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\begin{document}

\begin{center}

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{\Large\bf Optically-Stimulated Luminescence\\[5pt]
           in \alo }\\[1.0in]

{\large Physics Individual Project \\[2pt]
        Siemens-Westinghouse Competition \\[2pt]
        October 2002} \\[1.0in]

{\large\sc Evan Marshak} \\[1.0in]


{       Herricks High School \\
        New Hyde Park, New York } \\[10pt]

{\em and}\\[10pt]

{       Laser Teaching Center \\
        State University of New York at Stony Brook}\\

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\thispagestyle{empty}
\newpage

\begin{titlepage}
{\begin{center} \Large Optically-Stimulated Luminescence in {\alo} \end{center}}

\subsection*{Abstract}
Optically-stimulated luminescence (OSL) is the phenomenon of inducing luminescence in
a material by emitting optical light at the material.
OSL has come to be a new, effective
tool for radiation dosimetry; however, there are still uncertainties
in the relationship between absorbed dose and output luminescence.
The material must first be irradiated x-rays,
$\gamma$-rays, or $\beta$-rays.  The OSL output, then assumed
to be proportional to the absorbed dose, is then measured.  This study is to test the
possible effects of dose-rate on OSL output.  While there appears
to be such a relationship, no quantitative function relating the
two could be found from this study.
\subsection*{Research Topic Selection}
This summer, I studied in an optics laboratory.  I began the summer
by reading various articles and books on optics.  I ran across an
entry in one of the textbooks saying that it is possible for the index of
refraction to be less than 1 if the absorption frequency of the
material is near the frequency of the light.  This would make the
group velocity of the light exceed $c$.  In searching for materials
with appropriate frequencies, I found an entry about F-bands in
a textbook.  F-bands, as it was explained, are optical absorption
bands in certain alkali halides due to crystal defects called F-centers.  As I
read further into the matter, I found that many of these materials
were being tested as possibilities for radiation dosimetry.  Upon
contacting someone affiliated with a company that makes radiation
dosimeters, he told us about a crystal that had just recently
emerged in the industry that was starting, already, to be widely
used.  I then began to study the properties of the crystal and
found a paper regarding the actual significance of the OSL
output.

\end{titlepage}
{\begin{center} \Large Optically-Stimulated Luminescence in {\alo} \end{center}}

\section{Purpose}
The study of F-centers is just beginning its ``coming of age'' in
the scientific community.  Not until 1960 was the first definitive
paper on the matter published \cite{rabinklick}.  In its earliest
days, the study involved only the use of alkali halide ionic compounds.
It was discovered that NaCl (as well as various other such ionic
compounds) will release different colors of light after proper stimulation.
This emission is caused by single electrons taking the place of anions
in the lattice.  These positions in the lattice are known as ``F-centers,''
from the German word for color, ``fabre."

Initially, F-centers were created by heating the alkali halides.  The crystals
would be heated in the vapor of the alkali metal \cite{aip}.  The obvious
problem with this method is the very high reactivity of alkali metals.  Gradually,
other ways of creating the defects were found.  They may also be created by
a magnetic field, an electric field, or high-energy radiation.  Additionally, it
was found that the doping of crystals would form the same type of defects.  
Luminescence would then be induced by optical light, assuming proper high-energy
irradiation ($\beta$, $\gamma$, or x-ray) \cite{defects}.

During the 20th century, it became apparent that working around radioactive
materials was hazardous.  As a result, it became the quest of a portion of the
scientific community to find a way to measure the radiation to which one is
exposed.  This has come to be known as the study of radiation dosimetry.  The
usefulness of F-centers in this endeavor seems apparent.  F-centers respond
to the same type of hazardous irradiation from which people need to be protected.  They
can, therefore, wear badges containing these materials which will then respond
to the irradiation and be ready for optical stimulation.

