(*A)
(38)
and the total energy can then be derived. This is shown by
E Total = (1/2) X Ppo(HpD + F,^) + XXzaZbRAB'1 (38a)
4V A To achieve self-consistency an initial guess is made of the
molecular orbital coefficients. The diagonal elements of the Fock
matrix (i.e. F^jj.) come from experimental values for the ionization
potentials ( i.e. U^jj. in equation (38)). The off diagonal elements (i.e.
F|iv) are replaced by pABS^u. The electrons are then assigned to
M.O.s with the lowest energy (i.e. lowest eigenvalues). The density
matrix, which is given by
occ
P(i\)=X c^jc-uj, (39)
i
is calculated from the coefficients of the occupied atomic orbitals.
This matrix is used to formulate a new Fock matrix F^. When the
Fock matrix is diagonalized a new set of eigenvectors and

3 5
eigenvalues are produced. They are then used to reassign the
electrons in pairs to the molecular orbitals with the lowest energy
and to construct a new density matrix. These steps are repeated
until self-consistency is achieved [11]. Figure 2-6 shows the effect
of self consistency upon the radial part of a wavefunction. This
program utilizes the modifications made in the second
parameterization of CNDO. These modifications include the
incorporation of the "zero penetration effect" which equates the last
term in parenthesis in equation (38) to zero and the replacement of
the ionization potentials in the Ujj.(j. term with the average of the
ionization potential and the electron affinity (i.e. -1/2 (l^ + A^)).
CNDQ2/U
A relatively new CNDO algorithm was selected for this project.
Unlike the version written by Pople et al., [12,13] this program is
parameterized for the first 81 elements of the periodic table. This
is possible by the utilization of the concept of "fictitious atoms,"
whereby those elements which have their valence electrons
distributed over two or more subshells with different principal
quantum numbers, are treated as two or more atoms which are
centered at the same coordinate. Figure 2-7 illustrates this
principle.

36
Figure 2-6. Effect of SCF calculation upon the electron distribution.
Although this program retains the concepts outlined in the
previous section, one of the major differences between this
program and the earlier version is in the formulation of the
coulomb repulsion matrix.
3d
4s
First Row Transition Element
Figure 2-7. Illustration of how a first row transition element is
treated in CND02/U.

37
From the last section it was stated that there is one matrix element
calculated per atom pair. However for a first row transition element
there are ns and (n-1) d valence electrons. It therefore would be
necessary to calculate the following r values:
r (n-1)d (n-1)d I T(n-l)d ns I Tns ns.
In addition to this modification in the formulation of the coulomb
integral matrix, there is also a modification in the calculation of
the atomic energies of transition type elements. Since the transition
element is considered to be two atoms it is necessary to calculate
two atomic energies for each atom. The equation used is given by
AE = s*ENEG(s) + p*ENEG(p) + (TE2 r(l,l)/2.) + d*ENEG(d). (40)
where AE equals the atomic energy, ENEG is the average of the
ionization potential and the electron affinity for the respective
subshell. TE equals the total number of electrons and s, p, and d
equal the number of s, p, and d electrons, respectively.

CHAPTER 3
THE EFFECT OF VARIATION OF MOLECULAR GEOMETRY OF A
TRANSITION METAL OXIDE CLUSTER ON THE VALENCE BAND DENSITY
OF STATES
Background
Dispersed particles or clusters, which usually have catalytic
properties on inert substrates such as carbon, silica, or aluminum
oxide, have been the focus of much investigation [15-26].
Investigations have focused primarily on their electronic structure-
experimentally, through the use of electron spectroscopy and
theoretically, through various molecular orbital algorithms. The
electronic structure of these deposited clusters can be investigated
by observing the shifts in binding energy of the main photoelectron
peaks in the relevant core regions and through acquisition of valence
band spectra. It has been reported in a study on the electronic
structure of catalytic metal clusters (i.e. Pd and Pt) that the valence
band undergoes a narrowing and a shift away from the Fermi level
relative to the bulk metal as the metal clusters become more highly
dispersed [27]. Unlike dispersed metals on inert substrates,
relatively little attention has been paid to the electronic structure
of dispersed metal oxides on inert substrates. As a result, the
electronic structure of dispersed and bulk like MnO on carbon foil
has been performed by Zhao and Young [28]. It was determined that
38

Figure 3-1. Comparison of spectra of highly dispersed and
continuous film of MnO on carbon foil.
a) The valence band spectrum of highly dispersed MnO on
carbon foil.
b) The valence band spectrum of a thick continuous film
of MnO on carbon foil.

40
B.E. ( e V )

41
for highly dispersed MnO on carbon foil (a coverage of 0.22) the
valence band undergoes a narrowing and a shift in its binding energy
away from the Fermi level relative to bulk material, as can be seen
in Figure 3-1. In the case of supported metal particles, this behavior
led to investigations which sought to correlate XPS valence band
behavior with results from molecular orbital (M.O.) algorithms to
determine the minimum or threshold number of atoms required for a
cluster to exhibit properties of the bulk material. For example, R.C.
Baetzold et al. performed an investigation into the determination of
the particle size required for bulk metallic properties [29]. Extended
Huckel calculations were performed on clusters with face-centered
cubic (fee) geometry of sizes ranging from 13 to 79 atoms. The
results from the calculations were used to construct valence band
density of state curves and the width of the d band was determined.
For the largest cluster size (i.e. 79) it was determined that the d
bandwidth was 86% of that for the bulk material and for a cluster of
13 atoms the d bandwidth was 50% of that of the bulk material.
Table 3-1 shows the results.
Table 3-1
Comparison of d bandwidths with cluster size
cluster
Pd2
Pdi3
Pd31
Pd55
Pd79
d band-
width
0.80
1.54
2.26
2.57
2.65
3.08

42
What is done can be summed up by the following statement. For (M)x,
where X=1,2,3,4 , and where M is some monomer unit, as X is
increased the electronic structure evolves to that of the bulk
material. In Baetzold's study the selection of one geometry (i.e. fee)
for all cluster sizes is arbitrary. It seems reasonable that when a
substance is deposited either fractionally or partially on a substrate
that it will not form the same geometry for all possible values of X.
The goal of this research project is to see what effect the variation
of the molecular geometry for a given cluster size would have on the
valence band density of states (VBDOS). Could a "bulk like" VBDOS
curve be constructed by variation of the smallest possible cluster
size for MnO, namely (MnO)2 ?
As was mentioned briefly at the beginning of chapter 2, the
binding energy of the photoelectron is linked to eigenvalues derived
from molecular orbital theory by the rule of Koopman [7-8], which
can be represented by
-e (eigenvalue^ binding energy of the photoelectron. (41)
This rule is not entirely correct, however, because it is based on an
incorrect assumption-that the orbitals remain frozen orbitals
during photoemission. This is a "static" approximation. In actuality
the remaining electrons "relax" towards the site of photoemission
because of reduced screening of the nuclear charge. This relaxation
imparts a certain amount of kinetic energy to the ejected electron,
thus reducing its binding energy. If comparisons are being made
between clusters of different size, where the extent of relaxation is

different, this limitation of Koopmans rule could be a problem. In
addition, the rule of Koopman also neglects correlation energy,
which is due to electron repulsion. Since we are interested in the
relative eigenvalues for clusters where the number of atoms is held
constant, this limitation should not be a problem.
Modification of CNDO/2U Algorithm
In this work, the semiempirical molecular orbital method of
CNDO/2U [30] is utilized to determine the eigenvectors and
eigenvalues. This method treats the valence electrons as Slater
orbitals and used parameters which are fitted empirically [1]. This
new version of CNDO can be utilized on any element in the periodic
table whose atomic number is less than or equal to 81. One
fundamental difference between this method and the Pople method is
the way it treats elements whose valence electrons are distributed
over different subshells with different principal quantum numbers,
which is illustrated by Figure 2-7. The molecule TO for example,
where T is a transition element, would be treated as three atoms
with T accounting for two of them at the same coordinate. If this
treatment were carried over to the Lanthanides, where the valence
electrons are dispersed over three subshells, we would have three
atoms at the same coordinate (i.e. T(n_2)f, T(n-1)d. and Tn) [30].
Before the eigenvalues and eigenvectors of the various geometries
of (MnO)2 could be determined, it was necessary to check the
accuracy of the program by determining its ability to calculate
dissociation energies of various diatomic molecules. The author

44
performed such calculations, which are listed in Tables 3-2 and 3-3.
For those diatomic molecules which contain no transition elements,
most of the calculated dissociation energies are in good agreement
with experimental values, as seen in Table 3-2. When the
dissociation energies of diatomics which contained either one or
two transition elements are determined, there is very poor
agreement between the calculated results and experimental values,
as shown in Table 3-3. These results indicated that there is a
problem in the way transition elements are treated. It was decided
to modify those areas of the program which are a manifestation of
treating the transition element as two atoms centered at one
coordinate. One such area which needs to be modified is the
computation of the atomic energies.
In M.O. theory the atomic energy is related to the dissociation
energy by
Edissoc = Ebond = Etot Eatomic- (42)
Table 3-2
Bond Energies and Lengths of Selected Diatomic Molecules.
AB
Bond Length
(A)
Exp.a
Dissociation Energy
(eV)
Exp.a
HF
1.00
0.92
-6.01
-5.90
LiH
1.54
1.60
-6.71
-2.50
IH
1.63
1.61
-4.47
-3.09
CO
1.22
1.13
-21.96
-11.09
SnO
2.25
1.84
-1.46
-5.46
a) Ref [30]

4 5
Table 3-3
Bond Energies and Lengths of Selected Diatomic Molecules which
Contain one or more Transition Elements.
AB
Bond Length
(A)
Exp.
Dissociation Energy
(eV)
Exp.a
M n2
2.8
3.4b
-286.18
-0.23
FeO
1.58
1.57 a
-142.17
-4.20
FeS
1.90
-149.5
-3.31
MnBr
2.3
-108.
-3.22
Fe2
2.7
-179.24
-1 .06
a) Ref. [31] b) Ref. [32]
Since the transition element is being treated as two atoms it is
necessary to compute two atomic energies, as shown by
AE= s*ENEG(s) + p*ENEG(p) + (TE2 T(l,l)/2) + d*ENEG(d). (43)
The ENEG terms are equal to the average of the ionization potential
and the electron affinity of the respective subshell. TE is the total
number of electrons and s,p, and d are the number of s,p, and d
electrons respectively. The r(I,I) term is the monocenter coulomb
repulsion for either the s or d subshell. The total atomic energy is
then computed by adding the "atomic energy" of the s and d shells
together. The program is modified to compute one atomic element
per transition atom and this is done by determining the probability

46
of a valence electron being either an s (i.e. s/TE) or a d (i.e. d/TE).
The equation utilized is
AE = s*ENEG(s) +p*ENEG(p) +((s/TE)*TE2 r(l,l)/2.) + ((d/TE)*TE2*
r(l,l)/2.) + d*ENEG(d). (44)
The effect of this modification on the diatomic molecules containing
transition elements is shown in Table 3-4. The reason that these
diatomics are chosen to test the accuracy of the program is that
they represent the two types of bonds that are encountered when the
eigenvectors and eigenvalues of the (MnO)2 cluster are being
determined (i.e. the T-T and T-0 types where T is a transition
element).
Table 3-4
Results of atomic energy modification to CNDO/2U on selected
diatomics which contain one or more transition elements.
AB
Bond Length(A)
Dissociation Energy (eV)
Exp.(eV)
FeO
1.58
40.9
-4.20
Mn2
2.80
1.0
-0.23
MnO
1.70
38.0
-3.70
Fe2
3.0
-4.52
-1.06
FeS
1.90
33.02
-3.31
MnS
2.00
30.9
-2.85
For molecules representing the T-T bond, (i.e. Mn2 and Fe2) there is
good agreement between data and calculated results. For molecules

representing the T-0 type bond however, there is poor agreement.
This makes it necessary to modify the program so that it calculates
a lower total energy for T-0 and T-S bonds.
Another part of the algorithm which can be modified is that part
which computes the coulomb repulsion matrix. This matrix is a set
of values which represent the electrostatic repulsion between the
charge clouds occupied by the electrons in the system. Equation (28)
is the formula for the electrostatic repulsion between electrons (1)
and (2) distributed over orbitals i,j,k and I. When the approximations
of CNDO are applied to (28), equation (34) results. CNDO calculates
the average electrostatic repulsion between any electron on atom A
and any electron on atom B instead of the electrostatic repulsion
between orbitals.
Therefore,
one matrix
element is calculated per
atom pair. For
a T-0 type
* molecule
the following 3X3 coulomb
matrix is formulated.
0
4s
3d
0
TOO
ro4s
r03d
4s
T04s
T4s4s
T3d4s
3d
T03d
T4s3d
T3d3d
and for a T-T type atom the
following 4X4 matrix is formulated.
4s
3d
4s
3d
4s
T4s4s
T3d4s
T4s4s
T4s3d
3d
T4s3d
T3d3d
T3d4s
T3d3d
4s
T4s4s
T3d4s
T4s4s
T4s3d
3d
T4s3d
T3d3d
T4s3d
T3d3d

48
The relationship between' the electronic energy and the coulomb
integral matrix elements are seen by the equations derived from
CNDO approximations to SCF theory (i.e. equations 38 and 38a). The
term (ZbTab-Vab). which represents the potential difference
between the core ( the nucleus and non-valence electrons) and the
valence electrons of atom B, is set to zero as a result of CNDO
approximations. A valence electron on atom A experiences no
potential difference between these components of atom B, thus the
possibility of its penetration into B is eliminated. Such a
penetration would lead to a net attraction yielding a lower bond and
dissociation energy between A and B. To modify the program so that
a greater net attraction between A and B is realized, the term-
QbTab is modified. This term represents the effect of the potential
due to the total charge on atom B [11]. If Tab is increased, the
potential due to atom B (i.e. Mn or Fe) will be more negative. This
increase would have the same effect as increasing Vab which would
make the potential of the core of B greater than the valence
electrons of B. This should then cause a greater net attraction
between A and B to develop, which is what is desired. By looking at
the first matrix, it can be seen that Tab are represented by To 3d
and ro4s, both of which are bicenter. The problem is to determine
by how much these elements should be increased. Possibilities exist
that the best results might be obtained by multiplying the T04s and
r03d by the same or different amounts. By the process of trial and
error it has been determined that if each r value is multiplied by
1.1, the best fit between dissociation energy, ionization potential
and equilibrium bond distance results. After applying the above

