Download Superconductivity

Superconductivity
Purpose:
To observe two of the fudamental properties of superconductors. The first is the
levitation of a magnet by a superconductor which illustates the Meisner Effect.
Secondly, direct measurement of the resistance of the superconducting material as a
function of temperature reveals the zero resistance state below a certain temperature
(Hence the name superconductor).
Introduction
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) ..
The superconducting transition occurs over a relatively small change in
temperature. The temperature at which it occurs, which is called the critical
temperature TC , depends on the material. Until recently, the known superconductors
had a TC below 23K. The new ceramic superconductors (Nobel Prize: 1987) used in
this experiment have much higher critical temperatures ( 90-100K) than those of the
original metallic superconductors. Since easily available liquid nitrogen boils at 77K
,these materials make superconducting phenomenon easily 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. Noble Prize 1957). According to this theory a superconducting current is
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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 property of superconductors is that they are perfectly diamagnetic.
When superconducting, a superconductor will not allow any magnetic field to penetrate
it. This is the Meisner Effect!( named after the person who discovered this effect in
1933). Any external magnetic field which would penetrate the superconducting
material is cancelled by an opposing field produced by electric currents induced in the
superconductor. If this external field comes from a magnet, then the expulsion results in
a repulsive force on the magnet The magnet, if above the superconductor ,will be
levitated. This magnetic repulsion phenomenon is a manifistation of the the Meissner
Effect .
The purpose of this laboratory is to introduce students to superconductivity and
demonstrate the characteristic properties of superconductors. With the 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.
Prelab Homework
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.
Questions
1) 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?
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2) State the expression for Hook's law. If superconductor has a weigh of 10 g and it
levitated 5 cm. What is constant of superconductor if it was on normal earth
atmosphere ?
3) What is the critical temperature for a superconducting material?
4) a. What voltage given by the thermocouple in the experiment corresponds to the
temperature of liquid nitrogen? (Use the table in the appendix).
b. The critical temperature of your sample lies between 77K and 90K. What is the
corresponding range of thermocouple voltages ?
c. Suppose your thermocouple has a systematic error: at 77K it gives 6.12mV. What
temperature of the sample corresponds to 5.63 mV?
5)
What is the purpose of using the sand crystals?
Part IA: The Meissner Effect: Levitation.
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. Keep it away from the
water.
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