\section{Rationale}

As a result, it has become necessary to study the response of these materials
to such irradiation.  Several different methods of testing these have been
proposed.  First, and more commonly used, is thermoluminescence (TL).  The idea
behind TL is that the crystals are kept at a low temperature and then heated
to release the stored energy.  Often, the crystals are heated to create the
F-centers.  For TL, the crystal will then be quickly cooled, locking the defects into
the lattice.  Generally, gradual cooling anneals the crystals.
The lattice is then stimulated by heating.  (This heating is similar to annealing
in that the F-centers are lost, but the crystals need energetic stimulation.)  
At the same time, the
optical output is observed.  Typically, TL is used at liquid nitrogen or liquid
helium temperatures \cite{oster}.  A less studied form of such luminescence is
optically-stimulated luminescence (OSL).  With OSL, optical light of a specific
frequency is emitted into the crystal.  As the light dislocates the F-centers,
they emit light of a band that is, generally, close to that of a corresponding
TL band \cite{kristianpoller}.

\section{Literature Review}

The study of F-centers is marked by nebulous information.  Most notably, the
mechanism for annealing is not understood.  All that is known is that, in the
simplest case, the anions fall out of the lattice, and an electron remains in
its place.  It is not, however, known what happens to the anion.  Evidence
suggests that it does not simply leave the lattice as a neutral species.  If
it did, the result would be the release of chlorine gas from NaCl when exposed
to any sort of radiation, including background radiation.  In fact, KCl is
naturally radioactive (as potassium has several radioactive isotopes) and does
not, it seems, release chlorine gas constantly.

\begin{figure}[h]
\begin{center}
\epsfig{file=nacl.ps, width=1.712in}
\caption{Pure sample of NaCl.}
\vspace{-.25in}
\end{center}
\end{figure}

\begin{figure}[h]
\begin{center}
\epsfig{file=naclcenter.ps, width=1.712in}
\caption{NaCl with F-center.}
\vspace{-.25in}
\end{center}
\end{figure}

Generally, the vibrations of the electron can be described by a
``particle-in-a-box'' solution to the Schr\"{o}edinger wave equation.
This will yield the released photon, etc. for the electronic actions.
This is the best theoretical tool for describing the F-centers.

For this study two Al$_{2}$O$_{3}$:C crystals were provided.
Unlike in the simpler case in alkali halides, Al$_{2}$O$_{3}$:C does not acquire
defects as a result of irradiation.  The carbon-doping serves to create the
defects in the crystals.  The irradiation, then, acts to charge the holes 
\cite{kristianpoller}. (Again, the exact mechanism for this is still unknown.)
The case of Al$_{2}$O$_{3}$:C is, however, not that simple either.  Because
the oxide has two oxidation states, the holes can have an effective charge
of 0 or +1.  These correspond, respectively, to F-centers and F$^{+}$-centers.
F-centers are oxide vacancies replaced by two electrons; F$^{+}$-centers are
oxide vacancies replaced by single electrons.  These { \it appear } to be
analogous to F-centers in alkali halides.  There is much empirical idea to
support this data; however, there is no definitive proof that they are
actually the same phenomena \cite{lee}.  For the sake of calculations and some sort
of theoretical explanation, these will be treated in a manner analogous to
F-centers in alkali halides.

F-centers and F$^{+}$-centers, then have their own corresponding emission and
absorption spectra for OSL.  For TL, they have different input temperatures
and different emission spectra.  The spectra of TL and OSL are, however, close,
but clearly not the same.  With optical stimulation, the crystals respond to
stimulation at about 200 nm and 530 nm with an emission at about 410 nm and stimulation
at 230 nm or 260 nm with an emission at about 330 nm.  The former is ascribed to
F-centers; the latter, F$^{+}$-centers.  Similarly, with TL, at temperatures of
260, 280, and 450 K, the crystals respond with emissions at 410 nm and 330 nm.
(With TL, there are several other weaker and more complex bands, including one
around 310 nm which does not appear in OSL.)  All of these
seem to be the result of F- and F$^{+}$-centers \cite{kristianpoller}.

