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+\documentclass[./manual.tex]{subfiles}
+\begin{document}
+
+\chapter{Superconductivity}
+\setcounter{figure}{1}
+\setcounter{table}{1}
+\setcounter{equation}{1}
+
+ \textbf{Experiment objectives}: study behavior of a high temperature superconducting material
+    Yttrium-Barium-Copper-Oxide (YBCO, $YBa_2Cu_3O_7$) in magnetic field, measure the critical
+ temperature for a phase transition in a superconductor.
+
+\subsection*{History}
+
+Solids can be roughly divided into four classes, according to the way they
+conduct electricity. They are: Metals, Semiconductors, Insulators and
+Superconductors. The behavior of these types of materials is explained by
+quantum mechanics. Basically, when atoms form a solid, the atomic levels of the
+electrons combine to form bands. That is over a finite range of energy there
+are states available to electrons. Since only one electron can occupy a given
+state, the {\bf Pauli Exclusion Principle}, electrons will fill these states up
+to some maximum, the Fermi Energy: $E_f$.  A solid is a metal if it has an
+energy band which is not full; the electrons are then free to move about,
+making a metal a good conductor of electricity. If the solid has a band which
+is completely full, with an energy gap to the next band,  that solid will not
+conduct electricity very well, making it an insulator. A semiconductor is
+between a metal and insulator: while it has a full band (the valence band),
+the next band (the conduction band) is close enough in energy and so that the
+electrons can easily reach it. Superconductors are in a class by themselves.
+They can be metals or insulators at room temperature. Below a certain
+temperature, called the critical temperature, the electrons "pair" together (in
+Cooper pairs) and travel through the solid without resistance. Current in a
+superconductor below the critical temperature will travel indefinitely without
+dissipation.
+
+ Superconductivity was discovered in 1911 by  H. Onnes. He
+    discovered that simple metals (Pb, Nb) superconduct when
+    placed in liquid helium (4 K). This was an important
+    discovery, but the real excitement came in 1986 when Swiss
+    scientists discovered that certain ceramics would superconduct
+    at 35 K. Several groups later discovered materials that would
+    superconduct at temperatures up to 125 K. These materials are
+    called high temperature superconductors (HTS). Their discovery
+    was a breakthrough, because this means that these
+    superconductors will work in liquid nitrogen (at 77 K), which
+    is relatively cheap and abundant.
+
+    Some fascinating facts about superconductors: they will carry
+    a current nearly indefinitely, without
+    resistance. Superconductors have a critical temperature, above which they lose their
+    superconducting properties.
+
+    Another striking demonstrations of superconductivity is the \textbf{Meissner effect}.
+    Magnetic fields cannot penetrate superconducting surface, instead a
+    superconductor attempts to expel all magnetic field
+    lines. It is fairly simple to intuitively understand the Meissner effect, if you imagine a perfect
+    conductor of electricity. If placed in a magnetic field,
+    Faraday's Law says an induced current which opposes the field
+    would be setup. But unlike in an ordinary metal, this induced current does not dissipate in
+    a perfect conductor. So, this
+    induced current would always be present to produce a field
+    which opposes the external field. In addition, microscopic dipole moments
+    are induced in the superconductor that oppose the applied field. This induced field
+repels the source of the applied magnetic field, and will consequently repel
+the magnet associated with this field.  Thus, a superconductor will levitate a
+magnet placed upon it (this is known as magnetic levitation).
+
+\subsection*{Safety}
+\begin{itemize}
+\item Wear glasses when pouring liquid nitrogen. Do not get it on your
+skin or in your eyes!
+\item Do not touch anything that has been immersed in liquid nitrogen until the
+item warms up to the room temperature. Use the provided tweezers to remove and
+place items in the liquid nitrogen.
+\item Do not touch the superconductor, it contains poisonous materials!.
+\item Beware of the current leads, they are carrying a lethal current!
+\end{itemize}
+
+
+\section*{Experimental procedure}
+\textbf{Equipment needed}: YBCO disc, tweezers, styrofoam dish, small magnet.
+
+
+
+\subsection*{Magnetic Levitation (the Meissner effect)}
+
+\begin{enumerate}
+
+\item Place one of the small magnets (provided) on top of the superconducting
+disc at room temperature. Record the behavior of the magnet.