4 9
corrections to the original program, the values shown in Table 3-5
result. Increasing the bicenter matrix elements of a T-0 molecule
should have the effect of increasing the electron population in the
overlap between the oxygen and the d orbitals of the transition
element. This is substantiated by looking at the population matrix,
calculated from the equation
occ
Pjid = 2 Xc jj,¡ c\)j, (45)
i
where the c's are the coefficients of the atomic orbitals. This
matrix does indeed show an increased electron population in the
overlap between the oxygen and the d orbitals.
Table 3-5
Final values for the bond lengths, dissociation energies and
ionization potentials of selected diatomics after the atomic energy
and coulomb integral modifications were made to CNDO/2U.
AB
Bond
Length
(A)
Exp.
Ionization
Potential
(eV)
Exp.
Dissociation
Energy
(eV)
Exp.
FeO
1.40
1.57b
-11.69
-8.71 a
-6.77
-4.20
FeS
1.90
-5.02
-0.50
-3.70
Mn2
2.80
3.4
-7.08
-6.9C
1.00
-0.23
MnO
1.45
1.77b
-8.06
-5.68
-3.70
Fe2
3.00
-16.09
-6.30e
-4.52
-1.06
MnS
1.80
-11.53
-10.16
-2.85
a) Ref [33] b) Ref [31] C) Ref [34] d) Ref [35] e) Ref [32]

50
Construction of VBDOS curves
After the modifications were made to the program it was then
possible to begin the acquisition of the eigenvalues and eigenvectors
of various geometries of the formula (MnO)2- In order for the
eigenvalues and eigenvectors of a given geometry to qualify for
comparison with XPS valence band spectra, it is necessary for that
geometry to pass the self consistency test-i.e. two successive
iterations of the total electronic energy must agree to within 0.01
eV. To pass this test it was necessary that the program calculated a
total electronic energy that was within 0.01eV of the previous
value. The determination of suitable geometries was like the
coulomb matrix modification, a trial and error process, but after a
long and arduous process, six suitable geometries were found, which
are illustrated by Figure 3-2.
Mn 0 Mn 0
Linear
Semicircular
Cross tin
Rectangular
Figure 3-2. Suitable geometries for cluster (MnO)2-

51
After these geometries were determined, it was necessary to
construct valence band density of states (VBDOS) curves from the
eigenvalues and eigenvectors of each geometry. VBDOS curves are
constructed by centering a Gaussian distribution function about each
eigenvalue which has a FWHM of 0.85 eV (the natural line with for
AlKa radiation is this value) and then summing them over some
specified energy range. The relative heights of the Gaussian
distribution functions are determined by the following formula.
Ht. of Gaussian = X c2jj oj (46)
j
The c¡j 's are the coefficients of the atomic orbitals and the aj's are
the Scofield cross sections [36]. A VBDOS curve has been
constructed for each of the geometries shown in Figure 3-2. Figure
3-3 illustrates these VBDOS curves. Weighted distributions of these
geometries can be used to construct composites. These simulate the
effect of having active sites on the substrate surface which
stabilize different geometrical configurations of the clusters. The
weights simulate the relative fraction of each type of site on the
surface. One such composite, which can be seen by Figure 3-4,
shows a remarkable agreement with the lineshape obtained for very
thick MnO supported on carbon foil. Although there is no evidence
for "geometry* selective active sites on the supports normally used
for heterogeneous catalysts, there is also no evidence against such
sites. Based on Figure 3-4, the variation in the molecular geometry
for a given value of X does have an effect on the VBDOS. Valence band
broadening is not only due to an increase in the number of atoms in a

52
cluster, but can also be due to the formation of a distribution of
geometries of different stability on the surface. Thus a meaningful
interpretation of the experimental VBDOS curves of supported metal
oxide particles cannot be made without supplementary information
on the particle size distribution.

Figure 3-3. Valence band density of states for self-consistent
conformations of (MnO)2.

In-O

Figure 3-4.
Valence band density of states of a calculated (MnO)2
composite compared to spectrum of a continuous film
of MnO.

b) XPS Spectra
of bulk MnO
-12
-10^8
" 6 -4
eV

CHAPTER 4
PHOTOEMISSION STUDIES OF VAPOR DEPOSITED AND SOLUTION
DEPOSITED MANGANESE OXIDES AND SOLUTION DEPOSITED IRON
OXIDES ON CARBON FOIL
Introduction
A large number of heterogeneous catalysts are composed of a
material (e.g. a metal like Pt or Pd) which has been dispersed upon
an inert support like silica, alumina, or carbon. These dispersed
substances can be characterized by x-ray photoelectron
spectroscopy. More specifically, XPS can be used to determine the
relative concentrations of the various constituents and the relative
particle size distributions of the supported material. The relative
concentrations of the various constituents on a surface are
determined by determining the relative peak areas of the
constituents concerned. This then allows a value for the number
atom ratio of one constituent atom to another to be computed. The
effect of differences in the relative particle size distributions of
the supported material can be qualitatively determined from shifts
in binding energy within a given region. Such effects may be
observed in both the core level regions and in the valence band
regions. Valence band distribution narrowing is one of the most
dramatic changes which can occur. Zhao and Young [28] prepared
carbon surfaces containing submonolayers of MnO, as confirmed by
57

58
the relative concentrations- of the constituents on the surface.
Changes in the electronic structure which accompany reduction in
the particle size distributions are determined for the highly
dispersed MnO by comparing its valence band region with that of the
bulk oxide. In that investigation, the oxide was prepared by vapor
deposition. The number atom ratios calculated from XPS data
indicated a low coverage ( represented by (the assumption is made that the lower the coverage value, the more
highly dispersed is the oxide). It is also shown that it is possible to
form a thick continuous film of the oxide on the carbon foil when a
number atom ratio (i.e. N|\/|n/(Nc + NMn)) of 1.0 is achieved at take off
angles between 0 and 50 degrees. The effect of changes in the
particle size distribution consisted of shifts in the position of the
maximum of core, Auger and valence level spectra and a narrowing
of the valence band level. This chapter will report results of similar
experiments on other dispersed oxides of manganese and on
dispersed ferric oxide. These characterizations are based on data
acquired from samples prepared by vapor deposition and solution
deposition. Because in solution deposition it might be possible for
the oxide particles to diffuse in from the edge of the carbon foil, it
is necessary to also perform quantitative analyses of samples
which have had 0 edges, 1 edge and 2 edges directly exposed to the
solution which is used in the solution deposition method in addition
to the normal sample which has 4 edges directly exposed.

59
Variable Angle XPS (VAXPS1
In the introduction of this chapter the term take off angle is
mentioned. The take off angle is the angle between the electron
analyzer and the sample, which is commonly denoted by the Greek
letter 0. The angle 0 is varied in almost any quantitative analysis
undertaken, because its variation causes a variation in the effective
mean electron escape depth, which is more commonly referred to as
the probe depth. The mean electron escape depth is the average
distance a photoelectron will travel before it undergoes an inelastic
collision, a collision whereby it looses energy from the initial
energy acquired from the photoemission process. Unfortunately
inelastic collision is the fate that awaits most photoelectrons
which are generated. This is what severely limits the depth that one
can investigate in XPS.
Figure 4-1. Schematic showing the attenuation of the incident x-ray
radiation. The distance the photoelectron can travel
before it suffers inelastic collision is quite short
compared to the distance the x-ray can travel.

60
This is illustrated schematically in Figure 4-1. The distance the x-
rays can travel into the solid is much greater than the
photoelectrons can travel. The relationship between the mean and
the effective mean electron escape depth is illustrated in Figure 4-
2. Even though the mean electron escape depth is constant, the probe
depth, or the effective mean electron escape depth becomes smaller
as the take off angle becomes smaller until at a take off angle of 0
degrees, the photoelectrons generated are originating from the top
monolayers of atoms only. Conversely at a take off angle of 90
degrees, the spectra that are obtained are the most "bulklike". The
value of the effective mean electron escape depth depends upon the
substance that is being analyzed. For metals this depth can be as
small as 10 Angstroms. To change the take off angle in the KRATOS
XSAM 800, one simply rotates the sample probe.
EMEED = MEED*SIN0
Figure 4-2. Diagram showing the relationship between the take off
angle and the effective mean electron escape depth.

61
Quantitative Analysis bv XPS
XPS investigations often require that the relative concentrations
of the various components of a surface be determined. If one
averages over depth, then these relative concentrations can be
expressed as number atom ratios (i.e. Nx/Ny) which can be
calculated from the following equation.
Nx.i/Nyj = (lx.i/lyj) (ayj/oxt¡) (Xy(Ej)/Xx(Ej)) (F(Ej,Ea)/F(E¡,Ea))-
(T(Ej/Ea)/T(E¡,Ea)) (47)
The Ps are the time normalized intensity ratios, the a's are the
asymmetry corrected photoionization cross sections, Ej and Ej are
the kinetic energies of photoelectrons i and j respectively and Ea is
the analyzer pass energy. The subscripts x and y are the specific
elements and subscripts i and j represent specific levels in x and y
respectively [37], X(E¡) is the inelastic mean escape depth, F(E¡,Ea)
is the electron optical factor and T(E¡,Ea) is the analyzer
transmission function. Fortunately experimentation has given
results which allows equation 47 to be simplified. It has been shown
that the product of the electron optical factor, the analyzer
transmission function and the inelastic mean escape depth cancel
each other [38]. The simplified form of equation 47 is
Nx,i/NyJ = (lx,i/ly ,i)(ory ,i/ox,i)
(48)

62
If the elements x and y have not been recorded with identical
window widths, then the window width must be incorporated into
equation 48.
Nx.i/Ny.i = (Ixj/ly.i) (oy,i/ox,i) (Wx/Wy) (49)
The number atom ratio evaluated at 0=0 degrees is an estimate of
the coverage (O). The determination of the relative concentrations
of the various constituents of a sample is made relatively simple
with the DS800 software. After the spectra are acquired, the
operator constructs the desired window that needs to be quantified
and then simply types either "Q/A" or "Q/l" at the prompt, where
"Q/A" means quantify area and "Q/l" means quantify intensity. To
quantify area, "The peak area is calculated by summing the counts at
all energies within the appropriate window, multiplying by the
energy step between the channels and dividing by the total time
spent acquiring each channel (i.e. the dwell time)" [39]. The
quantification of peak intensity is determined by computing the
difference between the most intense and the least intense channels
within the spectral window, which is divided by the dwell time. The
dwell time is another name for time normalization that was
mentioned at the beginning of this section. Time normalization
ensures that the quantities obtained are not affected by the
operators choice of acquisition parameters. The atomic
concentration % is then calculated from equation (50).
[(xj/qj)/ I (xj/qi)] X 100.
(50)

63
The variable x¡ is the ratio of the raw area/intensity of the ith peak
and q¡ is the corresponding quantification factor (i.e. related to a
which was discussed earlier). The quantification factor or a is a
term which is a manifestation of how sensitive the instrument is to
an electron in a particular orbital. The quantification factor is a
function of the size of the atomic orbital.
Not only is the relative concentration of elemental constituents
which comprise a surface desired, but also the relative
concentrations of different chemical species which are contributing
to a given spectral window (i.e. Ois, C-|S)- Analysis of a given
photoelectron peak is achieved by peak fitting a number of different
symmetrical line shape functions (either Gaussian or Lorentzian) to
the peak. With the DS 800 software it is possible to express a
distribution as a combination of a Gaussian and Lorentzian function.
The distribution can be made to have as much as 50% Lorentzian
character. To fit these distribution functions to a photoelectron
peak, it is first necessary to construct a synthetic window (a
different type of window than needed to determine the relative
atomic concentrations). The synthetic window is first constructed
by typing "syn" at the prompt. After the operator states the name of
the window (i.e. Cis, Oi s etc.) the cursor appears and the window
width is determined by pressing the space bar at the desired
positions (in eV) at the beginning and the end of the window. After
the window is formed a table appears which requires the operator to
state what type(s) of function(s) are to be fit, (i.e. either Gaussian
or Lorentzian or combinations thereof), the element IDs, the
positions of maximum intensity of the component distributions and

64
the beginning and ending of a given distribution. Some degree of
estimation and guesswork is required here and it takes practice for
the operator to become proficient. In addition the operator can
require the computer to fit a given distribution to within a given
FWHM. After this is done, the interactive synthesis option is
selected and the spectral window that the peak fit is being
performed upon appears in the upper right portion of the display that
appears. The background is subtracted out and the distributions that
the operator selects appear under the photoelectron peak. The degree
of fit is displayed, which at this point is usually very high. Next,
the autofit command is utilized by typing "au" at the prompt. The
computer fits the distributions selected to the peak, calculates the
final fit value and displays it. The lower the value of the fit, the
better it is. Figure 4-3 is an example of four distributions being fit
to the Oi s region of four year old carbon foil, for which the 0-] s
contamination can not be completely eliminated.
Preparation of Samples
As is mentioned in the introduction section of this chapter,
vapor and solution deposition are utilized to prepare dispersed
manganese oxides on carbon foil, while the ferric oxide samples are
prepared by solution deposition only. To vapor deposit a manganese
oxide onto carbon foil, it is first necessary to vaporize the
manganese. Vaporization of the manganese is achieved by heating it
resistively in a tungsten filament basket. The vapor produced is
allowed to impinge upon a piece of carbon foil which is cut into a

