Critical Temperature Measurements of Superconductors

and Their Dependence on Current

By Joseph Dotzel

With Jedidiah Riebling

Date: 3/6/2014

Abstract

In this paper we will explore the science behind superconductivity. We

set out to find three things in this experiment, to determine the critical

temperature by using the Meissner Effect, to determine the critical

temperature by observing the resistance as a function of temperature, and

to determine the critical current density as a function of the temperature. We

were able to find the critical temperature of the two superconductors

Bi2Sr2Ca2Cu3O9 and YBa2Cu3O7 were respectively 110.616 ± 21.8 kelvin and

87.491±2.624 kelvin. Both were within 10% of the accepted values. We were

also able to plot the critical temperature vs. resistance at various currents,

however due to large error, were unable to calculate the critical current

density.

Introduction

When a current is applied to conductor, that conductor will dissipate

energy as heat. This energy which is given off is determined by the electrical

resistivity of the Conductor. However, when certain conductors are brought

below a certain temperature, the critical temperature Tc, this resistivity

disappears. This phenomenon is known as superconductivity.

The concept of superconductivity was discovered in 1911 by physicist

Heike Kamerlingh-Onnes. The understanding of super conductivity is still not

fully explained to this day, but the current accepted model involves bound

pairs of electrons which move through the superconductive materials without

losing any energy. Superconductivity’s lack of a measurable resistance

makes it a desirable technology for current carrying wires, as the wires in

use currently require a large voltage to overcome the resistance of

materials. However, currently the practical applications for superconductors

are minimal, as the superconductors must be kept at low temperatures to

perform properly. In addition to this problem, excess electrical current or

magnetic field strength can cause the conductor to stop acting as a

superconductor.12

In this experiment we will be using Bi2Sr2Ca2Cu3O9 and YBa2Cu3O7

superconductors and will have three goals. The first is to determine the

critical temperature by using the Meissner Effect. The second will be to

determine the critical temperature by observing the resistance as a function

of temperature. The last is to determine the critical current density as a

function of the temperature. The rest of this paper will cover the theory,

experimental method, data, and conclusion of the experiment.

Theory

In order to accomplish the first goal of this experiment, we will be

using the Meissner Effect. The Meissner effect was discovered by Robert

Ochsenfeld and Walther Meissner in 1933 and is the effect where, below

critical temperature, a superconductor will cancel out nearly all magnetic

fields inside. The superconductor accomplishes this by creating electrical

currents near its surface which cancel any magnetic fields within the

superconductor. We will observe this visibly by placing a magnet above the

superconductor and using the phenomena of flux pinning. Flux pinning

occurs when magnetic lines of force from the magnet become trapped within

the superconductor. This occurs within the superconductor in defects and

grain boundaries where the Meissner effect does not occur properly. This

causes the magnet to be held in place above the superconductor3,4. With this

background done we can now move on to the procedure.

Figure 1: Meissner Effect

Experimental Method

In order to perform this experiment we will be using a Colorado

Superconductor kit, a DC current source 2 Multimeters, a four point hall

probe, liquid nitrogen, a magnet, and Bi2Sr2Ca2Cu3O9 and YBa2Cu3O7 high Tc

superconductors. The experiment will be set up as described in the Colorado

Superconductor Experiment guide5 (See Figure 2.) The first part of the

experiment was done by placing the probe with the superconductors into

liquid nitrogen and allowing them to cool until the liquid nitrogen stopped

boiling. A magnet was then placed above the superconductor and held by

the flux pinning. A thermocouple reading was then taken when the magnet

was no longer suspended above the superconductor. Five sets of data were

taken for each superconductor.

Figure 2: 4 Point Probe Setup

The second part of the experiment was to measure the resistance as a

function of temperature over five different currents. To accomplish this, the

superconductor was again placed in liquid nitrogen and allowed to cool until

the boiling stopped. It was then removed from the liquid nitrogen, but was

allowed to remain inside the insulated container to cause it to heat at a

slower rate. Using the high Tc Labview program, the resistance as well as the

thermocouple readings were recorded approximately every 100 ms, and the

current was incremented by 0.1 amp intervals6.

Data and Analysis

For The determination of the critical temperature using the Meissner

Effect, 10 Points of data were collected (table 1). The values were then

averaged to get the critical temperature for the respective superconductor.