+
+\item  Using the tweezers, place the superconducting disk in the styrofoam
+   dish. Attach  the thermocouple leads (see diagram) to a multimeter
+   reading on the mV scale. Slowly pour liquid nitrogen over the disk,
+   filling the dish as much as you can. The nitrogen will boil, and
+   then settle down. When the multimeter reads about 6.4 mV, you are
+   at liquid nitrogen temperature (77 K).
+
+
+\item After the disc is completely covered by the liquid nitrogen, use the tweezers
+to pick up the provided magnet and attempt to balance it on top of the
+superconductor disk. Record what you observe.
+
+\item Try demonstrating a \emph{frictionless magnetic bearing}: if you carefully set the magnet rotating,
+you will observe that the magnet continues to rotate for a long time. Also, try
+moving the magnet across the superconductor. Do you feel any resistance? If you
+   feel resistance, why is this.
+
+\item Using tweezers, take the disk (with the magnet on it) out of the
+   nitrogen (just place it on side of disk), allowing it to
+   warm. Watch the thermocouple reading carefully, and take a reading
+   when the magnet fails to levitate any longer. This is a rough estimate of the
+   critical temperature. Make sure you record it!
+
+\item Repeat the experiment by starting with the magnet on top of the
+superconductor disc and observe if the magnet starts levitating when the disk's
+temperature falls below critical.
+
+\end{enumerate}
+\begin{figure}
+\includegraphics[height=2in]{./pdf_figs/scnut}
+\caption{\label{scnut} The superconducting disk with leads.}
+\end{figure}
+
+
+\subsection*{Measuring resistance and critical temperature}
+
+    We will measure the resistance by a {\bf four probe method}, as a
+    function of temperature. Using four probes (two for current
+    and two for voltage) eliminates the contribution of resistance
+    due to the contacts, and is good to use for samples with small
+    resistances. Connect a voltmeter (with 0.01 mV resolution) to
+    the yellow wires. Connect a current source through an ammeter
+    to the {\bf black} wires. Place a current of about 0.2 Amps (200 mA)
+    through black leads. Note: {\bf DO NOT EXCEED 0.5 AMP!!!!}
+    %On the
+%    Elinco power supplies, you hardly have to turn the knobs at
+%    all!
+At room temperature, you should be reading a non-zero
+    voltage reading.
+
+\begin{enumerate}
+ \item With the voltage, current and thermocouple leads attached,
+    carefully place disk in dish. Pour liquid nitrogen into the
+    dish. Wait until temperature reaches 77 K.
+\item With tweezers,  take disk out of nitrogen and place on a side of the
+   dish. {\bf Start quickly recording the current, voltage and thermocouple readings
+   as the disk warms up.} When superconducting, the disk should have
+   V=0 (R=0). At a critical temperature, you will see a voltage
+   (resistance) appear.
+
+\item Repeat this measurement several time to acquire significant number of data points
+near the critical temperature (6.4-4.5 mV). Make a plot of
+   resistance versus temperature, and make an estimate of the critical
+   temperature based on this plot.
+
+\end{enumerate}
+
+\section*{Resistance of a ceramic resistor}
+\begin{enumerate}
+\item Attach a ceramic resistor to a multimeter reading resistance ($k\Omega$ range). Record the room temperature resistance.
+
+\item Dunk the resistor in liquid nitrogen. Wait until it stops boiling. Record the resistance at this low temperature ($\approx$77 K).
+
+\item Take the resistor out of the nitrogen and carefully set it down. Record the resistance as the temperature increases. Make a plot of the measured resustance vs temperature. Compare the plots for the superconductor and the normal resistor, and explain the differences.
+\end{enumerate}
+
+\hskip-.8in\includegraphics[height=5in]{./pdf_figs/mvtok}
+
+
+%\begin{tabular}{|p{17mm}|p{17mm}|p{17mm}|p{35mm}|p{35mm}|}\hline
+% V (mV)& I (mA)& R ($\Omega$)& Thermocouple (mV)& Temperature (K)\\
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%&&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline &&&&\\\hline
+%\end{tabular}
+
+\end{document}
+