Figure 4-3. Peak fit of the Os photoelectron peak of carbon foil
not subject to deposition by MnC>2 (clean carbon foil).
The take off angle is 0 degrees.

t CLEAN CARBON FOIL. OIS REGION. THETA=0 DEGREES
Run: 2CCF05 Reg: 1
Scan: 1 Chans: 157
Start- eU: 535.50
End eU: 527.65
Fit-: 1.7
1OO: I n tens i ty: 579.
100: Area 39042.
Line
Elrot.
Energy
I n t.
FWHM
Area
lor 10
ols
533.5
31.0
1.6
15.2
gauss
ols
532.5
52.9
1.6
27.5
gauss
ols
531.6
61 .6
1.9
35.9
gauss
ols
530.0
34.3
2.0
21.5
534

6 7
rectangle with dimensions of approximately 1 cm X 1.2 cm. This is
done in a sample analysis chamber of a Hewlett Packard X-ray
photoelectron spectrometer at a base pressure of ~ 10'7 torr. Figure
4-4 illustrates that after the Mn is vaporized, it reacts with oxygen
to form either the Mn(ll) or Mn(lll) oxide, depending upon the
reaction conditions. These samples are outgassed by heating them
to 235 C for 20 minutes before recording spectra. If there is any
MnOOH on the surface, this procedure will convert it into Mn23.
Dispersed manganese dioxide on carbon foil is prepared by solution
deposition since is has been shown that Mn02 can be deposited by
means of the KMn04 decomposition [40]. Absence of KMn04 itself is
confirmed by the absence of K core level peaks in the survey scans.
The reaction for this decomposition is given by equation (51), where
the fate of the negative charge has not been established.
Mn(s)
W filament
basket
Mn(v)-
Oxidation
(poor vacuum)
MnO/C
250 C
atmosphere
M1123/c
Figure 4-4. Schematic showing method of vapor deposition of
manganese oxides on carbon foil.
Equation (51a) symbolizes deposition onto the carbon foil.
Mn04 MnC>2 + O2
Mn02 MnC>2/C
C foil
(51)
(51a)

68
Solution deposition is accomplished by placing carbon foil
rectangles into permanganate solution (= 3.3 X 10'4 F) and allowing
the dioxide to deposit. The samples are kept in solution for various
lengths of times. Some were left in for 2 hours, some for 20 hours,
and the remainder for 100 hours. To prepare the samples which
contained either 0, 1, or 2 edges, a relatively large piece of carbon
foil ( = 5cm X 5 cm) was placed in the permanganate solution for
100 hours. Figure 4-5 shows how the XPS samples with various
edges exposed to the permanganate solution were selected after the
100 hours of deposition time. The rectangles were cut from the
large rectangle with the use of a razor knife.
Figure 4-5. Diagram showing how samples containing the number of
edges indicated were harvested after they were allowed
to have Mn02 deposit on them for 100 hours.
Solution deposition of ferric oxide onto carbon foil necessitated the
precipitation of the ferric ion out of solution before the carbon foil
could be added. The precipitation was accomplished by adding a 1M

69
NaOH solution dropwise to a 0.1 N ferric nitrate solution. The NaOH
was added until there was no further change in the appearance of the
brown precipitate that was formed. The pH of the solution containing
the precipitate at this point was 14. The carbon foil was then placed
into the precipitate containing solution and the precipitate was
allowed to deposit for either 18 or 100 hours. After the time
allowed for the deposition to occur had expired the samples were
washed alternately with de-ionized water and acetone. The samples
resulting from manganese oxide deposition were also washed after
deposition. The acetone facilitated the removal of any organics on
the surface and aided in drying. Prior to letting either the Fe(lll) or
Mn(IV) oxide deposit onto the carbon foil, it is necessary to remove
contaminant oxygen from the surface of the foil. According to the
literature, this can be accomplished by heating the foil to 531 C in
ultrapure nitrogen [41] or by heating it to 210C in a vacuum [28].
Since the carbon foil is four years old, the oxygen peak could not
completely be removed. Quantitative analysis of the above samples
was performed after the acquisition of data by VAXPS. Regions in
which data are acquired are the Os. Cis. Mn2p, Fe2p, and the
valence band (VB). It is also necessary to acquire data in the the
regions just mentioned for the carbon foil not being subject to
deposition of manganese dioxide. This allows the determination of
the quantity of contaminant oxygen on the surface and comparison
with carbon foil which has been subject to deposition. The valence
band region is scanned from 15-0 eV.

70
Results
After the carbon foil rectangles are placed in the permanganate
solution for either 2, 20, or 100 hours, XPS data is acquired in the
regions mentioned in the previous section. The Oi s region of the
manganese free carbon foil is compared with the 0-|s regions of the
carbon foil samples which are subject to deposition to see if any
deposition had occurred. Figure 4-3 shows a peak fit of the Oi s
region of manganese free carbon foil acquired at a take off angle of
0 degrees. The manganese free carbon foil contains oxygens species
in four different chemical environments. Several of the oxygen
species have been identified in a paper written by Young [42]. The
additional species are probably due to the fact that the carbon foil
has aged. The carbon foil used by Young in the investigation to
identify inherent surface oxygen species was new. The carbon foil
used for the deposition of manganese dioxide is approximately 4
years old. Figure 4-6, which illustrates the Mn2p peaks of a sample
of carbon foil which has been allowed to soak in potassium
permanganate solution 100 hours, confirms that manganese
deposition has indeed occurred. Figure 4-7, which shows a peak fit
for the Ois region at a 0 degree take off angle for a sample prepared
with 100 hours of deposition time, shows that there is an additional
peak at 529.0 eV. This value compares very favorably with the
literature value of 529.3 eV for the 0-|s peak of bulk Mn02 [43]. The
O/Mn ratio is 1.72, within experimental error of the expected ratio
2.0. Figure 4-8 illustrates a peak fit for the Ois region of the same
sample at a 85 degree take off angle. In this case, the O/Mn ratio is

Figure 4-6.
Mn2p photoelectron peaks of a sample of carbon foil
which was allowed to have Mn02 deposit on it for 100
hours. These peaks were acquired at a take off angle of
35 degrees.

Intensi ty (c ounts)
3rd CCF HEATED FOR £ MO. lOOHR MN02 DEP. THETA=35 DEGREES.
Run: 3M10O4 Rey: 4 (MN2P ) Scan: 1 Base: 16816 Max Cts/s: 4£1
-o
to

Figure 4-7. Peak fit of the 0-|S photoelectron peak of a sample of
carbon foil which was prepared by allowing MnC>2 to
deposit on it for 100 hours. The take off angle is 0
degrees.

CLEAN C FOIL WHERE MH02 WAS DEPOSITED FOR 100HR. OIS REG. THETA=0 DEGREES
Run
: 3M1001
Reg:
2
Scan
: 1
Chans:
141
Start
eU:
534.S5
End
eU:
527.S5
Fit:
£.4
1Q0%
Intens
i ty:
576.
100%
Area
42
S67.
Line
Elmt.
Energy
Int.
FWHM
Ar
ea
gaUSS
ols
533.0
49.5
1.7
£3
.9
gauss
ols
532.2
45.5
1.4
IS
.1
gauss
ols
531.4
54.7
1.5
£2
.6
gauss
ols
530.1
40.0
1.8
£0
.0
gauss
o1s
529.0
44.9
1.3
15
.8

Figure 4-8. Peak fit of the Os photoelectron peak for a sample of
carbon foil which was prepared by allowing Mn02 to
deposit on it for 100 hours. The take off angle is 85
degrees.
I

1-CLEAN C FOIL MHERE MNOS NAS DEPOSITED FOR 100HR
Run: 3M1Q06 Reg: £
Scan: 1 Chans: 14S
Start- eU: 534.35
End eU: 527.00
Fit.: 1.0
100: Intensity: 8632.
100?: Area 360064.
Line
Elnt.
Energy
I n t.
FNHM
Area
gauss
ols
533.2
3.8
1.2
2.3
gauss
ols
532.1
13.0
1.2
7.9
gauss
ols
530.9
21.5
1.2
12.6
gauss
ols
523.6
33.7
1.4
24.0
gauss
ols
529.0
74.1
1.4
52.9
534
TO Oj
01S REG. THETA=S5 DEGREES.
-4
On

77
1.90. By comparison of the percent area values of the 529.0 eV
distribution of Figures 4-7 and 4-8, it can be seen that deposited
oxygen and therefore MnC>2 is being incorporated into the layers of
the carbon foil (i.e. MnC>2 increases with increasing take off angle).
This conclusion is substantiated by the number atom ratios NMn/NQ
calculated at increasing values of the take off angle. As the angle is
increased, the amount of Mn increased, as shown in Table 4-1. This
is quite surprising since we expected to be able to form a continuous
layer of the oxide at the surface like it was possible to do for vapor
deposited MnO and Mn2C>3. At 0=0 it is possible to form a continuous
film of the vapor deposited manganese oxide [28], as shown in
Table 4-2. It should be pointed out that the value of 1.00 is
determined not by NMn/NQ but by NMn/(NMn+Nc) in Table 4-2.
Table 4-1
Values of NMn/Nc for solution deposited MnC>2 on carbon foil.
0(degrees.)
2 hrs.
20 hrs.
100 hrs.
0
0.055 (O)
0.13 (O)
0.073(0)
15
0.13
0.20
35
0.26
0.83
55
0.046
0.22
1.24
85
0.041
0.18
1.07

Table 4-2
Coverage values for vapor deposited MnO and Mn2C>3.
78
OXIDE
O
MnO
0.18
MnO
1.00
(no discernible Cis)
Mn203
0.3
Mn203
0.65
Mn203
1.00
(no discernible Ci s)
Solution deposition of ferric oxide on carbon foil gave similar
quantitative results to that of the solution deposited manganese
dioxide. Figure 4-9, which illustrates the Fe2p peaks of a carbon
foil sample which was allowed to remain in the precipitated Fe
solution (see preparation of samples section) for 100 hours,
confirms that iron has indeed deposited onto the surface. In Figures
4-10 and 4-11, which are peaks fits of the Oi s region of solution
deposited ferric oxide on carbon foil at take off angles of 0 and 85
degrees respectively, a peak can be seen at 529.1 eV at 0 degrees
and a peak at 529.2 eV at 85 degrees. This compares very favorably
with a literature value of 529.3 eV for the Oi s peak for the bulk
Fe23. The O/Fe ratios for the sample analyzed at 0 and 85 degree
take off angles are 1.8 and 1.6 respectively, within experimental
error of the expected 1.5 for Fe23. There is incorporation of the
oxygen from the iron oxide into the layers of the surface of the
carbon, but the incorporation does not occur to the same extent as
for MnC>2. This conclusion is made from the 100% area values in
Figures 4-10 and 4-11.

Figure 4-9. Fe2p photoelectron peaks of a sample of carbon foil
which was allowed to have ferric oxide deposit on it
for 100 hours.

Intensity (counts)

1
Figure 4-10. Peak fit of the Os photoelectron peak for a sample of
carbon foil which is prepared by allowing Fe2C>3 to
deposit on it for 100 hours. The take off angle is 0
degrees.

Run: lFEl Re-3: 3
Scan: 1 Chans: 153
Start- eU: 534.60
End eU: 526.95
Fit-:
1 .6
100 V
Intens
i t.y:
100*.
Area
Line
El rat..
Ener;
Ejy
GAUSS
OIS
531
.9
GAUSS
01S
530
.7
GAUSS
OIS
529
1
GAUSS
OIS
529
.1
3042.
196991.
Int. FUHM Area
42.0 1.9 26.1
47.0 1.6 24.
57.1 1.5 28.
41.2 1.5 20.
f'- o OJ
00
to

Figure 4-11. Peak fit of the Os photoelectron peak for a sample of
carbon foil which is prepared by allowing Fe203 to
deposit on it for 100 hours. The take off angle is 85
degrees.

*CCF WHERE FES03 WAS DEPOSITED FOR 1Q0HR 05S' REGZGM. 7HETA=o5 DEGREES
Run: 1GFE
CL
Reg:
3
Scan: 1
Chans:
153
Start- eU:
534.60
End eU:
526.95
Fit-: £.0
100*: In tens
i ty:
5536.
100*-; Area
354465.
Line Elmi.
Energy
Int.
FWHM
Area
GAUSS OIS
532.0
41.8
1 .9
£6.3
GAUSS 01S
530.8
42.4
1.7
£3.9
GAUSS 01S
529.6
54.4
1 .6
£8.8
GAUSS CHS
=¡oq o
\ji_ 17 i_
Z'O ~r
V-"-* 1
1 .5
19.3
1 r 1
534 532 530
Binding Energy

85
At 0=0, it is 196991 and at 0=85 it is 354465. If the second value
for 100 % area is divided by the first a ratio of = 1.8 is obtained. The
same ratio for the MnC>2 deposition yields a ratio = 8.4, an
approximate 4 fold increase. The conclusion that ferric oxide is not
being incorporated to as great a degree into the layers of the carbon
foil as manganese dioxide can also be drawn from the area % of the
529 eV peak. At 85 degrees the 529 eV peak constitutes 52.9% of the
area under the curve for the sample prepared by the solution
deposition of Mn02 while it constitutes only 19.3% of the area under
the curve for the sample prepared by the solution deposition of
Fe23. The percentage of area contributed by the 529 eV peak is
greater at 0=0 degrees than at 85 degrees for dispersed ferric oxide.
This further substantiates the differences in the degree of
incorporation between the two oxides. The number atom ratios also
indicate that less of the oxide is being incorporated into the carbon
foil. Table 4-3 gives the number atom ratios for the Fe and C atoms
as resulting from solution deposition.
Table 4-3
NFe/Nc values for samples prepared from the solution deposition of
Fe23 on carbon foil.
take off angle
18 hours
100 hours
0
0.057
0.044
10
0.12
0.095
25
0.098
0.089
55
0.075
0.092
85
0.063
0.083

86
The photoemission results clearly show that there is a difference
between the way that particles deposit from the vapor onto carbon
foil and the way that particles deposit from solution onto carbon
foil. The foil itself contains numerous gross defects, which are
evident as microscopic tears from SEM photomicrographs. For a
defect free foil, the surface monolayer would be expected to act as a
barrier to deposition material, thus all particles would be confined
to the top monolayer. It is obvious that particles can penetrate a
defect-laden barrier. The extent of penetration might be expected to
depend upon the particle deposition rate, the deposition time, and
the defect density. Our results on vapor deposited manganese oxide
particles show that the particles are confined mainly to the surface,
and thus indicate that defect penetration is a minor process. This is
expected because the particle dose (deposition rate multiplied by
deposition time) is low and the defect density is small, as can be
judged qualitatively from the fact that x-ray diffraction results
show that the foil is semicrystalline. This means that it has more
defects than a crystalline solid, and less defects than a
polycrystalline solid. Thus, the probability that a particle deposits
in a defect or that it deposits close enough to a defect to fall in
from a random walk is expected to be small. Besides the possibility
of a particle depositing through a defect in the surface, there is also
the possibility that a particle can leave the surface of the carbon
once it has been deposited. For the solution deposition of MnC>2, at
least 4 scenarios can be envisaged, as follows:
1) Small particles of oxide produced by photodecomposition in the
solution phase deposit on the surface and penetrate through defects.