Early studies of F-centers led to the development of Smakula's formula.  Smakula's
formula relates several variables of the structure of the crystals:
{\begin{center} $N = 6 \times 10^{15} f^{-1}W\alpha $\end{center}}
\noindent where $N$ is the concentration of F-centers (m$^{-3}$), $f$ is the oscillator 
strength (determined
experimentally), $W$ is the half-width, and $\alpha$ is the optical-absorption
coefficient (m$^{-1}$) \cite{tardio}.  The half-width, $W$, is determined by:
{\begin{center} $W=W_{0}\sqrt{\coth\left(\frac{\hbar\omega}{2kT}\right)}$\end{center}}
\noindent where $T$ is the temperature and W$_{0}$ is the half-width at 0 K.  The frequency,
$\omega$ is associated with the vibrations of the lattice \cite{aip}.  It is
commonly given as $\nu$ so, obviously, $h\nu$ may be substituted for $\hbar\omega$.

Previous research suggests the following values for the properties of {\alo} \cite{lee}: 
{\begin{center} $W=.3 eV$; $f=.8$ \end{center}}
\noindent Additionally, $\alpha$ is defined by $I=I_0 \alpha l$.  Using this, it may be possible
to find $\alpha$ empirically.

\section{Applications}

One interesting application for this phenomenon, aside from radiation dosimetry,
is dating.  Because certain materials respond to optical stimulation, the length
of time during which rocks and minerals have been covered can be determined.
For pottery, the crystals would have been annealed when fired; they can then
be read by TL or OSL.  Generally, a linear relationship between age and absorbed
dose is assumed.  (Absorbed dose is a measurement of radiation energy per unit
mass \cite{dating}.  Its SI (m-k-s) unit is the Gray (Gy) which is equal to 1 J/kg.

The most recent research in the area has concentrated on radiation dosimetry.  The
idea is that those who work around hazardous radiation wear badges containing a
material that is responsive to the appropriate type of radiation.  The badges are
then sent away and read-out (usually by TL).  According to {\it Landauer}, their crystals
may be used for a year without degradation, assuming the appropriate packaging is
used and maintained \cite{landauer}.  One of the interesting questions that has
arisen from this study deals with the interpretation of the output.  The question
is:  What factors specifically affect the luminescent output?  Recently,
Reuven Chen has been studying the effects of dose-rate dependence on OSL with
alkali halides and alkali oxides \cite{chen}.

\subsection{Interpretation}

Chen's findings suggest that there should be a super-linear relationship between
dose and luminescent output.  His mathematical model yields a power-law
relationship between OSL output intensity and input dose.  It also implies
a relationship between dose-rate and output intensity.  This is not a result
hat may have been expected.  It seems that for equal doses, equal outputs
should be observed.  Chen admits that his model makes many simplifications,
but it still may hold that OSL luminescence is dependent on dose-rate.  It
should also be noted that Chen makes an important distinction.  When he
discusses the intensity of OSL, he is talking about the integral of the
intensity curve; so he is actually speaking of total output, not initial
output \cite{chen}.

This experiment was performed to test some of Chen's results.  The dose-rate
dependence was studied.  Additionally, the decay of the F-centers was
studied.

\section{Apparatus, Materials and Methods}
\subsection{Materials}
There were two {\it Landauer, Inc.} {\alo} crystals.  Each was a 2.5mm disc.  They are generally
used as industrial radiation dosimeters.  The discs were .5 mm in width.

The crystals were irradiated with x-rays from a copper anode.  The input
and output current and voltage could be adjusted; however, the efficiency
of the x-ray transitions is unknown.  The crystal was irradiated in a strip.
The x-rays pass through the slit, collimated,
and then hit the sample.

\begin{figure}[h]
\begin{center}
\epsfig{file=xray.ps} \epsfig{file=labsetup.ps, width=1.68in}
\caption{X-ray machine set-up and OSL setup.}
\vspace{-.25in}
\end{center}
\end{figure}

This effectively creates F-centers in the crystal.  The output current
was varied between 60$\mu$A and 100$\mu$A (the machine maximum) and the voltage held at a
constant 25.0kV.

A Nd:YAG laser pointer was mounted above the sample, filter, and PMT.  This allowed
stimulation to be direct and easily observed.  The
Nd:YAG laser pointer is actually a pulsed laser.  It is frequency-doubled
from a wavelength of 1064 nm to 532 nm.  The pulse-frequency is approximately
7.1kHz.

