Superconductivity

To observe the levitation of the magnet due to the Meisner Effect, calculate the critical temperature of a superconducting material by direct observations of the levitation and by measuring the resistance of the superconducting material as a function of temperature.

The flow of current in normal conductors dissipates energy (producing heat). This "frictional" dissipation is measured by the resistivity of the material and is the origin of Ohm's Law.

At lower temperatures some materials called superconductors lose measurable electrical resistivity. Without any driving voltage, superconducting currents will flow indefinitely with no discernible decay. This phenomenon was originally discovered in 1911 by the Dutch physicist Heike Kamerlingh-Onnes (Nobel Prize: 1913) as a byproduct of his ability to liquefy Helium.

The superconducting transition occurs over a relatively small change in temperature. The temperature at which it occurs, which is called the critical temperature , depends on the material. Until recently the known superconductors had a below 23K. The new (Nobel Prize: 1987) ceramic superconductors used in this experiment have much higher critical temperatures (around 90K) and have less abrupt transitions than those of the original metallic superconductors. Since easily available liquid nitrogen boils at 77K these materials make superconducting phenomenon observable above 77K.

The theoretical understanding of the phenomena of superconductivity in these materials is not entirely understood. Before the discovery of the ceramic superconductors in 1986, the accepted model was the BCS theory (Bardeen, Cooper and Schrieffer). According to this theory a superconducting current is carried by bound pairs of electrons (Cooper pairs) which move through a metal without energy dissipation. The mechanism for the new ceramic superconductors remains unknown and is the subject of present day research.

Another striking feature of superconductors is that they are perfectly diamagnetic. When superconducting, a superconductor will not allow any magnetic field to penetrate it. The presence of an external magnetic field that would penetrate an ordinary conductor produces a "supercurrent" on the surface of a superconductor which generates a magnetic field that precisely cancels the external field in the interior of the superconductor. This induced field, opposing the external field, repels it. A magnet, for instance, producing such an external field will be repelled. Therefore, this magnetic repulsion phenomenon is called the Meissner Effect named after the person who discovered it in 1933. It is a unique signature of superconductors.

The purpose of this laboratory is to introduce students to superconductivity and demonstrate the characteristic properties of superconductors. By use of the ceramic high temperature superconductors provided, you will observe the Meissner effect in which a magnetic field is excluded from the interior of a superconductor. Also you will observe that the electrical resistance vanishes when the material becomes superconducting, and you will measure the critical temperature and determine the Resistance vs. Temperature characteristic. In the process you will learn the principle (based on Ohm's law) of the use of a four point probe to measure the resistance of a material (in spite of the interfering effects of contact resistance) by making voltage and current measurements.

This prelab homework must be done at home and handed to the lab TA before you start the lab. Students should read the instructions for this lab, and consult the sections on Electricity and Magnetism in your textbook in order to answer the questions below.

• State the expression for Ohm's law. If a voltage of 10 Volts is placed across a 3 Ohm resistor, what is the current through the resistor?

• What is the critical temperature for a superconducting material?

• What voltage given by the thermocouple in the experiment corresponds to the temperature of liquid nitrogen? (Use the table in the appendix).

• The critical temperature of your sample lies between 77K and 90K. What is the corresponding range of thermocouple voltages ?

• Suppose your thermocouple has a systematic error: at 77K it gives 6.12 mV. What temperature of the sample corresponds to 5.63 mV?

With a strong enough magnet, the repulsion due to the Meissner effect can be sufficient to support the weight of the magnet. Such a magnet will levitate above a superconductor.

Precautions

In this experiment you will handle liquid nitrogen which can cause severe "burns" because of its extremely low temperature. Certain precautions need to be taken. You should read the following instructions carefully and practice these safety measures in the experiment.

• Wear safety glasses at all times in the presence of liquid nitrogen. Do not allow any liquid nitrogen to touch your body, and do not touch anything that has been immersed in it until that item warms to room temperature.

• Be extremely careful not to overfill or to spill liquid nitrogen from any vessel. Never store liquid nitrogen in a container with a tight-fitting lid because over pressure by the evaporated nitrogen may cause an explosion.

• The superconductors are made of metal oxides that may be potentially toxic. For your safety, never handle the superconductor with your bare hands. Use the tweezers provided. Wash your hands with soap and water after the experiment is completed.

Procedure for Part IA:

• Carefully pour a small amount of liquid nitrogen in the cylindrical section of styrofoam tray. Wait until it stops boiling.