87
2) Small particles of oxide produced by photoemission in the
solution phase deposit on the surface and intercalate between layers
of carbon by penetrating along exposed edges. They then can leave or
"fall off" the carbon foil edges at a later time.
3) Permanganate anions intercalate the carbon foil and particles of
Mn02 are produced by in-situ decomposition, while small particles
produced by photodecomposition in solution phase deposit only on
the surface.
4) Some combination of all three.
Photoemission results can be used to investigate these scenarios.
Based on an earlier study of fresh carbon foil [42], the Os peaks at
532.1 eV and 533.2 eV may be associated with graphite oxide, Cx+
(OH')y (H20)2, where the 532.1 eV peak is due to OH' and the 533.2
eV peak is due to H2O. For the four year old carbon foil, there is no
significant difference between the ratios of the areas of O1 s peaks
at 529.8 eV and 530.9 eV to the area of the Os peak at 532.1 eV for
take off angles of 35 and 85 degrees, as shown in Figures 4-12 and
4-13. Thus, the subsurface has an almost homogeneous distribution
of carbon oxidation species (the relative amount of the peak at 533.2
eV increases slightly with the take off angle) and segregating
species in the depth explored. However after exposure of 4-year old
carbon foil to dilute, neutral permanganate for 100 hours, the
situation is that shown in Table 4-4. There are significant changes
( 5%) in the peaks at 533.2 eV and 529.7 eV. Similar results are
obtained in the case of the deposition of iron (III) as the hydrous
oxide, which can be seen in Table 4-5. The drastic reduction in the

Figure 4-12. Peak fit of Os photoelectron peak of carbon foil.
The peak was acquired at a take off angle of 35
degrees.

*CLEAN CARBON FOIL. OIS REGION. THETA=35 DEGREES
Run: 2CCF06 Reg: £
Scan: 1 Chans: 160
Start. eU: 535.55
End eU: 537.60
Fit: 2.£
100'-: I n tens i ty: 656.
100'i Area 50640.
Line
Elmt.
Energy
I n t.
FMHM
Area
LORIO
01S
533. £
43.9
£.0
£4 .£
GAUSS
01S
532.1
64.4
1.7
30.1
GAUSS
01 s
530.9
56.4
1.8
£7.9
l it'll I'-O
ills
529.5
y 3 y
£. A
1 IS H
Binding Energy

Figure 4-13. Peak fit of 0-|S photoelectron peak of carbon foil.
The peak was acquired at a take off angle of 85
degrees.

*CLEAN CARBON FOIL. OIS REGION. THETA=S5 DEGREES
Run: ECCFIO Reg: £
Scan: 1 Chans: 160
Start- eU: 535.55
End eU: 527.60
Fit: £.8
100* I n t ens i t y: 5SS.
100:-; Area 42973.
Line
E1 m t.
Energy
Int.
FWHM
Area
LOR 10
01S
533.2
54.6
£.0
31.8
GAUSS
01S
532.1
63.6
1.6
£8.6
GAUSS
OIS
530.9
51 .0
1 .7
£4.4
IJlj! :vv
01 S
. C*
j .- Q
£ .6
14 .3
Binding Energy

92
533.2 eV peak is probably due to the dehydration of the surface
caused by the evaporating acetone wash. The increase in the peak at
529.7 eV cannot be directly correlated to the amount of the deposit.
There is a greater amount of deposited Mn02 than of deposited Fe23
after 100 hours. The ratio of NMn/Nc to NFe/NQ is 12.9 at a take off
angle of 85 degrees. The corresponding ratio of the change on Os at
529.7 eV, column 4- column 3, is 1.7. Thus, the increase in the
species at 529.7 eV cannot be due to attack on carbon by Mn04~ or
Fe+3, since it should be much larger in the case of Mn04- attack. If
we regard each pair of planes of carbon as a "two wall cuvette", then
they could entrain permanganate solution between them by capillary
action provided the interplane separation is large enough. One would
then expect to observe potassium peaks in the XPS spectra, but none
are observed. It seems unlikely that Mn04* would be selectively
drawn in, because of the charging problem. If the interplane
separation is the same as that of the graphite, then both K+ and
Mn04- are too large to be drawn in.
Table 4-4
0-|s levels for carbon foil-- new [42], 4 year old (take off angle=85)
and after deposition of Mn02 for 100 hours on the latter ( take off
angle=85)
Peak Relative % of Total Non Metal Oxygen
BE(eV) NEW 4-YR OLD DEPOSITED ASSIGNMENT
529.7
14.3
51.3
?
530.9
24.4
26.9
?
532.1
60.0
28.6
16.9
graphite oxide
533.2
40.0
31.8
4.9
bound water

93
Table 4-5
Os levels for carbon foil-- new [42], 4 year old (take off angle=85)
and after deposition of Fe2C>3 for 100 hours on the latter (take off
angle=85)
Peak Relative % of Total Non Metal Oxygen
BE (eV) NEW 4-YR OLD DEPOSITED ASSIGNMENT
529.9
14.3
36.5
?
530.8
24.4
30.2
?
532.1
60.0
28.6
33.3
graphite oxide
533.2
40.0
31.8
0
bound water
Thus scenario 3 is at best a minor process. Resolving the importance
of this scenario would allow the catalysis results to be better
addressed. Figure 4-5 illustrates how samples were prepared which
have either 0, 1, or 2 edges exposed to the solution during the
deposition process. It was stated that the samples were cut from
the large rectangle of carbon foil with a razor knife. It is possible
that the knife edge may have dislodged some of the manganese
dioxide particles in the area of the cut. This is probably not a
serious problem however since the x-ray beam is confined to the
center of the carbon foil. The results of the "edge" experiment are
shown in Table 4-6. The table indicates that an increase in the
number of edges does not cause an increase in the amount of
manganese oxide that is being incorporated in to the carbon foil. In
fact, the opposite effect seems to be occurring. If scenario 1 is the
major method for interlayer incorporation of MnC>2, one would expect

94
the three samples to show the same distributions, because the
defects are uniformly distributed. Thus, the results do not support
the initial expectations for either scenario 1 or scenario 2. However
reflection shows that these results could be obtained for either
scenario 1 or scenario 2. Because the particles are more mobile at
edges, in the 0 edge region, a particle must perform a sequence of
directed "kicks" on a nearest neighbor in order to escape. However
particles near an edge can easily fall off into the dilute colloid
medium. If scenario 2 is occurring, then a decrease in the number of
particles which have intercalated into the surface should be seen if
the number of edges exposed to the permanganate solution is
increased. Likewise, if particles are being uniformly incorporated
into depths, they will be depleted more rapidly where 2 edges are
available for escape and least rapidly where 0 edges are available
for escape. Table 4-6 shows the largest number atom ratios for the
0 edge sample and the smallest number atoms ratios for the 2 edge
sample. Thus, these results cannot distinguish between scenario 1
and scenario 2; many more experiments will be needed before the
mechanism of particle incorporation can be established.
Besides being able to determine the relative concentrations of
various constituents on a surface, XPS can also be used to study the
electronic structure of particles on inert supports. The change in the
electronic structure of these particles can be monitored by
variations in the valence band density of states (VBDOS), which was
discussed in the previous chapter. One of the variations which
VBDOS undergoes when there is a change in the electronic structure

95
is a change in its width (FWHM). Changes in the FWHM can be
attributed to three sources [27].
Table 4-6
NMn/Nc values for solution deposited Mn02 on carbon foil with
either 0,1, or 2 edges having been exposed to permanganate solution.
(All samples were result of 100 hours of
deposition time).
0
0 edges
1 edge
2 edges
0
0.15
0.079
0.12
35
0.32
0.17
0.18
55
0.33
0.18
85
0.29
0.21
0.13
1) An increase in the spin-orbit interactions from the
renormalization of the d-electron wave functions in going from a
free atom to a metal.
2) The splitting of atomic d levels by the crystal field into a
doublet.
3) The mixing of the atomic levels throughout the Brillouin zone.
Items 2 and 3 are considered to be almost totally responsible for the
increase of the FWHM with the increase in particle size. The two
factors should also operate to increase the FWHM of nonmetals. Not
only can changes in the electronic structure change the FWHM, but it
can also change the value of the binding energy of the centroid
region of the VBDOS (ed). This shift is brought about in metals by an
increase in the d atomic orbital population when the supported atom
undergoes transformation to the bulk material. For example, the

96
metals Pt and Pd have an electronic configuration of d9s1 when
they are supported by other atoms. However the configuration
changes to d9-6s-4 per atom for the bulk metal. The correlation
between increased d electron population and the shift in the binding
energy towards the Fermi level makes sense, since the electrons in
the d atomic orbitals require less energy to undergo ionization. The
reason for increased electron population in the d orbitals when an
atom is part of the bulk material can be explained by
renormalization of the Wigner-Seitz cell [27]. To achieve charge
neutrality within this cell, the atomic wavefunction is truncated at
the radius of the cell and the Wigner-Seitz sphere is renormalized.
This renormalization places more change outside the cell and thus
causes more energy to be required to compress it. Since in transition
metals ns orbitals are more diffuse than (n+1)d orbitals, most of the
s electron population will reside outside the radius of the cell.
When the atom undergoes the transition from atom to bulk, the
compression of the atoms will require less energy if the electrons
shift into the d atomic orbitals. This shifting lessens the amount of
charge external to the Wigner-Seitz cell, thus making its
compression easier. This shifting of electrons into the d atomic
orbitals from the s atomic orbitals may be of importance in
understanding catalytic reactions which show increased rates with
decreasing coverage because it is believed that d electron vacancy
is related to catalytic activity. Thus the dispersed material by the
virtue of having less electrons in the d orbitals should have greater
catalytic activity. An example is Ni deposition from solution. The

97
reaction proceeds spontaneously when small Pt clusters are used
and then becomes completely quenched at higher Pt coverages [27].
Variation in the electronic structure of highly dispersed MnO on
carbon foil can be seen when its VBDOS is compared to that of a
thick continuous film of the oxide, which can be seen in Figure 3-1.
The important thing to notice is that the VBDOS for the dispersed
Mn(ll) oxide is narrower and the binding energy of the centroid
region has shifted away from the Fermi level. If indeed the theory
discussed in the preceding paragraph is correct, then there is an
increased s electron population in the Mn of the dispersed oxide
particles as compared to the bulk oxide. The variation in the
electronic structure of highly dispersed Mn203 on carbon foil is
similar to that of MnO when the VBDOS of the dispersed Mn(lll) oxide
is compared with its bulk oxide. This variation can be seen by
looking at Figure 4-14. Note the spectra for two dispersed samples
with coverages of 0.3 and 0.65. Since the VBDOS of the sample with
a coverage of 0.3 is narrower than the VBDOS of the sample with a
coverage of 0.65, there is apparently a difference in the electronic
structure of these two samples also. Since the VBDOS is narrower
for the samples with a coverage of 0.3, there is probably a larger s
electron population in its Mn atoms, like in the highly dispersed MnO.
For dispersed Mn02 on carbon foil, which unlike the previous oxides
was prepared by solution deposition, dissimilar results were
obtained. For dispersed Mn02, there is not as great a shift in binding
energy and not as great a change in the FWHM in its VBDOS relative
to the bulk oxide VBDOS. These smaller changes can be seen in Table
4-7 and Figure 4-15. From these results, the particles are more

98
"bulklike" than the particles prepared by vapor deposition. This
dissimilarity between particles prepared by solution deposition and
vapor deposition is no doubt due to the vast difference between the
two methods of deposition as opposed to the differences between
the MnO, Mn23, and MnC>2 oxides. In vapor deposition the Mn probably
becomes highly dispersed when vaporized and impinges upon the foil
in a highly dispersed fashion. In solution deposition, the Mn02 may
grow in solution before it becomes lodged to the carbon foil surface.
It would be of interest to compare the catalytic activity of the
dispersed oxide with its bulk counterpart to see if the presumed
decreased d electron population found in Mn of the more dispersed
oxides can affect the rate of a catalytic reaction. This is in fact the
topic of the next chapter.
Table 4-7
FWHM and binding energy values for dispersed and bulk Mn2<33 and
MnC>2
Oxide
FWHM (eV)*
B.E.(eV)*
Mn203 (coverage=0.3)
6.2
4.3
Mn23 (coverage=0.65)
6.6
3.0
Bulk Mn23
6.9
2.5
Mn02 (coverage=0.07)
6.3
4.5
Bulk Mn02
6.3
4.2
see Appendix

99
In conclusion, quantitative analysis of dispersed manganese
oxides which were prepared by vapor deposition (i.e. Mn23 and MnO)
gave number atom ratios which indicated that the oxide particles
stayed in the vicinity of the surface. This statement can be made
because of the high coverage values at a take off angle of 0 degrees.
Not only are the particles confined to the surface, but they are small
enough to cause a change in the appearance in the valence band
density of states and in addition shifts in binding energies of core
level photoelectron peaks relative to the bulk oxide. Solution
deposition gives completely different results. Number atom ratios
show that the oxide particles diffuse into the layers of the carbon
foil as time of deposition is increased. The particles which are
solution deposited are larger than those which are vapor deposited.
This may be due to the particle being able to grow in size in solution
before it becomes lodged onto the surface of the carbon foil. This is
especially true for solution deposited ferric oxide.

