Electrical Resistivity in

SuperconductorsThe electrical resistivity of many metals and alloys drops suddenly to zero when the specimen is cooled to a sufficiently low temperature. This phenomenon is known as Superconductivity.

Course Name: Superconductivity

Author/sAnura Kenkre

Sameer Sahasrabudhe

Learning objectives

After interacting with this Learning Object, the learner will be able to:

– Explain the meaning of electrical resistivity in superconductors.

– Predict the effect of temperature changes on the electrical resistivity of superconducting samples.

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Definitions and Keywords

The electrical resistivity of many metals and alloys drops

suddenly to zero when the specimen is cooled to a

sufficiently low temperature. This phenomenon is known

as Superconductivity.

The temperature at which the transition to the

superconducting state takes place is called the critical

temperature(Tc)or the superconducting transition

temperature.

Add more slides if required

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Sample placed in cryostat for

cooling

Constant current supply

0.00

0.00

T=4.4K

mA

µ

Master Layout:A: Circuit diagram

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1Ammeter

Temperature

Control Voltmeter

Ammeter reading

Voltmeter

reading

Temperature

reading

Slide only for reference::NOT TO BE ANIMATED

Master Layout:B: Visual representation

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:electrons

:atoms of the lattice.

Fig2

Path on which the electrons are moving

Slide only for reference::NOT TO BE ANIMATED

Master Layout:C: Graph

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Blinking red dot denoting:

Temperature

Slide only for reference::NOT TO BE ANIMATED

Sample placed in cryostat for

cooling

Constant current supply

0.00

0.00

T=4.4K

mA

µ

Instructions/ Working area

Credits

Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07Introduction

Graphical representationChange the temperature and observe the motion of electrons in the Microscopic view

Microscopic view

Electrical Resistivity in

Superconductors

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mA

0.50

60

Voltmeter

Superconducting Sample placed in cryostat for coolingT=4.3K

Instructions/ Working area

Credits

Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07Introduction

Graphical representation

Microscopic view

Electrical Resistivity in

Superconductors

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mA

0.50

50

Voltmeter

Superconducting Sample placed in cryostat for cooling

T=4.2K

Instructions/ Working area

Credits

Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07Introduction

Graphical representation

Microscopic view

Electrical Resistivity in

Superconductors

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mA

0.50

0.00

Voltmeter

Superconducting Sample placed in cryostat for cooling

T=4.15K

Instructions/ Working area

Credits

Tab 02 Tab 03 Tab 04 Tab 05 Tab 06 Tab 07Introduction

Graphical representation

Microscopic view

Electrical Resistivity in

Superconductors

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Analogy / Scenario / Action

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2A Mechanical Analogy of Resistance- Visualize the orange balls as electrons, flowing through a normal conductor. The nails in the board are like the atoms of the conductor, and the tilt of the board represents the voltage applied across the conductor (gravitational potential represents electrical potential). Obviously, these orange balls are going to bounce around a bit on the nails (like a pachinko machine), rather than simply falling straight through. This bouncing is analogous to electron interactions with conductor atoms which is the cause of resistance.

Slide only for reference::NOT TO BE ANIMATED

Step 1:

Audio Narration (if any)

Text to be displayed (if any)

(DT)Description of the Action / Interactivity

T1: Title of the step, to appear as heading of the screen (if any)

Screen as shown in Slide 7

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31. Show the Animation design screen (Slide 7)2. The temperature meter shows T= 4.4K as shown.3. The electrons are seen moving in the 'microscopic view

window. (They are at their fastest speed at this setting)4. A pop up will appear on the ‘Click to change the

temperature'– If the user clicks on ‘click to go to lower

temperature',go to Step 2 (Slide 8)

– If the user to clicks 'click to go to higher temperature', show the feedback pop-up 'Making it more would be...so try to lower it'.

Click on these buttons to change the temperature

Step 1:

Audio Narration (if any)

Text to be displayed (if any)

(DT)Description of the Action / Interactivity

T1: Title of the step, to appear as heading of the screen (if any)

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31. Display this if

the temperature is lowered:If the temperature is lowered, you can se that the electrons move slower.

1. Show the changes in A, B and C as per the slide numbers:8, 9, 10

2. Keep the unit of change to 0.5, and decrease the speed of the electrons respectively.– Ex: 4.4, 4.35, 4.3, 4.25, 4.2, 4.15, 4.1, 4.05, 4.0,

3.95, 3.9, 3.85...etc3. Show the appropriate feedback, based on the

temperature selected by the user– Ex: for all the settings above 4.4, display:-------– For all the settings below 4.15, display:------

Screen as shown in Slide 7Screen as shown in Slide 7

Step 1:

Audio Narration (if any)

Text to be displayed (if any)

(DT)Description of the Action / Interactivity

T1: Title of the step, to appear as heading of the screen (if any)

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31. Set the specific limit for the interactivity to --- attempts.