The sample is placed on the filter,
and the laser is then shone on the sample and a potential difference is created
across the photo-multiplier tube (PMT) because of the light.  This is then
read by a voltmeter.

\subsection{Filter}
The problem with direct transmission of the light from the sample to
the detector is that the green light would also be detected.  The blue
light is several orders of magnitude less intense than the green light
from the laser.

For this reason, a blue filter was used.  The Kopp 5-58 filter (glass
number 5113) was used.  It is about 4.0mm thick.  Its maximum
transmittance is at approximately 410nm and steeply drops off up to
500nm.  This allowed the detector to accurately measure the luminescent
light, not just the laser light (though, the laser light still needed
to be considered in the calculations.)

\begin{figure}[h]
\begin{center}
\epsfig{file=filter.ps, width=6.00in}
\caption{Filter 5-58 was used \cite{kopp}.}
\vspace{-.25in}
\end{center}
\end{figure}

\subsection{Photodetector}
The photodiode was used to detect incoming light.  It operates on the
photovoltaic effect (a variation of the photoelectric effect).  The
incoming light induces a photocurrent which is then read either on
an oscilloscope or on an ammeter.  The sensitivity of the device can
easily be changed by placing a resistor in parallel in the circuit.

\begin{figure}[h]
\begin{center}
\epsfig{file=circuit.ps, width=3.287in}
\caption{Photodiode set-up.}
\vspace{-.25in}
\end{center}
\end{figure}

Initially, POSL (pulsed optically-stimulated luminescence) was attempted;
however, the required sensitivity could not be accomplished for several
reasons.  First, the required increase in resistance would make the most
eminent data from the oscilloscope be the fluctuations of the RC circuit.
The RC circuit would charge by:
$\varepsilon = \varepsilon_{0}(1 - e^{-t/RC})$
and after exceeding a threshold voltage, discharge, governed by:
$\varepsilon = \varepsilon_{0}e^{-t/RC}$.
The resulting wave-like figure would show itself on the oscilloscope.  The
other problem with the photodetector is that it is far more sensitive to
the 532 nm light than the 410 nm light.  Therefore, much of the light that
it detects, even after the filter, is green.  For this reason, the
photodiode was only used to study the laser.

\subsection{Photomultiplier Tube}
The photomultiplier tube (PMT) operates on the photoelectric effect and is
used to detect light in a similar manner to the photodiode.  The light
creates a potential difference that can be measured by a voltmeter.  The
major advantage to using the PMT is that its responsivity to 410 nm light
is far higher than that of 532 nm light.  The opposite is the case with
the photodiode.  The PMT has a variable input power supply as well; a
potentiometer is used to change the input voltage.

\subsection{Overview of Methods}
The {\alo} was first irradiated in the x-ray machine.  It was irradiated
at 100$\mu$A for 1 hour.  The crystal was then placed in an apparatus
where it would be read by the photodiode in a set-up the same as that of the PMT.
Because of the shortcomings
of the photodetector, the readings were inconclusive.  The \alo was then
irradiated again for 1 hour at 100$\mu$A.  During this time period, the
sample was exposed to light, so annealing did take place.  However, it
was demonstrated that the PMT was a valuable and effective measuring
device.  At this point, the initial OSL luminescence was tested with
both crystals (one that had not been irradiated and one that had), and
a standard attenuation fraction for the crystals was determined.  Also,
the responsivity of the PMT was tested with filtered laser light.
The input voltage was varied
and the output voltage was recorded.

After each trial, the crystals were annealed with a 150 W incandescent
light-bulb.  This was done for 10 minutes.  After the 10 minutes, no
observable difference was created when the crystals were further irradiated
by the incandescent light.

