# Physics 451: Fall 2000

Nuclear Magnetic Resonance
Superconductivity I -- electrical and magnetic properties of superconductors
Superconductivity II -- tunnel functions & Mr. SQUID
Superfluidity
X-ray Diffraction

### Nuclear Magnetic Resonance

In general "resonance" in a physical system involves the absorption of energy from an external source at a "natural" frequency of the system. In an NMR experiment the resonant frequency is determined by the energy states of the magnetic moment of the nucleus in an applied magnetic field and the energy is absorbed from an electromagnetic wave.  By sending pulses of radio frequency electromagnetic radiation into your sample, you can get the nuclear spins to play some very interesting tricks.

In addition to the physics of the phenomema, you will learn something about tuned LC circuits and impedance matching, about how to produce an inhomogeneous magnetic field and to measure it. Having picked up a black box for measuring magnetic fields, you may well decide that you should find out how it works and do a "mini-experiment" on how magnetic fields are measured. In the end you may relate what you have learned to Magnetic Resonance Imaging (MRI) which is used universally as a medical diagnostic tool.

### Superconductivity I

When someone says "superconductor" the first thing you think of is a substance with zero electrical resistance.  In this first experiment, you will fabricate you own superconducting thin film samples, and watch the resistance drop suddenly to zero as they become superconducting at low temperature.  Superconductors also have very interesting magnetic properties.  A superconductor tries to expell all magnetic field from its interior.  You will study how superconductivy is destroyed by a sufficiently large magnetic field or electric current.

### Superconductivity II

Once you have done the preceeding set of experiments, you can move on to more advanced topics.  Now you can fabricate you own NIS (normal metal -- insulator -- superconductor) or maybe even SIS tunnel junctions.  The latter exhibit the famous Josephson effect, whereby an electrical current flows across the junction without any voltage drop.  When you make a circuit with 2 such junctions, you get a "SQUID", i.e. a Superconducting QUantum Interference Device.  We won't make our own SQUID's, but we will use a commercial SQUID made from high-Tc superconductors, which it operates at liquid nitrogen temperature.

Historically superconductivity appeared only in metals and alloys and only near liquid Helium temperatures (~4 to 20 K), but within the past 10 years a very large family of superconductors have appeared in rather complex metallic cuprates, most of which are superconductiving above liquid N temperatures (70 to 150 K). You will investigate some properties of both high and low temperature superconductors. If you are interested, you might think about some practical questions, such as "Are magnetically levitated superconducting trains technologically and economically practical?"

### Superfluidity

Helium gas becomes a liquid at about 4.2 K. If you cool it to still lower temperatures, there is a phase transition at about 2.2K to a new liquid state called a superfluid. Below 2.2K the real liquid is a mixture of normal and superfluid. In this regime many properties of the two components are different. You will learn to handle liquid helium; to learn about the different properties; to determine which properties we can measure and to do such measurements. In particular:
1. Measure the velocity and attenuation of a thermal wave at several temperatures in the superfluid phase.
2. Measure the heat capacity of the liquid near the superfluid transition temperature.
3. Superfluids can do strange things.  For example, the fluid can sometimes creep up over the sides of its container.

### X-ray Diffraction

You all know about the optical diffraction (interference) grating and roughly how it works. In fact, any periodic structure will produce an interference pattern when it is irradiated by an electromagnetic (or deBroglie) wave whose wavelength is approximately equal to the spacing, d, of the periodic structure. Starting with a system in which both d and the wavelength are about 3 cm, you will learn how both the geometrical and physical properties are important in the interaction. You will then proceed to the case where both d and the wavelength are about 10-8 cm and finally if we are lucky, take some data on a real crystal using a "state of the art" x-ray system and do a careful analysis of the crystal structure of the crystal. We may consider the connection between what you have learned and the medical diagnostic tool, the CAT scan.