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diff --git a/chapters/supcon.tex b/chapters/supcon.tex new file mode 100644 index 0000000..c74b856 --- /dev/null +++ b/chapters/supcon.tex @@ -0,0 +1,193 @@ +%\chapter*{Properties of Solids: Superconductivity} \author{} \date{} +%\addcontentsline{toc}{chapter}{Superconductivity} + +%\documentclass{article} +%\usepackage{tabularx,amsmath,boxedminipage,epsfig} +% \oddsidemargin 0.0in +% \evensidemargin 0.0in +% \textwidth 6.5in +% \headheight 0.0in +% \topmargin 0.0in +% \textheight=9.0in + + +\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$77 K). + +\item Take the resistor out of the nitrogen and carefully set it down. Record the resistance as the temperature increases. Make a plot of the measured resustance vs temperature. Compare the plots for the superconductor and the normal resistor, and explain the differences. +\end{enumerate} + +\hskip-.8in\includegraphics[height=5in]{./pdf_figs/mvtok} +%\end{document} + + +%\begin{tabular}{|p{17mm}|p{17mm}|p{17mm}|p{35mm}|p{35mm}|}\hline +% V (mV)& I (mA)& R ($\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} + +\newpage |