Figure 4-14.
XPS spectra of dispersed and bulk Mn23.
a) Highly dispersed oxide (coverage =0.3);
b) Less highly dispersed oxide (coverage =0.65);
c) Bulk Mn203.

101
B.E. (eV)

Figure 4-15. XPS spectra of valence band region of MnC>2-
Spectrum with higher binding energy is that for
dispersed MnC>2 on carbon foil. The other spectrum
is for bulk Mn02.

Intensity (counts)
10GHR MN02 DEPOST I ON ON CCF. UALENCE BAND REG. THETA=10 DEG.
Run: 3MN4 Regs 1 (UB ) Scan: 1 Bases 1980 Max Cts's:
Run: BULK6 Regs 1 (UB ) Scans 1 Bases -9 Scales 1.2381
Binding Energy (eU)
103

CHAPTER 5
EFFECT OF DISPERSED MANGANESE OXIDES ON THE DECOMPOSITION OF
PERMANGANATE SOLUTIONS
Introduction
Heterogeneous catalysts have been the subject of much research
over the years. One of the largest users of this type of catalyst, the
petroleum industry, is devoting considerable effort in order to
improve catalyst performance and efficiency. At present the
fabrication of heterogeneous catalysts is relatively imprecise, thus
the field of heterogeneous catalysts has been referred to as a
technologically advanced field without a sound scientific foundation
[44], A heterogeneous catalyst is one which is in a different phase
than the reactants and products. The best example of such a catalyst
is that of a catalytic converter in an automobile. In this case,
substances in the gaseous phase (i.e. CO and unburned hydrocarbons)
react with a catalyst in the solid phase. As a result of research
conducted to improve performance, the catalytic substance is
frequently dispersed on an inert support, in the form of clusters. The
data acquired by XPS can be used to characterize clusters of
deposited materials on inert supports. The data can be interpreted to
obtain the number atom ratios of the catalytic substance to the
104

105
supporting substance (i.e. NMn/Nc discussed in the previous chapter)
at the surface by the acquisition of data at a take off angle of 0=0
and at various depths below the surface (0>O). XPS can also be used
to determine the particle size distribution. These two pieces of
information can be correlated with the rate of the reaction the
catalyst is enhancing. It is possible then to determine if the rate of
the catalytic reaction is being affected due to the catalyst
dispersion. In this chapter the results obtained when the
decomposition of permanganate is carried out in the presence of
dispersed MnO, Mn23 and Mn02 on carbon foil is discussed. It is
necessary that the reaction be carried out in neutral solution
because strongly alkaline or acidic solutions affect the rate of
decomposition [45-46], Light also affects the rate of decomposition
of permanganate [47]. While MnC>2 has been shown to catalyze the
decomposition of permanganate [46], neither Mn23 or MnO have been
shown to catalyze its decomposition. However, Mn(lll) in the solid
is proposed as an intermediate in the propagation steps for the
decomposition of manganate [48] and Mn+2 has been shown to react
with permanganate in 3M HCLO4 solution [49], It seems reasonable
that both MnO and Mn203 can affect the decomposition of Mn04~
even though they cannot be regarded as true catalysts. Fortunately,
the kinetics of this decomposition are slow enough so as to allow
spectrophotometric monitoring [47,50], The electronic structure
data reported in the last chapter will then be correlated with the
catalytic activity (i.e. the rate of decomposition of permanganate
solution) to determine the effect of dispersion on the rate of the
decomposition reaction.

106
Kinetics of Reactions
In this research project the relative amounts of catalytic
reactivity for various samples of dispersed manganese oxides on
carbon foil are reported. Catalytic activity affects the rate of
reaction, which is defined as the "rate of change of concentration of
a substance involved in the reaction with a minus or plus sign
attached, depending on whether the substance is a reactant or a
product" [51]. If we examine the equation given by
aA +bB = gG +hH (52)
the rate of reaction can be defined by any of the following
-d[A]/dt, -d[B]/dt, +d[G]/dt, or +d[H]/dt.
From the above relationships it can be seen that the rate of reaction
is affected by the concentration of the components of the reaction.
Usually, it is affected only by the concentration of the reactants. If
the concentration of the products does affect the reaction rate, then
the reaction is referred to as autocatalytic. If an equation is formed
which shows the relationship between the rate of reaction and the
concentration of a component, then that equation is a rate
expression. The reaction of hydrogen and iodine to produce hydrogen
iodine is given by
H2 + l2 = 2 HI.
(53)

107
The rate expression for equation (53) is
d[HI]/dt = k[H2][l2], (54)
where k is the reaction constant. It is not possible to derive the rate
expression from the stoichiometric equation and therefore it must
be determined as the result of experimentation. The order of a
reaction is determined by summing the values of the exponents of
the concentrations of the rate expression. The rate expression for
the formation of HI is given by
d[HI]/dt = k[H2]1[l2]1-
The order of the reaction overall is simply the sum of all exponents
of the concentrations. Each individual exponent is called the order
with respect to that component. The above reaction is then first
order with respect to hydrogen and first order with respect to iodine
and second order overall. The rate constant k has dimensions of
[conc.]1*n [time]'1 .
Commonly used units for the rate constant are moles/liter,
moles/cc, molecules/cc, or pressure in mm Hg or in atmospheres.
The preferred unit for time is seconds.
Since it is not possible to determine the rate expression from the
stoichiometric equation, it is necessary to fit experimental data to
a rate equation. The data is acquired by recording the decrease in
concentration of a reactant over time. From the data, a curve is
plotted of concentration vs. time. The rate of the reaction at any

108
particular time would be the negative of the slope of the curve. For
the nth order reaction of a single component we have the following
-dc/dt=kcn (55)
after integration for n=1
ln(co/c) = kt (56)
or c=Coe'kt (57)
The data should then fit a plot of log c vs. t in order for it to be a
reaction which is first order overall.
log c
Figure 5-1. Linear plot for a first-order reaction.
For a second order reaction, n=2 and the integrated form of the rate
equation is
1/c 1/Co = kt.
(58)

109
From the above equation, a plot of 1/c vs. t should be linear, with a
positive slope.
Figure 5-2. Linear plot for a second order reaction.
Data for a second order reaction should fit a plot as seen in Figure
5-2. The decomposition of permanganate solutions, which is the
focus of this chapter, is an example of an autocatalytic reaction,
where the rate of the reaction is affected by the amount of the
manganese dioxide that is being produced. The decomposition of
permanganate is represented by the following equation
MnC>4- = MnC>2 + 02 + e". (59)
It is not known where the electron is resident in equation (59)
however [45], Generically, an autodecomposition reaction can be
represented by the equation
A= B +
where A is the reactant and B is a product which catalyzes the
reaction. The rate expression for such a reaction is given by

110
-dA/dt=k[A][B]. (60)
If Aq and B0 equal the initial concentrations of A and B, then A0-A =
B Bo or B = A0 + B0 A. If equation (60) is integrated the following
rate expression results.
1/(A0 +B0)ln (A0B/B0A)= kt (61)
Experimental
As was mentioned in the previous chapter, vapor deposition was
used to prepare dispersed MnO and Mn23 on carbon foil and solution
deposition was used to prepare dispersed MnC>2 on carbon foil. The
carbon foil which was used as a support of these oxides was from
Goodfellow metals and is assayed at 99.8% C. The foil is cut into
rectangles with dimensions of 1 cm X 1.2 cm. There is oxygen
contamination on the surface of this foil, which can be almost
completely removed by heating to 210 C in vacuum [28]. Some of
the carbon foil that was used was four years old; not as much of its
oxygen could be removed by heating. The method of vapor and
solution deposition was discussed in the previous chapter and will
not be repeated here. The coverages (O) (i.e. NMn/Nc at 0=0) of the
oxides were determined by variable angle XPS. The names of the
oxides and their coverages for the samples used in this investigation
are listed in Table 5-1. A value of O =1 means a continuous film of
the oxide is present. This value is obtained only when no discernible
C-|s peak is present for 0 0. No discernible Ci s peak was
observed for a take off angle of 50 degrees. The composition of

Ill
these deposits are unchanged even after four months in a drybox
filled with ultrapure nitrogen. It has been shown that MnO is quite
stable to air exposure at room temperature for short periods of time
[45,50,52],
Table 5-1
Coverage () values for vapor deposited MnO and Mn203 and
solution deposited Mn02 on carbon foil.
Oxide
0
length of time for
solution deposition
MnO
0.18
MnO
1.00 (no discernible Ci s peak)
Mn203
0.23
Mn203
1.00 (no discernible Ci s peak)
Mn02
0.055
2 hours
Mn02
0.133
20 hours
Mn02
0.073
100 hours
In addition there are results for samples of dispersed Mn02 on
carbon foil which were prepared and studied four years ago, but for
which the coverages were not determined. The effects of all of the
samples listed in Table 5-1 upon the decomposition of permanganate
solution are determined by placing them into a permanganate
solution and measuring the absorbance of permanganate at 525 nm at
12 hour intervals for a total time of 48 hours. From this data plots

Figure 5-3. Absorbance versus time data for MnO and Mn23
samples.
(o) permanganate solution; () permanganate solution
+ carbon foil; (+) permanganate + dispersed MnO on
carbon foil; (X) permanganate solution + dispersed
Mn203 on carbon foil; (A) permanganate solution + thick
Mn23 on carbon foil.

Absorbance
0 550
0500 -
0.450 -
24 36
time (hours)
48
113

Figure 5-4. Absorbance versus time data for colloidal Mn02
deposited from a 2.0 X 10"4 F potassium permanganate
solution.
(o) permanganate solution; () permanganate solution +
100 hour deposit; (+) permanganate solution + 20 hour
deposit; (A) permanganate + carbon foil;
(X) permanganate + 4 hour deposit; (A) permanganate
+ 2 hour deposit.

Absorbance
115

Figure 5-5. Absorbance versus time data for colloidal Mn02
deposited from a 3.3 X 10'4 F potassium permanganate
solution.
(o) permanganate solution; (A) permanganate + carbon
foil; () permanganate + 20 hour deposit;
(+) permanganate + 2 hour deposit; (X) permanganate +
100 hour deposit.


118
of absorbance versus time are constructed, which can be seen in
Figures 5-3 to 5-5.
Results
Before the raw data in Figures 5-3 to 5-5 can be interpreted, it
needs to be normalized so the increase in the rate of decomposition
due to the oxide alone can be realized. Two factors for normalization
must be considered. The first factor is the differing concentrations
of the permanganate solutions. The vapor deposited samples and the
solution deposited MnC>2 samples which were prepared four years
ago were allowed to decompose a 2.0 X 10'4 F permanganate
solution while the freshly prepared MnC>2 samples are allowed to
decompose a 3.3 X 10"4 F solution. The second factor which is
factored into the normalized equation is the differing areas of
coverage of the carbon foil with the oxide particles due to the
differences in vapor and solution deposition. With solution
deposition the oxide particles are covered on both sides while for
vapor deposition, only a circular area of one side is covered. This can
be seen by Figure 5-6. Because of this difference, the effective
coverage is determined. Since in solution deposition both sides are
being covered, the effective coverage is equal to the measured
coverage. But for samples prepared by vapor deposition, the
measured coverage must be multiplied by the area of the circle and
divided by two times the area of one side of the carbon rectangle.

119
Figure 5-6. Illustration of vapor deposited oxide particles on one
side of carbon foil.
Thus, the effective coverage is less than the measured coverage (i.e.
d>eff <0). By taking these two factors into account, it is possible to
formulate an equation which is normalized for the catalytic effect
due to the oxide alone. The normalized equation is given by
Y = |Aabs| /(Oeff C0). (62)
|Aabs| is the magnitude of the absorbance change due to the oxide
alone, Co is the initial concentration of the permanganate solution,
and Oeff has been defined above. Plots of Y vs. t (time) are shown in
Figures 5-7 and 5-8. It has been determined that the data for MnO on
carbon foil and Mn02 on carbon foil with a coverage of 0.073 can be
fit with a high correlation to an equation of the form
Y=a In (t+1) +b
(63)

and the data for Mn23 on carbon foil, bulk Mn203, and Mn02 with
coverages of 0.055 and 0.133 on carbon foil can be fit with high
correlation to a linear equation of the form
120
Y=at+b. (64)
Table 5-2 shows the values for a,b, and the degree of correlation
when equations 63 and 64 are fitted to experimental data. The solid
lines in Figures 5-7 and 5-8 correspond to the best fits.
Table 5-2
Fit Parameters for Experimental Data.
Sample
a
Equation 63
b CORR
a
Equations 64
b CORR
Dispersed MnO
33.2
-1.65
0.992
Dispersed Mn23
43.4
-16.6
0.913
3.89
5.32
0.991
Thick Mn23
11.2
-2.63
0.965
0.94
4.68
0.976
Bulk Mn23
11.4
-3.32
0.947
0.98
3.44
0.987
Mn02 (O=.055)
114
-49.5
0.878
10.5
2.20
0.977
Mn02 (O=.073)
117
-19.1
0.981
9.33
66.8
0.951
Mn02 ($=.133)
3.70
-42.0
0.998

Figure 5-7. Normalized change in absorbance magnitude (see text)
versus time for MnO and Mn23 samples. The original is
a point for each.
(o) dispersed Mn23 on carbon foil; () dispersed MnO on
carbon foil; (A) thick Mn23 on carbon foil; (+) bulk
Mn203.