• Using the plastic tweezers provided, place the superconductor disk flat in the liquid. Wait until it stops boiling. The liquid should be level with the top of the disk.

• Using the tweezers pick up one of the magnets provided and place it on top of the superconductor disk. Observe whether the magnet is touching the surface of the disk.

• Record your qualitative observations of this phenomena.

B: Meisner Effect. The Critical Temperature of the Superconductor.

You can determine by observing the Meissner effect. Above the critical temperature a material will be in a normal state and will no longer expel magnetic field. By measuring the temperature at which the Meissner effect disappears as the superconductor is warming up you can determine the .

The temperature of the superconductor will be determined with a thermocouple attached to the superconductor. Figure 9.1 the actual device and gives the color code of the six leads. At this stage only the thermocouple leads (blue and red) will be used.

The thermocouple junction thermometer consists of two different metals connected at a point to form a junction. This kind of bi-metallic junction produces a small electrical voltage which varies with the temperature of the thermocouple junction. The voltage to temperature conversion is given in Table 9.1.

Figure 9.1

Procedure for Part IB:

• Connect the thermocouple leads to the voltmeter provided.

• Select the right range to read to an accuracy of 0.01 mV.

• Immerse the superconducting device completely in liquid nitrogen. Wait until the boiling stops. The voltmeter should read 6.43 mV corresponding to the liquid nitrogen temperature of 77K. If your voltmeter reads a different value then there is an error which may be due to contact potentials or changes in the thermocouple. You can assume that when immersed in liquid nitrogen that the temperature of the thermocouple is 77K. For example if the thermocouple reads 6.23 mV, then you must add 0.20 mV to all readings to determine the temperature in all later measurements.

• Remove the device from the liquid nitrogen and place it flat on an insulating surface with the superconductor's surface exposed. The superconducting material will start to warm up from 77K.

• Carefully place the magnet provided on top of the superconductor so that it "floats" over the center of the disk via the Meissner Effect.

• When the magnet drops onto the surface of the superconductor disk, record the voltmeter reading of the thermocouple. The corresponding temperature from the table is the superconducting transition temperature . The expected transition temperature is about 90K or less for some of the samples. You will see from the table that this is a change of about 0.5 mV. The magnets will drop after about 40 to 120s depending on your apparatus.

• Repeat procedure one more time.

You will measure the resistance of the superconductor device as a function of temperature to determine . You will use the thermocouple to measure the temperature, as above, and use a four point probe to measure the resistance.

When a simple measurement of the resistance of an electrical test sample is performed by attaching two wires to it, the resistance of the wire-to-sample contact point or bond is also inadvertently included. If the sample resistance is very small, the contact resistance can dominate and completely obscure the temperature dependence of the sample resistance. The solution to this problem is to use the four point probe shown schematically in the Figure 9.2. A constant current (~ 0.5 A) is made to flow the length of the sample through two probes labeled 1 and 4. If the sample has any resistance to the flow of the electrical current, there will be a voltage drop between the two center probes labeled 2 and 3. The voltage drop between probes 2 and 3 can be measured by a voltmeter. The high input impedance of the voltmeter minimizes the current flow through it. Then the potential drop across the contact resistance associated with probes 2 and 3 is negligible. Therefore, the resistance of the sample between probes 2 and 3 is the ratio of the voltage drop to the current ,

. (9.1)

Figure 9.2. Schematic of a Four Point Probe

Procedure for Part II.

• Set up equipment shown for the four point probe. The color code of the leads is given in Figure 9.1. In this section the voltmeter that you used to measure the voltage will now be used to measure . The voltage of the thermocouple will be measured with another voltmeter which is supplied.

• Carefully pour liquid nitrogen over the device until it is just submerged. Wait until the boiling stops.

• Adjust the DC power supply to have a current of about 0.5A through probes 1 and 4. Even though the resistance is supposed to be zero and hence , your voltmeter will show a small voltage.

  Caution: Don't leave the superconducting sample with the current going through it for long without cooling it with liquid nitrogen, or it will cook and damage the sample.

• Remove the superconducting device from the liquid nitrogen and place it on an insulated surface. It will begin to warm up toward .

• Record simultaneously, the readings of the voltmeter connected to probes 2 and 3 and of the one connected to the thermocouple as the superconductor device warms up, this takes about 2 to 3 minutes. Try to take these readings as the thermocouple changes by 0.1 mV increments. You can stop taking data when T has reached about 130K. Repeat the vs. temperature measurements.