Next, one of the crystals was irradiated with x-rays at 80$\mu$A, and
the decay of the F-centers was observed.  It was placed in the apparatus
and observed at 60 second intervals for 28 minutes.
The crystals were then continually reirradiated with the x-rays, first
at 60$\mu$A, then at 80$\mu$A, and then at 100$\mu$A.  This effectively
varies the dose-rate, but the time was adjusted so that the dose was the
same.   The initial OSL
output was recorded in each situation.  Each irradiation was done so that
the total output of the x-ray machine was 1000 J.

\section{Results}
\subsection{PMT Responsivity}

The first stage of the study was determining the ideal input voltage
for the PMT so as to yield sufficient output results.  The results show
\begin{figure}[h]
\begin{center}
\epsfig{file=inoutlogy.ps}
\caption{The input-output relationship is clearly exponential.}
\vspace{-.25in}
\end{center}
\end{figure}
an exponential  relationship between input voltage and output voltage.
They also show that the ``unirradiated'' crystal had absorbed background
radiation throughout its lifetime.

\subsection{Optical Properties of the Crystals}
It was determined through the experiment that an attenuation
coefficient of approximately 1/2.7 is associated with the crystals
as they act as optical devices.  This means that the background from
the laser and other sources must be measured, and then divided by 2.7
and subtracted from all other data to obtain the appropriate results.
This is akin to ``taring'' a scale.  The background radiation must
be subtracted from the relevant radiation.

With an input of 550mV, the background ``noise'' is approximately
60.mV.  This is divided by 2.7 to yield 22mV for background.  This
factor of 1/2.7 for attenuation corresponds to a proportional intensity.
It is, therefore, possible to find the attenuation coefficient now.
Solving, it is found that $\alpha=1/13.5 mm^{-1}$.

\newpage

\subsection{Annealing}
The next phase of research was to study the annealing of the crystals.
\begin{figure}[h]
\begin{center}
\epsfig{file=lineline.ps}
\caption{Annealing of F-centers.}
\vspace{-.25in}
\end{center}
\end{figure}
The curve shows a nearly logarithmic decay curve; however, it is not
precisely logarithmic. (See also Figure 8.)

\begin{figure}[h]
\begin{center}
\epsfig{file=logline.ps}
\caption{The curve is nearly logarithmic.}
\vspace{-.25in}
\end{center}
\end{figure}

\subsection{Dose-Rate Dependence}
Finally, the effect of varying dose-rate was studied.  The results
are somewhat inconclusive.  It seems that after such a large amount
of irradiation, the crystals were no longer able to absorb more.
The trials seem to indicate that there is some sort of correlation
between dose-rate and initial luminous intensity.
The results are
not, however, conclusive.

All crystals were irradiated with 1000J of output from the filament;
this does not correspond to 1000J of x-ray radiation.  The efficiency
of the x-ray machine is not known.

\section{Discussion}
\subsection{Annealing}
The data suggest that the annealing of F-centers is logarithmic with
respect to time.  This implies a relationship such that:\\
{\begin{center} $I = C - k \ log \ t$ \end{center}} 
\noindent where $I$ is the initial intensity, $k$ is an arbitrary constant
(with a negative sign because the function is decreasing), C is the initial intensity and
$t$ is time.  This, further, implies a differential equation
in the form:\\
{\begin{center}$dI = {\frac{-k dt}{t}}$\\
or\\
${\frac{dI}{dt}}=-{\frac{k}{t}}$\end{center}}.\\
\noindent
Therefore, the rate of annealing of F-centers (if assumed to be directly
proportional to intensity) decreases with time.  One possible physical
explanation of this phenomenon is that the F-centers are more sparse and,
therefore, the light hits them less often.

By symmetry, it might be assumed that F-centers are more efficiently created
during the beginning of the irradiation process.  By the same argument,
there should be more anion-deficient holes in the lattice which can be
charged.  (This is {\it not} dose-rate dependence because an inverse relationship
between time and dose-rate may be assumed for this stimulation.)
\subsection{Concentration}
Using the above data, it is now possible to find the concentration of F-centers
at the maximum value.  Using Smakula's formula, $N = 2*10^{17} m^{-3}$.
\subsection{Dose-Rate Dependence}
The dose-rate dependence experiment yielded mixed results.  The first 5
sets of trials support the idea that OSL output is proportional to
dose-rate in some way.  The last 2 trials, however, suggest otherwise.
They show a result that was completely unpredicted.  It is entirely possible,
however, that these results are simply the result of the crystal losing
its ability to retain F-centers. 

\begin{figure}[h]
\begin{center}
\epsfig{file=doserate.ps}
\caption{Dose-rate dependency of OSL.}
\vspace{-.25in}
\end{center}
\end{figure}

The mechanism for the deterioration of {\alo} crystals is also unknown.
The sharp drop-off in OSL output suggests some that there is some
exotic phenomenon governing the deterioration of the crystals.