Figure 5-8. Normalized change in absorbance magnitude (see text)
versus time for colloidally deposited Mn02- The origin
is a point for each.
(o) 100 hour deposit; () 2 hour deposit; (A) 20 hour
deposit.

>-
500 *
300 -
100 -
12
24
time
36
(hours )
48
124

125
Correlation of Rate Law Expressions with Experimental Data
One can investigate the fit of various rate law expressions to the
experimental data. Since the decomposition of neutral permanganate
in the absence of carbon supported manganese oxide particles is
autocatalytic with colloidally dispersed Mn02 particles catalyzing
the reaction, it is reasonable to assume that the decomposition
remains autocatalytic in the presence of carbon supported
manganese oxide particles. Unfortunately, such a fit cannot be made
directly, because the activity of permanganate is not known.
Nevertheless it is possible to simulate data from a second order
autocatalytic reaction and to explore the limiting behavior of such a
reaction. Equation (61) requires initial values for the concentrations
of A0 and B0. Arbitrary values of 1.00 M are chosen for A0 and 0.20 M
is chosen for B. Recalling that Ao-A=B-Bo and by the substitution of
the values chosen for A0 and B0 into equation 61, we have the
following the equation given by
(1/1.2)ln(5B/A) = kt.
By knowing t and k, one can solve for 5B/A which represents one
equation with two unknowns. If A0-A = B-B0, then 1.00-A=B-0.20.
There are now two equations with two unknowns, and A and B can be
uniquely determined. Knowing A and A0 for each value of time t, the
quantity |A-Ao|/Ao can be determined for each value of t. The
relationship between t and | A A 01 / A0 can be fit with high
correlation to the following linear functions

126
[A-AqI/Aq = a In (t+1) +b (65)
when k is large and
|A-A0|/A0 = at + b (66)
when k is small.
The values for a, b, and the degree of correlation for a given rate
constant k are shown in Table 5-3. Thus in fact, the empirical fits to
the experimental data can be regarded as limiting forms of a 2nc*
order autocatalytic reaction.
Table 5-3
Example of 2nc) order Autocatalytic Simulation for various Rate
Constants on Time Intervals Corresponding to Those Used
Experimentally.
A0 = 1.00 M; B0 = 0.20 M
Equation 65* Equation 66*
Rate Constant(hr1) a b CORR a b CORR
1/6
0.271
-0.005
0.990
0.020
0.241
0.874
1/12
0.236
-0.085
0.927
0.021
0.046
0.983
1/24
0.138
-0.070
0.858
0.013
-0.021
0.998
*Y=|A-A0|/Aq

127
On the basis of the simulation results, the conclusion is made that
the rate of reaction is greater in the presence of dispersed MnO
particles than dispersed Mn23 particles. Also the rate of reaction
for carbon supported dispersed Mn2C>3 particles is greater than for
thick continuous films of Mn23 on carbon and for bulk Mn203. It is
interesting that the curves for continuous film and bulk Mn23 are
coincident. This should be the case since thick film is expected to
exhibit bulk behavior based on its electronic structure. The rates of
reaction for Mn02 are probably too high. This may be due to the
intercalated particles contributing to the catalytic activity, which
are not accounted for in Oeff. Presently experiments are being
performed on other layered and unlayered solid supports to help
clarify this situation. Figure 5-9 shows a proposed mechanism for
the autodecomposition of neutral permanganate [48]. The role of the
dispersed Mn2C>3 can be seen in steps 4 & 5. The Mn(lll) allows the
cycle to go from step 2 to 5 without having to go through step 4. As
a result of this, MnC>2 can build up faster. Since the concentration of
H+ is low in neutral solution, it is advantageous that step 4 be
avoided.

128
1. Mn04'
-Mn04
hv
2. Mn04*' + Mn04
radiationless relaxation
Mn04'2 + Mn02 + 02(g)
-Mn04
3. Mn04' + Mn02
-Mn02 Mn04
-2
4. Mn02 Mn04 '2 + 2 H +
-Mn04" + Mn(lll) (ppt.)
5. 2 Mn(lll) + Mn04
-2
3 Mn02
6. Mn02 (active)
-Mn02 (inactive)
Figure 5-9. Proposed mechanism for the autodecomposition of
neutral permanganate [48].

CHAPTER 6
CONCLUSIONS AND FUTURE WORK
By the variation of the molecular geometry of the smallest
cluster size for manganese monoxide, namely (MnO)2, it is possible
to construct a VBDOS curve from the eigenvectors and eigenvalues of
the CND02/U algorithm which shows remarkable similarity to the
spectrum of a thick continuous film of MnO. The significance of this
is that it shows that there is another component to XPS valence band
broadening which has here-to-fore been overlooked. In past
investigations valence band broadening was considered to be due
solely from an increase in the size of number of atoms in a cluster
on a substrate. In these past investigations the calculated VBDOS
curve was broadened by increasing the number of atoms within a
given molecular geometry. The geometry most frequently used was
face centered cubic (fee). No consideration was given to the
interface between the carbon foil and the dispersed material. In
consideration of the interface it is assumed that the substrate
contains "sites" which will accommodate certain geometries over
others. If certain geometries are accommodated over others it
stands to reason that some are going to be less energetically
favorable than others. If less energetically favorable geometries are
contributing to the photoelectron spectrum, then there is going to
129

130
be a broadening in that spectrum. The greater the number of
geometries present on the surface of the substrate, the greater the
number of molecular orbital energies (i.e. eigenvalues) which are
going to contribute to the XPS spectrum. The overall effect of
considering the interface between the substrate and the dispersed
material is that it demonstrates a limitation in the methodology
previously used to interprete XPS valence band broadening.
When the method of deposition of a transition metal oxide onto
the carbon substrate is varied there is a variation in the results of
the quantitative analysis and in the electronic structure of the
surface. When vapor deposition is used to disperse the oxide,
samples are obtained whose particles were confined to the surface
region. It is even possible to construct a continuous film of MnO on
the surface of the carbon substrate by this method. When solution
deposition is used to disperse the oxide, the samples obtained have
the majority of their dispersed particles incorporated below the
surface of the substrate. The electronic structure of the particles
dispersed by these two methods is determined by acquisition of data
in the valence band region. Particles deposited by the vapor
deposition method show a greater valence band narrowing and a
greater shift in binding energy away from the Fermi level relative to
their bulk oxide than do particles deposited by solution deposition.
Thus, vapor deposition seems to cause smaller particles to be
deposited on the surface than does solution deposition.
When the dispersed Mn oxide samples produced by both methods
are placed into a solution of potassium permanganate, they have an
effect on the autocatalytic decomposition of permanganate. It is

131
shown that the dispersed Mn02 has the greatest effect on the
decomposition. This would be expected since the Mn02 catalyzes the
reaction. However the effect of dispersed Mn02 may be
overestimated. The reason for this may be because the particles
incorporated below the surface are contributing to the
decomposition. These particles are not considered in the coverage
value. The dispersed MnO has the second greatest and then the
dispersed Mn(lll) oxide has the third greatest effect. The continuous
film and bulk of the Mn(lll) oxide had the least effect. An explanation
as to how the MnO affects the reaction is not clear at this point. An
explanation is given for why the Mn(lll) oxide affects the reaction
however. Its presence may allow the bypassing of several steps in a
mechanism proposed by Duke [48]. The bypassing of these steps
would eliminate the need for hydrogen ion, which is very low in a
neutral solution.
Future work in the area should center on investigating the effect,
if any, of the incorporation of the manganese dioxide particles into
the carbon substrate upon the autocatalytic decomposition of
permanganate. At present there is experimentation underway which
is involved with the deposition of Mn02 on mica and glass. Mica is a
layered and glass is an unlayered substrate. Knowing the effect of
these samples upon the autocatalytic decomposition would enable
conclusions to be drawn as to whether the incorporated manganese
dioxide particles are responsible for the rate of the permanganate
reaction being too high. Future work should also be focused on the
quantification of the catalytic activity of dispersed ferric oxide on

132
carbon foil. The bulk and dispersed samples could be allowed to
catalyze the reaction given by
2 CO + 02 = 2 CO2.
The monitoring of the catalytic activity could be accomplished by
gas chromatography (GC) or by in situ reaction in a gas cell. In the
former case, the gases involved along with the ferric oxide sample
could be placed into a sealed container and samples could be
withdrawn at selected time intervals. GC would tell how much of the
gases were present at any one particular time. In the latter case,
core level C1 s and O s XPS spectra can be used to monitor the
reaction.

APPENDIX
STATISTICAL ANALYSIS OF XPS VALENCE BAND DATA
Because interpretations are being made due to the differences in
binding energies and FWHMs of valence band data, it is necessary to
perform a statistical analysis of data acquired from this region. To
do this, the data of 10 different scans of bulk Mn23 are acquired at
a take off angle of 0 degrees between 15 and 0 electron volts. After
the scans are acquired, the appropriate windows are constructed and
the background is subtracted out. The binding energies and the
FWHMs of the distributions are determined and the mean and the
standard deviations are computed. Table A-1 lists the results.
Table A-1
Binding energies and FWHMs of the distributions in the valence band
region of bulk Mn2C>3
Scan Binding Energy (eV) FWHM (eV)
1
3.93
5.34
2
4.25
5.77
3
4.40
6.07
4
3.85
5.16
5
4.22
5.88
6
4.33
5.82
7
4.33
6.25
8
4.51
6.10
9
4.25
5.74
10
4.33
5.96
133

134
These values resulted in a mean binding energy of 4.26 eV with a
a standard deviation of 0.18 eV. The mean FWHM is 5.78 eV with a
standard deviation of 0.30 eV.

REFERENCES
1. Carlson, T. Photoelectron and Auger Spectroscopy (Plenum Press,
New York, London 1978).
2. Fellner-Felldegg, H.; Gelius, U.; Wannberg, A.; Nilsson, G.;
Basilier, E. Siegbahn, K. J. Electron Spectrosc. 1974, 5, 643.
3. Wannberg, B.; Gelius, U.; Siegbahn, K., Uppsala University,
Institute of Physics Report No. 818 (1973).
4. Wiley, W.; Hendee, C. I.R.E. Trans. Nucl. Sci. 1972, NS-9, 103.
5. Brundle, C.; Baker, A. (editors) Electron Spectroscopy: Theory,
Techniques and Applications ( Academic Press, London, New York,
San Francisco 1978).
6. Ballard, R. Photoelectron Spectroscopy and Molecular Orbital
Theory (John Wiley & Sons, New York 1978).
7. Koopmans, T. Physica 1934, 1, 104.
8. Lowe, J. Quantum Chemistry (Academic Press, New York, London
1978).
9. Claude, C.; Bernard, D.; Frank, L. Quantum Mechanics Vols. 1&2.
(John Wiley & Sons New York, London 1977).
10. Slater, J. Phys, Rev. 1959, 34, 1293.
11. Pople, J.; Beveridge, D.; Approximate Molecular Orbital Theory
(McGraw-Hill Book Company, New York, London 1970).
12. Pople, J.; Segal, G. J. Chem. Phys. 1965, 43, S136.
135

136
13. Pople, J,; Segal, G. J. Chem. Phys. 1966, 44, 3289.
14. Roothaan, C. J. Rev. Mod. Phys. 1962, 36, 33.
15. Ross, P.; Kinoshita, K.; Stonehart, P. J. Catal. 1974, 32, 163.
16. Steiner, P.; Hochst, H.; Huffner, S. J. Phys. F7 1977, L105.
17. Tibbetts, G.; Egelhoff, Jr., W. Phys. Rev. Letters 1978, 41, 188.
18. Liang, K.; Salaneck,W.; Aksay, I. Solid State Commun. 1976, 19,
329.
19. Takasu, Y.; Unwin, R.; Tesche, B.; Bradshaw, A. Surface Sci.
1978, 77, 219.
20. Egelhoff, Jr., W.; Tibbetts, G. Phys. Rev. B 1979, B19, 5028.
21. Roulet, H.; Mariot, R.; Dufour, G.; Hague, C. J. Phys. F10 1980,
1025.
22. Oberli, L.; Monot, R.; Mathieu, H.; Landolt, D.; Buttet, J. Surface
Sci. 1981, 106, 301.
23. Cheung, T. Surface Sci. 1983, 127, L129.
24. Baetzold, R.; Mason, M.; Hamilton, J. J. Chem. Phys. 1980, 72, 366.
25. Baetzold, R. Surface Sci. 1981, 106, 243.
26. Young, V.; Gibbs, R.; Winograd, N. J. Chem. Phys. 1979, 70, 5714.
27. Mason, M.; Gerenser, L.; Lee, S. Phys. Rev. Letters 1977, 39, 288.
28. Young, V.; Zhao, L. Chem. Phys. Lett. 1983, 102, 455.
29. Baetzold, R.; Mason, M.; Hamilton, J. J. Chem. Phys. 1980, 72,
366.
30. Baba-Ahmed, A.; Gayoso, J. Theoret. Chim. Acta. (Berl.) 1983, 62
507.

137
31. Huber, T.; Herzberg, G. Molecular Structure and Molecular Spectra
(Van Nostrand Reinhold & Co., New York, London 1979).
32. Baumann, C.; Van Zee, R.; Bhat, S.; Weltner, Jr., W.; J. Chem. Phys.
1983, 78, 190.
33. Hildenbrand, D. Chem. Phys. Lett. 1975, 34, 352.
34. Ervin, K.; Loh, S.; Aristov, N.; Armentrout, P. J. Chem. Phys. 1983,
3593.
35. Rohlfing, E.; Cox, D.; Kaldor, A. J. Chem. Phys. 1984, 81, 3846.
36. Scofield, J. J. Electron Spectrosc. Relat. Phenom. 1976, 8, 129.
37. Young, V.; McCaslin, P. Anal. Chem. 1985, 57, 880.
38. Kelly, M.; Scharpen, L. Surface Science Laboratories, Palo Alto,
CA, private communication.
39. Reference Manual for DS 800 Software (KRATOS Analytical,
Ramsey, New Jersey 1987).
40. Shabalina, O.; Ryzhen'kov, A.; Egorov, Y.; Stotskii, V.; Popov,V.; .
Kotel'nikov, A. Deposited Document SPSTL 422 khp-D8 1980:
CA 96: 208570a.
41. Helsop, R.; Jones, P. Inorganic Chemistry (Elsevier Scientific
Publishing Company, New York 1976).
42. Young, V. Carbon 1982, 20, 35.
43. Rao, C.; Sarma, D.; Vasudevan, S.; Hedge, M. Proc. R. Soc. Lond.
1979, A 367, 239.
44. Young, V. Preparation and Characterization of Surface Dispersed
Metal Oxides (Proposal submitted to the Petroleum Research
Fund, 1984).
45. Zimmerman, G. J. Chem. Phys. 1955, 23, 825.