Critical Temp Critical Temp

Bi2Sr2Ca2Cu3O9 YBa2Cu3O791.456 ± 0.001 86.808 ± 0.001113.764 ± 0.001 87.441 ± 0.001118.929 ± 0.001 89.771 ± 0.001113.377 ± 0.001 86.62 ± 0.001115.554 ± 0.001 86.815 ± 0.001

Table 1: Critical Temperature using Meissner Effect

After averaging the values, we obtained a critical temperature of 110.616 ±

21.864 for the Bi2Sr2Ca2Cu3O9 sample and 87.491±2.624 Kelvin for the

YBa2Cu3O7 sample. Comparing to the accepted values of 108 Kelvin and 95

Kelvin respectively. Our experimental values are a little off. This may be due

to the unequal heating of superconductors after cooling. By changing the

location of the magnet, we could visibly observe the Flux pinning effect

disappear in one area of the superconductor while it was still active in

another. It could also be due to impurities within the superconductor which

could affect the behavior of the superconductor.

For the second part of the experiment we took five sets of data for

each superconductor. These five sets of data were taken at different currents

varying from 0.1 amps to 0.5 amps. We then determined the critical

temperature of each data set. To do this, we graphed the data (figure 3) and

observed the linear trends at the beginning and the end of each graph.

Where these linear trends changed we took those points to be the beginning

and end of the shift from a conductor to superconductor (figure 4). We then

averaged these points to get our critical temperatures at five different

currents (table 2).

Figure 3: Temperature vs. Resistance

Figure 4: Critical Temperature Determination

Bi2Sr2Ca2Cu3O9 Critical Temperature YBa2Cu3O7 Critical TemperatureCurrent (Amps) Critical Temperature (k) Current (Amps) Critical Temperature (k)

0.1 109±7.07 0.1 85±5.00.2 101±5.00 0.2 86±3.60.3 105±7.81 0.3 86±5.00.4 110±8.49 0.4 86±3.60.5 105±11.4 0.5 86±2.8

Table 2: Critical Temperature vs. Current

The final goal of this experiment was to determine the critical current

density of each superconductor. To accomplish this we used the Critical

Temperature vs. Current information from table 2 and graphed the five

points for each superconductor (figure 5).

Figure 5: Current vs. Critical Temperature

In order to find the critical current of each super conductor we must

extrapolate the trend line to 77 kelvin, the temperature of liquid nitrogen.

Our two equations for these graphs are Y=0.0038683 x for the Bi2Sr2Ca2Cu3O9

sample and Y=0.0027078 x for the YBa2Cu3O7 sample. Solving for Y at 77 kelvin

gives us 0.30 amps and 0.21 amps for the respective samples. We know for

a fact that this is incorrect data because the samples were still acting as a

superconductor under that current. Given this we were unable to determine

the Critical current Density of the samples. We will justify the data from

figure 5 in the conclusion section.

The error of this experiment come first from the precision of the

equipment we used. From there we used standard error propagation to

determine any error propagation.

δC=√(δA )2+( δB )2 and

δCC

=√( δXX )2+( δYY )

2+( δZZ )

2

Where δx δy δz , δa δb are your error terms of x y z, and a b and δC is your

final error.

For the averages we calculated in this experiment, we calculated the error as

the standard deviation of the data sets given by

Where N is the number of data points and μ is the average of the data set.

Conclusion

This experiment set out to complete three objectives, to determine the

critical temperature by using the Meissner Effect, to determine the critical

temperature by observing the resistance as a function of temperature, and

to determine the critical current density as a function of the temperature. In

the end only two of these were accomplished and with varying success. The

critical temperature for our Bi2Sr2Ca2Cu3O9 sample fell within error bars, but

the error bars were very large. The critical temperature for our YBa2Cu3O7

sample did not fall within our error bars. This being said, both samples were

within 10% of accepted values.

We also managed to find the critical temperature at various currents

by observing the resistance as a function of temperature. However, when the

time came to use this data to find the critical current density, we found the

data was significantly flawed. If we look at possible sources of error for this I

believe the main source of error is the lack purity of the superconductor. The

impurity of the superconductor could cause the transition period from normal

conductor to superconductor to increase. This made determining the critical

temperature of the sample very imprecise. Other sources of error could be

unequal heating or cooling of the superconductor, making it hard to ensure

the data for each current was taken under the same conditions. In

conclusion, this experiment was still able to show many aspects of

superconductivity, as well as the difficulties involved.

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