Short introduction to superconductivity effect

Superconductivity  refers to the effect in which the resistivity of a material drops to zero at low temperatures (see a very brief description).

The underlying physics of this effect is rather complex, and requires understanding of quantum behavior of electrons inside a conductor. You may get to it at the end of Modern Physics course (or not). This video attempts to give the explanation on a layman level, but actually it is not entirely accurate.

Instead of trying to grasp the complicated nature of superconductivity, we instead concentrate on measuring the critical temperature, i.e. the temperature at which the resistivity of the sample goes to zero. Because measuring a very low resistance is not easy, please make sure to watch the video about the four-probe method

Setup

Temperature probe

There are several types of temperature sensor. Two common types which use electric signals are:

• thermocouple which generates voltage in relation to temperature gradient between it ends;
• thermistor which has resistance changing with temperature.

In this lab we will use pt-100 thermistor. It suppose to have a linear dependence of its resistance vs temperature. This is not exactly true (see calibration chart or local copy), but corrections are quite small. Our first task is to calibrate the temperature sensor.

1. Measure its resistance at the room temperature
2. Later we will measure its resistance at the boiling nitrogen temperature, which will give us the 2nd point of the calibration curve.

Sample resistance measurement

Since resistance of our sample will be negligible relative to resistance of the hookup wires. We need a method which allows us to measure sample resistance directly. We will employ 4-point probe method.

Measurement Procedure

Track the voltage drop and current through the sample vs the temperature of the sample. Do it when samples cools down in the liquid Nitrogen and when it warms up. The most convenient way is to make a video recording of your sensors and plot it after wards (the transition to and from super conductivity happens quite quickly).

Do this several times. Make sure that instructors approve at least one of your plots.

What should be on your plot(s)

Analyze all data runs (make about 6) and plot the resistance change vs temperature for all of them in one plot. Since the measured curves are expected to be relatively similar, make sure they are distinguishable by color and/or marker type, and that you provide the legend, clearly indicating which curve corresponds to each trial. (You don’t need to have any theory fits this time!)

Don’t forget to include the caption! It should briefly summarize what is plotted,  and what the different traces mean. It is also a good idea to put the constant experimental parameters, like current (which is more or less constant)

Do not worry if some of your runs do not cover full range between boiling liquid Nitrogen and room temperature. The most interesting location is around when the sample becomes superconductive. Think if you need to add a separate plot which shows only this region.

Discussion

As for discussion, you may consider the following aspects:

• Why the apparent critical temperature is different for cooling and heating cycle? Which one is closer to the true one? How would you carry out the experiment to increase the accuracy?
• Does the sample truly reaches superconductivity? Explain.
• How repeatable the data sets are? What uncertainty does it introduce to the measured critical temperature?
• If you are to add the error bars for each point, how would you determine them? Previously, we used the smallest division on the meter stick as experimental uncertainty - do you think it is valid to use the last available digit on a multimeter? (You don’t have to actually add error bars to the plot this time).