138
46. Narita, E.; Hashimoto, T;. Yoshida, S.; Okabe, T. Bull. Chem. Soc.
Jpn. 1982, 55, 963.
47. Kachan, A.; Sherstoboeva, M.; Zhur. Neorg. Khim. 1958, 3, 1089.
48. Duke, F. J Phys. Chem. 1952, 56, 882.
49. Adamson, A.; J. Phys. & Colloid Chem. 1951, 55, 293.
50. logansen A.; Grushina, N. Khim. Fiz. 1982, 1, 121.
51. Frost, A.; Pearson, R. Kinetics and Mechanism (John Wiley & Sons
Inc., New York, London 1961).
52. Oku, M.; Hirokawa, K. J. Electron Spectrosc. Relat. Phenom. 1975,
7, 465.

BIOGRAPHICAL SKETCH
Jack Davis was born on June 21, 1950, in Kansas City, Missouri.
He was raised in nearby Independence where he received his high
school diploma in 1968 from William Chrisman High School.
After graduation Jack attended the University of Missouri-
Columbia and graduated from there in 1972 with a Bachelor of
Science degree in chemistry. Upon graduation he accepted
employment with the Speas Company, where he worked as a quality
control chemist for a period of five years. In 1979 he began his
tenure as a graduate student in the Chemistry Department of the
University of Missouri-Kansas City. He worked for Dr. Jerry R. Dias
there and in 1981 received a Master of Science in chemistry. In 1982
he moved to College Station Texas so he could attend Texas A&M
University. While there he partially completed the requirements for
the Ph.D. degree in analytical chemistry. In 1984 he transferred to
the University of Florida to complete the requirements for the
degree.
139

I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy. r t ,
^ M / V>TQ /Q-\-L,
Vaneica Y. Young, Chairperson
Associate Professor of Chemistr
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy.
J
.
Anna Brajter/j
Associate Prc
Toth
ifessor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy. ^ j ^ r ^
Christopher D. Batich
Professor of Materials Science
and Engineering
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as dissertation for the degree
of Doctor of Philosophy. (O
' irO:
Associate Professor of Chemistry
I certify that I have read this study and that in my opinion it
conforms to acceptable standards of scholarly presentation and is
fully adequate, in scope and quality, as a dissertation for the degree
of Doctor of Philosophy. (\ Q
Japfies D. Winefordrier
Graduate Research Professor of
Chemistry

This dissertation was submitted to the Graduate Faculty of the
Department of Chemistry in the College of Liberal Arts and Sciences
and to the Graduate School and was accepted as partial fulfillment
of the requirements for the degree of Doctor of Philosophy.
December, 1988
Dean, Graduate School



CHAPTER 6
CONCLUSIONS AND FUTURE WORK
By the variation of the molecular geometry of the smallest
cluster size for manganese monoxide, namely (MnO)2, it is possible
to construct a VBDOS curve from the eigenvectors and eigenvalues of
the CND02/U algorithm which shows remarkable similarity to the
spectrum of a thick continuous film of MnO. The significance of this
is that it shows that there is another component to XPS valence band
broadening which has here-to-fore been overlooked. In past
investigations valence band broadening was considered to be due
solely from an increase in the size of number of atoms in a cluster
on a substrate. In these past investigations the calculated VBDOS
curve was broadened by increasing the number of atoms within a
given molecular geometry. The geometry most frequently used was
face centered cubic (fee). No consideration was given to the
interface between the carbon foil and the dispersed material. In
consideration of the interface it is assumed that the substrate
contains "sites" which will accommodate certain geometries over
others. If certain geometries are accommodated over others it
stands to reason that some are going to be less energetically
favorable than others. If less energetically favorable geometries are
contributing to the photoelectron spectrum, then there is going to
129


132
carbon foil. The bulk and dispersed samples could be allowed to
catalyze the reaction given by
2 CO + 02 = 2 CO2.
The monitoring of the catalytic activity could be accomplished by
gas chromatography (GC) or by in situ reaction in a gas cell. In the
former case, the gases involved along with the ferric oxide sample
could be placed into a sealed container and samples could be
withdrawn at selected time intervals. GC would tell how much of the
gases were present at any one particular time. In the latter case,
core level C1 s and O s XPS spectra can be used to monitor the
reaction.


42
What is done can be summed up by the following statement. For (M)x,
where X=1,2,3,4 , and where M is some monomer unit, as X is
increased the electronic structure evolves to that of the bulk
material. In Baetzold's study the selection of one geometry (i.e. fee)
for all cluster sizes is arbitrary. It seems reasonable that when a
substance is deposited either fractionally or partially on a substrate
that it will not form the same geometry for all possible values of X.
The goal of this research project is to see what effect the variation
of the molecular geometry for a given cluster size would have on the
valence band density of states (VBDOS). Could a "bulk like" VBDOS
curve be constructed by variation of the smallest possible cluster
size for MnO, namely (MnO)2 ?
As was mentioned briefly at the beginning of chapter 2, the
binding energy of the photoelectron is linked to eigenvalues derived
from molecular orbital theory by the rule of Koopman [7-8], which
can be represented by
-e (eigenvalue^ binding energy of the photoelectron. (41)
This rule is not entirely correct, however, because it is based on an
incorrect assumption-that the orbitals remain frozen orbitals
during photoemission. This is a "static" approximation. In actuality
the remaining electrons "relax" towards the site of photoemission
because of reduced screening of the nuclear charge. This relaxation
imparts a certain amount of kinetic energy to the ejected electron,
thus reducing its binding energy. If comparisons are being made
between clusters of different size, where the extent of relaxation is


APPENDIX
STATISTICAL ANALYSIS OF XPS VALENCE BAND DATA
Because interpretations are being made due to the differences in
binding energies and FWHMs of valence band data, it is necessary to
perform a statistical analysis of data acquired from this region. To
do this, the data of 10 different scans of bulk Mn23 are acquired at
a take off angle of 0 degrees between 15 and 0 electron volts. After
the scans are acquired, the appropriate windows are constructed and
the background is subtracted out. The binding energies and the
FWHMs of the distributions are determined and the mean and the
standard deviations are computed. Table A-1 lists the results.
Table A-1
Binding energies and FWHMs of the distributions in the valence band
region of bulk Mn2C>3
Scan Binding Energy (eV) FWHM (eV)
1
3.93
5.34
2
4.25
5.77
3
4.40
6.07
4
3.85
5.16
5
4.22
5.88
6
4.33
5.82
7
4.33
6.25
8
4.51
6.10
9
4.25
5.74
10
4.33
5.96
133


15
down to the operating range of 10*9 torr. The specifications of the
machine state that it is capable of reaching a pressure as low as
5X10*"*1 torr. To reach this pressure, however, it is necessary to add
liquid nitrogen to the cold trap in the SAC. This procedure is very
time consuming and is usually not necessary. To improve the
efficiency of the ion pump, it may be used in conjunction with a
titanium sublimation pump.
After the SAC has been pumped down to the 10*9 torr range and
the X-ray source has been activated, data can be acquired. This can
be done with or without computer control. Almost always computer
control is the option chosen. As stated previously the computer is a
Digital Micro PDP-11 with the RT-11 operating system and 256K
bytes of RAM. DS800, the software written by KRATOS, allows the
user to acquire and process data off line. To acquire data, one simply
chooses that option from the master menu which first appears after
the system is booted. After the data acquisition menu appears one
selects the region(s) which is (are) to be scanned, the number of
sweeps to be performed in that region and the time allowed for each
sweep. In addition, the operator has the choice of excitation source
(either Al or Mg), low or high magnification, low or high resolution,
and analyzer mode (either FRR or FAT). After the parameters have
been selected, data acquisition can begin. One chooses the run option
and assigns a file name to that run. The file name can be anything
with six or fewer characters. One parameter that the computer
cannot control on our instrument is the angle between the analyzer
and the sample (sometimes referred to as the take off angle). This
has to be adjusted manually. After the data has been collected and


*CLEAN CARBON FOIL. OIS REGION. THETA=35 DEGREES
Run: 2CCF06 Reg: £
Scan: 1 Chans: 160
Start. eU: 535.55
End eU: 537.60
Fit: 2.£
100'-: I n tens i ty: 656.
100'i Area 50640.
Line
Elmt.
Energy
I n t.
FMHM
Area
LORIO
01S
533. £
43.9
£.0
£4 .£
GAUSS
01S
532.1
64.4
1.7
30.1
GAUSS
01 s
530.9
56.4
1.8
£7.9
l it'll I'-O
ills
529.5
y 3 y
£. A
1 IS H
Binding Energy




9
The magnetic field is B, m and x> are the mass and velocity of the
electron and p0 is the radius of the orbit of the electron. Double
focusing can be understood by looking at Figure 1-4. If the
photoelectron enters the analyzer; at an angle 0 to po (the optic
circle), in the xy plane or at an angle ji with respect to the z-axis,
then it will return to the optic circle after it has traversed an angle
of 7W2 or 255 degrees. In other words, the analyzer has the ability
to redirect the deviation of the photoelectron whether it deviates in
or out of the plane of p0. The major advantage of the magnetic
dispersion analyzers is that a greater field can be supplied for the
study of high energy (>5000eV) photoelectrons. At this energy
relativistic effects become significant and the optics needed to
study such electrons are better understood for magnetic
instruments^ ]. -
Figure 1-4. Principle of Magnetic Double Focusing Electron Analyzer.


*CCF WHERE FES03 WAS DEPOSITED FOR 1Q0HR 05S' REGZGM. 7HETA=o5 DEGREES
Run: 1GFE
CL
Reg:
3
Scan: 1
Chans:
153
Start- eU:
534.60
End eU:
526.95
Fit-: £.0
100*: In tens
i ty:
5536.
100*-; Area
354465.
Line Elmi.
Energy
Int.
FWHM
Area
GAUSS OIS
532.0
41.8
1 .9
£6.3
GAUSS 01S
530.8
42.4
1.7
£3.9
GAUSS 01S
529.6
54.4
1 .6
£8.8
GAUSS CHS
=¡oq o
\ji_ 17 i_
Z'O ~r
V-"-* 1
1 .5
19.3
1 r 1
534 532 530
Binding Energy


36
Figure 2-6. Effect of SCF calculation upon the electron distribution.
Although this program retains the concepts outlined in the
previous section, one of the major differences between this
program and the earlier version is in the formulation of the
coulomb repulsion matrix.
3d
4s
First Row Transition Element
Figure 2-7. Illustration of how a first row transition element is
treated in CND02/U.


Figure 4-11. Peak fit of the Os photoelectron peak for a sample of
carbon foil which is prepared by allowing Fe203 to
deposit on it for 100 hours. The take off angle is 85
degrees.


64
the beginning and ending of a given distribution. Some degree of
estimation and guesswork is required here and it takes practice for
the operator to become proficient. In addition the operator can
require the computer to fit a given distribution to within a given
FWHM. After this is done, the interactive synthesis option is
selected and the spectral window that the peak fit is being
performed upon appears in the upper right portion of the display that
appears. The background is subtracted out and the distributions that
the operator selects appear under the photoelectron peak. The degree
of fit is displayed, which at this point is usually very high. Next,
the autofit command is utilized by typing "au" at the prompt. The
computer fits the distributions selected to the peak, calculates the
final fit value and displays it. The lower the value of the fit, the
better it is. Figure 4-3 is an example of four distributions being fit
to the Oi s region of four year old carbon foil, for which the 0-] s
contamination can not be completely eliminated.
Preparation of Samples
As is mentioned in the introduction section of this chapter,
vapor and solution deposition are utilized to prepare dispersed
manganese oxides on carbon foil, while the ferric oxide samples are
prepared by solution deposition only. To vapor deposit a manganese
oxide onto carbon foil, it is first necessary to vaporize the
manganese. Vaporization of the manganese is achieved by heating it
resistively in a tungsten filament basket. The vapor produced is
allowed to impinge upon a piece of carbon foil which is cut into a


28
Figure 2-5. Schematic showing the effect of the Slater exponent
on the radial portion of an atomic orbital.
Self-Consistent Field Theory
As was mentioned in the previous section, it is necessary to
determine eigenvalues and eigenvectors which are the result of
electrons moving in a self-consistent field. From equation (13), the
energy is obtained by allowing the Hamiltonian operator H to operate
on the probability density VF*VF. H can be broken down into a one
electron part H-| and a two electron part H2 as illustrated by
H = Hi + H2. (22)
The one electron part is a function of the kinetic energy of the ith
electron and the potential between that electron and the nucleus. If
summed over all electrons we have
Hi =E Hcore (p)> (23)
P
Hcore (p) (-1/2) Ap2 £ ZArpA-1.
A
where
(24)


CHAPTERS
5 EFFECT OF DISPERSED MANGANESE OXIDES ON THE
DECOMPOSITION OF PERMANGANATE SOLUTIONS 104
Introduction 104
Kinetics of Reactions 106
Experimental 110
Results 118
Correlation of Rate Law Expressions
with Experimental Data 125
6 CONCLUSIONS AND FUTURE WORK 129
APPENDIX
STATISTICAL ANALYSIS OF XPS VALENCE BAND DATA 133
REFERENCES 135
BIOGRAPHICAL SKETCH 139