• The ceramic superconductors are sensitive to moisture and will degrade in a humid environment. After completing the experiment, please carefully wipe the superconductor to remove frost or water. Then warm (don't cook it!) it carefully under a lamp (at least 12 inches away!) for about 3 minutes (only!) to completely dry it.

• Plot vs. temperature.

• Discuss the determined both by measuring the resistance and by observing the Meissner Effect. Is there any difference? Why?

• The Meissner Effect allows a magnet to float above a superconductor (or vice versa). Can you think of any potential applications using this effect?

Ashcroft and Mermin, Solid State Physics. New York: pp. 726-755

Tinkham, Superconductivity. New York:

Prochnow, David. Superconductivity, Experimenting in a New Technology. Blue Ridge Summit, PA: TAB Books Inc., 1989.

Kinzie, P. A. Thermocouple Temperature Measurement. NY: Wiley-Interscience, 1973.

Table for converting Voltage given by thermocouple (mV) to Temperature (K)

   0K  0     1     2     3     4     5     6     7     8     9     10    deg.K  
60     7.60  7.53  7.46  7.40  7.33  7.26  7.19  7.12  7.05  6.99  6.92  60     
70     6.92  6.85  6.78  6.71  6.64  6.56  6.49  6.42  6.37  6.33  6.29  70     
80     6.29  6.25  6.21  6.17  6.13  6.09  6.05  6.01  5.97  5.93  5.90  80     
90     5.90  5.86  5.83  5.79  5.75  5.72  5.68  5.64  5.60  5.56  5.52  90     
100    5.52  5.48  5.44  5.41  5.37  5.34  5.30  5.27  5.23  5.20  5.16  100    
110    5.16  5.13  5.09  5.06  5.02  4.99  4.95  4.91  4.88  4.84  4.81  110    
120    4.81  4.77  4.74  4.70  4.67  4.63  4.60  4.56  4.53  4.49  4.46  120    
130    4.46  4.42  4.39  4.35  4.32  4.28  4.25  4.21  4.18  4.14  4.11  130    
140    4.11  4.07  4.04  4.00  3.97  3.93  3.90  3.86  3.83  3.79  3.76  140    
150    3.76  3.73  3.69  3.66  3.63  3.60  3.56  3.53  3.50  3.47  3.43  150    
160    3.43  3.40  3.37  3.34  3.30  3.27  3.24  3.21  3.18  3.15  3.12  160    
170    3.12  3.09  3.06  3.03  3.00  2.97  2.94  2.91  2.88  2.85  2.82  170    
180    2.82  2.79  2.76  2.73  2.70  2.67  2.64  2.61  2.58  2.53  2.52  180    
190    2.52  2.49  2.46  2.43  2.40  2.37  2.34  2.31  2.29  2.26  2.23  190    
200    2.23  2.20  2.17  2.14  2.11  2.08  2.05  2.02  1.99  1.96  1.93  200    
210    1.93  1.90  1.87  1.84  1.81  1.78  1.75  1.72  1.69  1.66  1.64  210    
220    1.64  1.61  1.59  1.56  1.54  1.51  1.49  1.46  1.44  1.41  1.39  220    
230    1.39  1.36  1.34  1.31  1.29  1.26  1.24  1.21  1.19  1.16  1.14  230    
240    1.14  1.11  1.09  1.07  1.04  1.02  0.99  0.97  0.94  0.92  0.89  240    
250    0.89  0.87  0.84  0.82  0.79  0.77  0.74  0.72  0.69  0.67  0.65  250    
260    0.65  0.62  0.60  0.58  0.55  0.53  0.50  0.48  0.45  0.42  0.40  260    
270    0.40  0.38  0.36  0.34  0.32  0.30  0.28  0.26  0.24  0.22  0.20  270    
280    0.20  0.18  0.16  0.14  0.12  0.10  0.08  0.06  0.04  0.02  0.00  280    
290    0.00  -.02  -.04  -.06  -.08  -.10  -.12  -.14  -.16  -.18  -.20  290    
300    -.20  -.22  -.24  -.26  -.28  -.30  -.32  -.34  -.36  -.38  -.40  300    
deg.K  0     1     2     3     4     5     6     7     8     9     10    deg.K  

Table 9.1. Conversion from mV to K for the thermocouple