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 I A-1:
(The components [Colorado Superconductor] for this part are listed in the end. Your
TA will show them to you)
1) Carefully pour a small amount of liquid nitrogen in the cylindrical section of the
styrofoam tray. Wait until it stops boiling.
2) 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.
3) 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.
4) Record your observations of this phenomena.
Procedure for Part I A-2:
(The components [Superconductive Components] for this part are listed in the end.
Your TA will show them to you)
1) Place the superconducting levitator ring assembly in the Petri dish and slowly pour
liquid N2 until the ring is completely cooled and the liquid N2 has settled to a slow
boil.
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2) Pick up the magnet ring and carefully move it toward the sample. One should feel a
strong repulsive force as the magnet is moved towards the sample.
3) Stabilize the magnet [ push it down and release it] and give it a small spin. The
magnet will keep rotating for some time, though it will slow down primarily
because of air drag.
[The following steps 5-7 are optional for the fall 1996 term.]
4)
Place the plastic plate on the magnet ring.
5) Add weigh on top of plastic plate (it already mark weigh , 10g, 20g, 50g, ...) and
record weigh. Record levitate distance between magnet ring and levitator ring
assembly.
6)
Repeat step 5) until magnet ring falls down completely.
7)
Plot the data , Force Vs distance.
Part I B: Meisner Effect: Critical Temperature.
You can determine T c 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 T c .
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.
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Procedure for Part I B:
1) Connect the thermocouple leads to the voltmeter provided.
2) Select the right range to read to an accuracy of 0.01mV.
3) Cover the sample and holder with a plastic bag before immersing in liquid nitrogen.
( This will prevent moisture from condensing.) Wait until the boiling stops. The
voltmeter should read 6.43mV corresponding to the liquid nitrogen temperature of
77K. If your voltmeter reads a different value then there is a systematic error which
may be due to contact potentials associated with the thermocouple. If this is the
case, you should assume that when immersed in liquid nitrogen that the
temperature of the thermocouple is 77K. For example if the thermocouple voltage
reads 6.23mV, then you must add 0.20mV to all readings to determine the
temperature in all later measurements.
4) Remove the sample and holder from the liquid nitrogen and remove the plastic.
Place it into the styofoam holder with the superconductor's surface exposed and
close the cover. The superconducting material and holder will start to warm from
77K.
5) Open the cover and carefully place the provided magnet
ceramic
superconductor
disk
on top of the
6 red thermocouple lead
5 blue thermocouple lead
1 black current probe
4 black current probe
2 yellow current probe
3 yellow current probe
brass
shield
Figure 9.1
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superconductor so that it "floats" over the center of the disk (via the Meissner
Effect!).
6) 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 T c . The expected transition
temperature is about 110K( or somewhat less for some of the samples). You will see
from the table below that this is a change of about 1.23mV ( or less). The magnets
will fall after about 40 to 120s depending on your apparatus.
7) Repeat one more time.
Part II: Resistance vs Temperature.
You will measure the resistance of the superconductor device as a function of
temperature to determine T c . 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 I14 (~0.25A) 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 V 23 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 V 23 to the current I14
,
R
V 23
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I14
(9.1)
Procedure for Part II.
1) Set up equipment shown in fig 2 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 V 23 .
2) Put the superconductor and holder into the Crystat chamber (Plastice Cup) (see fig
9.3). Pour the sand into of cup until the superconductor is covered by sand ( Do not
fill the entire cup). Carefully pour some liquid nitrogen into the cup and wait until
the boiling stops. Continue to pour the liquid nitrogen until thermocouple reachs
6.43mV or comes to equilibrium near this value as discribed above.
3) Adjust the DC power supply to have a current of about 0.25A through electrical lead
and 4. Even though the resistance is supposed to be zero and hence V 23 , your
voltmeter will show a small voltage. (Due to some resistance in the electrical leads.)
Caution: Don't leave the current passing through the sample is above 200K for very
long or it will cook and damage the sample.
4) Record simultaneously, the readings of the voltmeter connected to electrical leads 2
and 3 and of those connected to the
thermocouple
as
the
superconductor device warms up.
This takes about 20 to 30 minutes.
Try to take these readings as the
thermocouple changes by 0.1mV
increments and record the time .
You may stop taking data when T
has reached about 130K.
constant current
DC Power Supply
ammeter
A
Power Supply
V
1
2
5) Repeat the V 23 vs. temperature
measurements.(Go back to step 2)
6) The ceramic superconductors are
sensitive to moisture and will
degrade in a humid environment.
test
voltage
pr
ob
es
voltmeter
dc
po
we
r
su
pp
ly
vo
3lt
m
et
er
sa
m
pl
e
4
current probes
Figure 9.2. Schematic of a Four Point Probe
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After completing the experiment, warm (don't cook it!) it carefully with hair dryer
(at least 12 inches away!) for about 3 minutes (only!) to completely dry it.
Figure 9.3: Cross Section of the Sand Cryostat containing a CSI four-point probe
device
Data Analysis
1) Plot temperature and R (= V23 / I14) vs time.
2) Plot R (= V23 / I14)
temperature.
vs. temperature. From this plot indicate the transition
3) Discuss the T c determined both from the above plot and by the observation the
Meissner Effect. Is there any difference? Why?
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Questions
1) The Meissner Effect allows a magnet to float above a superconductor (or vice versa).
Can you think of any potential applications using this effect?
References
1) Ashcroft and Mermin, Solid State Physics. New York: pp. 726-755
2) Prochnow, David. Superconductivity, Experimenting in a New Technology. Blue
Ridge Summit, PA: TAB Books Inc., 1989.
3) Kinzie, P. A. Thermocouple Temperature Measurement. NY: Wiley-Interscience,
1973.
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Table for converting Voltage given by thermocouple (mV) to the Temperature (0K)
0
0
1
2
3
4
5
6
7
8
9
10
°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
-0.02
-0.04
-0.06
-0.08
-0.10
-0.12
-0.14
-0.16
-.0.18 -0.20
290
300
-0.20
-0.22
-0.24
-0.26
-0.28
-0.30
-0.32
-0.34
-0.36
-0.38
-0.40
300
°K
0
1
2
3
4
5
6
7
8
9
10
°K
K
Conversion from mV to K for the thermocouple
Table 9.1
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Equipment:








rubber gloves
safety glasses
liquid nitrogen
tweezers
superconducting material ( Bi ceramic, Tc~110K)
two magnets
cylinder
Sand Crystal




Styrofoam container
thermocouple
two voltmeters
current supply
For the person giving the lab lecture:
1. Go over prelabs
2. Go over lab setup
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To: The student doing this experiment:: Superconductivity.
From: David Douglass
B&L 156
e-mail: [email protected]
I have been involved in the improvement of the undergraduate
Physics 100-level laboratories. This experiment is 1 of 15 total. I have
not yet, however, put the latest modifications into this particular
experiment. Your input is important and essential for this upgrade..
I would appreciate any comments that you wish to make. Simply
write them below, remove, fold, and drop into any university mailbox. I
will respond individually to all signed comments.
DAVID DOUGLASS
B&L 156
-------------------------------------------------------revised aug 15,1996 : jp/dhd
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