92
533.2 eV peak is probably due to the dehydration of the surface
caused by the evaporating acetone wash. The increase in the peak at
529.7 eV cannot be directly correlated to the amount of the deposit.
There is a greater amount of deposited Mn02 than of deposited Fe23
after 100 hours. The ratio of NMn/Nc to NFe/NQ is 12.9 at a take off
angle of 85 degrees. The corresponding ratio of the change on Os at
529.7 eV, column 4- column 3, is 1.7. Thus, the increase in the
species at 529.7 eV cannot be due to attack on carbon by Mn04~ or
Fe+3, since it should be much larger in the case of Mn04- attack. If
we regard each pair of planes of carbon as a "two wall cuvette", then
they could entrain permanganate solution between them by capillary
action provided the interplane separation is large enough. One would
then expect to observe potassium peaks in the XPS spectra, but none
are observed. It seems unlikely that Mn04* would be selectively
drawn in, because of the charging problem. If the interplane
separation is the same as that of the graphite, then both K+ and
Mn04- are too large to be drawn in.
Table 4-4
0-|s levels for carbon foil-- new [42], 4 year old (take off angle=85)
and after deposition of Mn02 for 100 hours on the latter ( take off
angle=85)
Peak Relative % of Total Non Metal Oxygen
BE(eV) NEW 4-YR OLD DEPOSITED ASSIGNMENT
529.7
14.3
51.3
?
530.9
24.4
26.9
?
532.1
60.0
28.6
16.9
graphite oxide
533.2
40.0
31.8
4.9
bound water


4 5
Table 3-3
Bond Energies and Lengths of Selected Diatomic Molecules which
Contain one or more Transition Elements.
AB
Bond Length
(A)
Exp.
Dissociation Energy
(eV)
Exp.a
M n2
2.8
3.4b
-286.18
-0.23
FeO
1.58
1.57 a
-142.17
-4.20
FeS
1.90
-149.5
-3.31
MnBr
2.3
-108.
-3.22
Fe2
2.7
-179.24
-1 .06
a) Ref. [31] b) Ref. [32]
Since the transition element is being treated as two atoms it is
necessary to compute two atomic energies, as shown by
AE= s*ENEG(s) + p*ENEG(p) + (TE2 T(l,l)/2) + d*ENEG(d). (43)
The ENEG terms are equal to the average of the ionization potential
and the electron affinity of the respective subshell. TE is the total
number of electrons and s,p, and d are the number of s,p, and d
electrons respectively. The r(I,I) term is the monocenter coulomb
repulsion for either the s or d subshell. The total atomic energy is
then computed by adding the "atomic energy" of the s and d shells
together. The program is modified to compute one atomic element
per transition atom and this is done by determining the probability


3 5
eigenvalues are produced. They are then used to reassign the
electrons in pairs to the molecular orbitals with the lowest energy
and to construct a new density matrix. These steps are repeated
until self-consistency is achieved [11]. Figure 2-6 shows the effect
of self consistency upon the radial part of a wavefunction. This
program utilizes the modifications made in the second
parameterization of CNDO. These modifications include the
incorporation of the "zero penetration effect" which equates the last
term in parenthesis in equation (38) to zero and the replacement of
the ionization potentials in the Ujj.(j. term with the average of the
ionization potential and the electron affinity (i.e. -1/2 (l^ + A^)).
CNDQ2/U
A relatively new CNDO algorithm was selected for this project.
Unlike the version written by Pople et al., [12,13] this program is
parameterized for the first 81 elements of the periodic table. This
is possible by the utilization of the concept of "fictitious atoms,"
whereby those elements which have their valence electrons
distributed over two or more subshells with different principal
quantum numbers, are treated as two or more atoms which are
centered at the same coordinate. Figure 2-7 illustrates this
principle.


>-
500 *
300 -
100 -
12
24
time
36
(hours )
48
124


3 3
result in a different set of eigenvalues and eigenvectors. To restore
invariance, there is an additional approximation made. The remaining
two electrons integrals will not be dependent upon the nature of the
atomic orbitals, but on the atoms to which and ''k belong [11].
This can be shown as
(ii|kk) = Tab for all i on atom A and for all k on atom B.
TAB is the average electrostatic repulsion between any electron on
atom A and any on atom B [11], The value of TAB is given by
TAB = SS sa2(1) (1/ri2) sb2(2) dxidt2- (34)
As equation (34) shows all orbitals are taken to be of the "s" type.
The fourth approximation is to neglect differential overlap in the
interaction integrals involving the cores of other atoms where
(¡IVb|k) = Vab if i=k. If i*k the integral vanishes.
Vab is the interaction between any electron on atom A with the
core of atom B. Therefore, any differential overlap between two
atomic orbitals on atom A will be ignored in the calculation of this
interaction.
The last approximation made in CNDO is to allow off diagonal
matrix elements in the Hamiltonian to be proportional to the
overlap integrals. This is shown by
Hik = pABSik,
(35)


59
Variable Angle XPS (VAXPS1
In the introduction of this chapter the term take off angle is
mentioned. The take off angle is the angle between the electron
analyzer and the sample, which is commonly denoted by the Greek
letter 0. The angle 0 is varied in almost any quantitative analysis
undertaken, because its variation causes a variation in the effective
mean electron escape depth, which is more commonly referred to as
the probe depth. The mean electron escape depth is the average
distance a photoelectron will travel before it undergoes an inelastic
collision, a collision whereby it looses energy from the initial
energy acquired from the photoemission process. Unfortunately
inelastic collision is the fate that awaits most photoelectrons
which are generated. This is what severely limits the depth that one
can investigate in XPS.
Figure 4-1. Schematic showing the attenuation of the incident x-ray
radiation. The distance the photoelectron can travel
before it suffers inelastic collision is quite short
compared to the distance the x-ray can travel.


20
The more familiar form of the Schrodinger equation (7) is
H'f' = E^, (8)
where H is the Hamiltonian operator and E is the energy. Equation (8)
is an example of a class of equations called eigenvalue equations as
shown by
Opf-cf, (9)
where Op is an operator, f is a function called an eigenfunction and c
is a constant called an eigenvalue. Therefore ¥ is an eigenfunction.
In equation (7) V is the potential energy, and the second derivatives
of the wavefunction ¥ are related to the kinetic energy. This is so
because the second derivative of T* with respect to a given direction
of measure is the rate of change of slope (i.e. the curvature) of ¥ in
that direction. A wave function with more curvature will yield a
greater kinetic energy. This is in agreement with the de Broglie
relationship which states that a wave with a shorter wavelength
will have a greater kinetic energy. Since we have a constant E, the
wave must have more curvature in regions where the potential
energy is low and visa versa [8]. The wavefunctions which are
associated with a particle are related to its momentum by equation
(6). In addition, the wavefunctions are eigenfunctions of the
Schrodinger equation (8) and must meet the conditions which are
illustrated in Figure 2-2. Also, the absolute square of the
wavefunctions (i.e. I'FI2) is proportional to the probability density
for finding a particle. If H' is an eigenfunction of equation (8), then
k*F is also an eigenfunction, where k is a constant. Since k can be any


Figure 4-7. Peak fit of the 0-|S photoelectron peak of a sample of
carbon foil which was prepared by allowing MnC>2 to
deposit on it for 100 hours. The take off angle is 0
degrees.




130
be a broadening in that spectrum. The greater the number of
geometries present on the surface of the substrate, the greater the
number of molecular orbital energies (i.e. eigenvalues) which are
going to contribute to the XPS spectrum. The overall effect of
considering the interface between the substrate and the dispersed
material is that it demonstrates a limitation in the methodology
previously used to interprete XPS valence band broadening.
When the method of deposition of a transition metal oxide onto
the carbon substrate is varied there is a variation in the results of
the quantitative analysis and in the electronic structure of the
surface. When vapor deposition is used to disperse the oxide,
samples are obtained whose particles were confined to the surface
region. It is even possible to construct a continuous film of MnO on
the surface of the carbon substrate by this method. When solution
deposition is used to disperse the oxide, the samples obtained have
the majority of their dispersed particles incorporated below the
surface of the substrate. The electronic structure of the particles
dispersed by these two methods is determined by acquisition of data
in the valence band region. Particles deposited by the vapor
deposition method show a greater valence band narrowing and a
greater shift in binding energy away from the Fermi level relative to
their bulk oxide than do particles deposited by solution deposition.
Thus, vapor deposition seems to cause smaller particles to be
deposited on the surface than does solution deposition.
When the dispersed Mn oxide samples produced by both methods
are placed into a solution of potassium permanganate, they have an
effect on the autocatalytic decomposition of permanganate. It is


4 9
corrections to the original program, the values shown in Table 3-5
result. Increasing the bicenter matrix elements of a T-0 molecule
should have the effect of increasing the electron population in the
overlap between the oxygen and the d orbitals of the transition
element. This is substantiated by looking at the population matrix,
calculated from the equation
occ
Pjid = 2 Xc jj,¡ c\)j, (45)
i
where the c's are the coefficients of the atomic orbitals. This
matrix does indeed show an increased electron population in the
overlap between the oxygen and the d orbitals.
Table 3-5
Final values for the bond lengths, dissociation energies and
ionization potentials of selected diatomics after the atomic energy
and coulomb integral modifications were made to CNDO/2U.
AB
Bond
Length
(A)
Exp.
Ionization
Potential
(eV)
Exp.
Dissociation
Energy
(eV)
Exp.
FeO
1.40
1.57b
-11.69
-8.71 a
-6.77
-4.20
FeS
1.90
-5.02
-0.50
-3.70
Mn2
2.80
3.4
-7.08
-6.9C
1.00
-0.23
MnO
1.45
1.77b
-8.06
-5.68
-3.70
Fe2
3.00
-16.09
-6.30e
-4.52
-1.06
MnS
1.80
-11.53
-10.16
-2.85
a) Ref [33] b) Ref [31] C) Ref [34] d) Ref [35] e) Ref [32]


Figure 3-4.
Valence band density of states of a calculated (MnO)2
composite compared to spectrum of a continuous film
of MnO.


Figure 4-6.
Mn2p photoelectron peaks of a sample of carbon foil
which was allowed to have Mn02 deposit on it for 100
hours. These peaks were acquired at a take off angle of
35 degrees.


107
The rate expression for equation (53) is
d[HI]/dt = k[H2][l2], (54)
where k is the reaction constant. It is not possible to derive the rate
expression from the stoichiometric equation and therefore it must
be determined as the result of experimentation. The order of a
reaction is determined by summing the values of the exponents of
the concentrations of the rate expression. The rate expression for
the formation of HI is given by
d[HI]/dt = k[H2]1[l2]1-
The order of the reaction overall is simply the sum of all exponents
of the concentrations. Each individual exponent is called the order
with respect to that component. The above reaction is then first
order with respect to hydrogen and first order with respect to iodine
and second order overall. The rate constant k has dimensions of
[conc.]1*n [time]'1 .
Commonly used units for the rate constant are moles/liter,
moles/cc, molecules/cc, or pressure in mm Hg or in atmospheres.
The preferred unit for time is seconds.
Since it is not possible to determine the rate expression from the
stoichiometric equation, it is necessary to fit experimental data to
a rate equation. The data is acquired by recording the decrease in
concentration of a reactant over time. From the data, a curve is
plotted of concentration vs. time. The rate of the reaction at any


3
da(e)/dft= oj(e)/4 [1 + BP2(cos(0)]. (3)
It is seen that the intensity is a function of the total cross section
for photoionization, which is the probability of observing an
electron of a given energy for ionization, and the angle 0 between
the incident photon beam and the direction of ejection of the
photoelectron. The 3 term is known as the asymmetry parameter
and is a term which is characteristic of a given molecular orbital.
The value of I3 indicates what the preferred direction of the
photoelectrons will be with respect to the incident photon beam. If
3=+2 as is the case for a spherically symmetric distribution of
charge (an atomic s orbital), then the phbtoelectrons will be
preferentially ejected at angles of 90 to the photon beam [1]. For
orbitals having angular momentum (i.e. p, d or f), 3 values will be
less than +2, which will cause the photoelectron to be preferentially
ejected at different angles. If the intensity is plotted against 0 for
many different values of 3 it is found that there is a "magic angle"
of 54.7 where the intensity is independent of 0. When
spectrometers are operated at this magic angle, total cross sections
can be used directly in quantitative analysis.
Instrumentation
General Principles
An X-ray photoelectron spectrometer is composed of a x-ray
source, a sample analysis chamber (SAC), an electron or energy
analyzer, and a detector system, which is usually interfaced with a
computer. X-rays are generated by bombarding a material (target)


29
The two electron part of equation (22) is H2 = 22 rpq-1. (25)
p Equation (13a) is given by
E = c''l H \x¥>,
where E = c'i'l H-j |VF> + . (26)
The wavefunction ¥ must be written as a Slater determinant so that
electron exchange can be incorporated into it. Allowing a
permutation operator P to act on the wavefunction is the equivalent
to writing the wavefunction as a Slater determinant. The
expectation value of the one electron operator is
Hj, = / 'Fj(l) Hcore ^¡(1) dxl. (27)
The two electron Hamiltonian is a function of the two electron
operator 1/rpg (equation 25). This operator gives the electrostatic
coulomb repulsion energy between two charge clouds [8]. A matrix
element of this electrostatic coulomb repulsion is defined as
Jij = JJ xFi*(1)xFj*(2) (1/rpq) ^k(1)^l(2) dxidx2- (28)
The value of this integral represents the repulsion between electron
(1) on orbitals 'Fj and 4^ and electron (2) on orbital 4^ and 4/|. Since
the charge clouds are everywhere negative, their product causes J to
be everywhere positive. The entire matrix would represent the
electrostatic repulsions between all orbitals in the molecule
including differential overlap where 4'j*(1)4'k(1)- Another integral