Ensure the correctness of the 'feedback' to be displayed for every attempt which is OUTSIDE the chosen range for this particular sample– Ex: 4.4 to 4.15

2. After the ---attempts. Display a box with: 'Answer the questions in the following questionnaire to test your understanding'

3. Change the screen to the animation design slide number XX and display the questionnaire.

Screen as shown in Slide 7Screen as shown in Slide 7

Step 1:

Audio Narration (if any)

Text to be displayed (if any)

(DT)Description of the Action / Interactivity

T1: Title of the step, to appear as heading of the screen (if any)

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31. Display appropriate feedback for the answers submitted

by the user.2. After the user finishes the questionnaire, display the

summary as given in slide XX

Screen as shown in Slide 7Screen as shown in Slide 7

Step 1:

Audio Narration (if any)

Text to be displayed (if any)

(DT)Description of the Action / Interactivity

T1: Title of the step, to appear as heading of the screen (if any)

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31. Display appropriate feedback for the answers submitted

by the user.2. After the user finishes the questionnaire, display the

summary as given in slide XX

Screen as shown in Slide 7Screen as shown in Slide 7

Instructions for the animatorInstruction

to the learner

Results and OutputBoundary

limitsInteractivity

type

Interactivity option 1: Step No: 1

Image/graphic for explaining the interactivity options

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1. Interactivity options in this animation is already explained in STEPS earlier.

2. Please follow them

Lowest for showing animation in 'B' is______

Highest for showing animation in 'B'is______

Questionnaire:

The questions along with the answer options are given in the next few slides

Justification is also provided for the incorrect answers, which has to be displayed in case the user selects incorrect answers.

APPENDIX 1

Links for further reading

Reference websites:

http://www.msm.cam.ac.uk/doitpoms//tlplib/index.php

Books:

Introduction to Solid state physics-Charles Kittel(Chapter 12)

Solid state physics-MA Wahab.(Chapter 17)

Solid state physics-Ashcroft/Mermin. (Chapter 34)

APPENDIX 2

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Questionnaire1. At what temperature does the sample enter the superconducting

state?

Answers: a) 4.4K b) 4.3K c) 4.15K

d)4.10K

Correct Answers: 1)C

Feedback:If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display

“Have a look at the animation and Try again!”

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Questionnaire2. What happens to the resistivity of the sample as the temperature

decreases?

Answers: a) increases b) decreases c) remains same

d)becomes zero

Correct Answers: 2)b

Feedback:If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display

“Have a look at the animation and Try again!”

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Questionnaire3. What happens to the resistivity of the sample at the transition

temperature?

Answers: a)increases b) decreases c) remains same

d)becomes zero

Correct Answers: 3)d

Feedback:If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display

“Have a look at the animation and Try again!”

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Questionnaire4. What happens to the resistivity of the sample below the transition

temperature?

Answers: a) returns to normal b) decreases further c)it

is zero d)increases a lot.

Correct Answers: 4)c

Feedback:If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display

“Have a look at the animation and Try again!”

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Questionnaire

5. What happens to the number of collisions between the electron and the

atoms of the lattice as the temperature decreases?

Answers: a) increases b) decreases c)remains constant

d)becomes zero.

Correct Answers: 5)b

Feedback:If user clicks correct answer then display “Correct! Make sure you can explain the reasoning!” If user clicks incorrect answer then display

“Have a look at the animation and Try again!”

Questionnaire1

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6. What happens to the electrons when the material enters

the superconducting state?

Answers: a)each electron flows through the sample without

any resistance

b)each electron flows through the sample with lot

of resistance

c)Two electrons pair up and flow together through

the sample without any resistance.

d)Two electrons pair up and flow through the

sample with lot of resistance.Correct Answers: 6)c

Feedback:If user clicks on correct answer then display ”Yes !The electrons pair up and flow through the sample together. These pair of electrons are known as Cooper Pairs. Have a look at the animation on Cooper Pairs to get a better understanding of this concept.” If user clicks incorrect answer then display “Have a look at the animation and Try again!”

Summary

When you reduce the temperature sufficiently, certain metals conduct electricity without any resistance. This phenomenon is known as Superconductivity.

The resistivity of the metals goes on reducing as you lower the temperature and becomes zero at the superconducting transition temperature.

The temperature at which the transition to the superconducting state takes place is called the critical temperature(Tc)or the superconducting transition temperature.

When the metal enters the superconducting state, the electrons in the metal pair up and flow through the sample together. These pair of electrons are known as Cooper Pairs.

APPENDIX 3