Perhaps, for example, the crystal constantly loses its F-centers as
it is annealed.  Rather than simply losing the electrons in the anion-deficient
holes, the anion deficiencies are filled by oxide ions.  This could
simply be the result of exposure to air.  The oxygen would not,
however, do this when the electrons are in the vacancies.  The crystal
would, therefore, have to be exposed to the air while being annealed
in order for this to occur or have to be in the open air when annealed. 

The crystals were annealed on a nightly-basis while doing the project.
The crystals were annealed after each trial, including the last.  That
means that it was sitting, exposed to the air, overnight without a
significant source of radiation.  The first 5 trials and the last 2
trials are, in fact, separated by one night.  This could explain the
drastic drop in the output from the last two trials.

\section{Conclusion and Future Plans}
This study suggests that dose-rate may be closely linked to OSL output.
The data to show this, however, are not consistent enough that a solid
conclusion could be drawn from it.  In the research, however, there
seems to be a possible explanation for the deterioration of the crystals
and why they do not have a very long lifetime.

Conclusively, it seems that the decay curve of the F-centers (due to
annealing) is nearly logarithmic.  This suggests some possible
physical explanations for the annealing of F-centers.  It seems likely
that annealing slows down in an inverse proportion to time as a result
of the F-centers being more sparsely located throughout the crystal.

The obvious future of this experiment is to study a wider range of
crystals.  Additionally, the x-ray irradiation rates should be varied
further with these new crystals.  The filament current should then
be, in some way, compared to the absorbed dose on the crystal so that
the radiation dosimetry analog becomes clearer.

The crystals should also be placed in different conditions and tested
to see how quickly they deteriorate.  For example, one might trying
putting them in an oxygen-deficient environment so that the oxide ions
cannot refill the lattice (though it is possible that some other
similar element will take its place).

\newpage
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of F Centers at Low and Room Temperatures.'' {\it Physical Review A}, 1960.
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\bibitem{oster}Oster, L, D Weiss, and N Kristianpoller. ``A study of photostimulated
thermoluminescence in C-Doped ${\alpha}$-Al$_{2}$O$_{3}$ crystals''.
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\bibitem{kristianpoller}Kristianpoller, A. Rehavi, et al.. ``Radiation Effects in
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\bibitem{lee}Lee, K.H. and J.H. Crawford, Jr.. ``Electron Centers in Single-Crystal
Al$_{2}$O$_{3}$''. { \it Physical Review B}15, 1977: 4065.
\bibitem{dating}The Basic Principle of Luminescence Dating.\\{\tt
http://www.ph.ed.ac.uk/courseinfo/postgrad/html/node70.html}
\bibitem{tardio}Tardio, M. M, et al.. ``p-type Semiconducting Properties in
Lithium-Doped MgO Single Crystals''. arXiv:cond-mat/0201502 v1, 28 Jan 2002.\\
{\tt http://arxiv.org/pdf/cond-mat/0201502 }
\bibitem{landauer}Landauer Inc.. ``Luxel''.\\{\tt
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\bibitem{chen}Chen, R. and P.L. Leun. ``Nonlinear dose dependence and dose-rate
dependence of optically stimulated luminescence and thermoluminescence''. {\it
Radiation Measurements} 33, 2001.
\bibitem{kopp}Bes Optics, Inc.. "Kopp Blue Filters".\\{\tt
http://www.besoptics.com/html/body\_kopp\_blue\_filters.html}
\end{thebibliography}
\end{document}