Document that explains the chosen concept to the

Document that explains the chosen concept to the animator 1

Electrical Resistivity in Superconductors 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. Course Name: Superconductivity Authors: Anura. B. Kenkre 2

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. 3

1 2 Definitions of the components/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. 3 4 5 4

INSTRUCTIONS SLIDE 1 2 Master layout or diagram • Make a schematic diagram of the concept • Explain to the animator about the beginning and ending of the process. • Draw image big enough for explaining. 3 4 5 • In above image, identify and label different components of the process/phenomenon. (These are like characters in a film) • Illustrate the basic flow of action by using arrows. Use BOLD lines in the diagram, (minimum 2 pts. ) • In the slide after that, provide the definitions of ALL the labels used in the diagram 5

INSTRUCTIONS SLIDE 1 2 3 4 5 Master layout or diagram • You may have multiple master layouts. – In this case, number the master layout. ( e. g. Master layout 1) – Each Master layout should be followed by the stepwise description of the animation stages related to it. 6

IMPORTANT NOTE TO THE ANIMATOR: • All the instructions/labels or anything WRITTEN in blue are CONTENT NOT TO BE DISPLAYED! • All the instructions WRITTEN in black are CONTENT TO BE DISPLAYED! • This is not applicable for images as there can be overlapping of these colours there. This should be followed for all the instructions, labels, etc… Kindly keep a note of this while displaying text in the animation. 7

1 2 Master Layout 1 A Display this data in the LED display for the voltmeter Use LED font for display here too Gas flow control T=4. 4 K Temperature controller 3 Liquid helium reservoir voltmeter Use this font for the display. this is the LED display for the voltmeter 0. 00 µV 0. 50 m. A Heat exchanger Constant ammeter current supply Display this data in the LED display for the ammeter Use this font for the display. this is the LED display for the ammeter 4 Redraw the images for the voltmeter and ammeter. the ones given here are for reference. and do not retain the company names on them… 5 Experimental Set up: FOUR PROBE METHOD

1 Master Layout 2 B 2 3 4 : electrons 5 : atoms of the lattice. Microscopic View of the superconducting sample. Redraw the above images. the ones given here are for reference.

1 2 Master Layout 3 C 3 4 GRAPHICAL REPRESENTATION 5 (Resistance versus temperature) Plot a graph of R versus T according to the values on slide 35. . this image is for reference.

1 Master Layout 4 This arrange the gray ball called the la 2 3 4 5 This assembly of the two dark blue balls surrounded by the light blue cloud is called a cooper pair.

Master Layout 5 1 A 2 Gas flow control B 0. 00 T=4. 4 K µV Temperature controller 3 0. 00 Liquid helium reservoir Heat exchanger m. A Constant current supply : electrons : atoms of the lattice. Microscopic View of the superconducting sample. C 4 5 Experimental Set up: FOUR PROBE METHOD GRAPHICAL REPRESENTATION (Resistance versus temperature)

1 2 3 4 5 Animation design • Please see the design template provided in the next slide. • This is a sample template, and you are free to change as per your design requirements. • Try and recreate the sections/subsections as shown in the template. 13

Credits What will you learn Radio buttons (if any)/Drop down (if any) Play/pause Restart Lets Learn! Definitions est your understanding (questionnaire) Gas flow control Lets Sum up (summary) Want to know more… (Further Reading) 0. 00 T=4. 4 K µV Temperature controller 0. 00 Liquid helium reservoir : electrons : atoms of the lattice. Microscopic View of the superconducting sample. m. A Heat exchanger Constant current supply Experimental Set up: FOUR PROBE METHOD GRAPHICAL REPRESENTATION (Resistance versus temperature) 14

1 2 3 Explain the process 4 5 In this step, use an example to explain the concept. It can be an analogy, a scenario, or an action which explains this concept/process/topic Try to use examples from day-to-day life to make it more clear You have to describe what steps the animator should take to make your concept come alive as a series of moving images. Keep the examples simple to understand, and also to illustrate/animate. 15

1 2 3 4 5 Analogy / Scenario / Action A 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. 16

1 Stepwise description of process 2 3 4 5 The goal of the document is to provide instructions to an animator who is not a expert. You have to describe what steps the animator should take to make your concept come alive as a moving visualization. Use one slide per step. This will ensure clarity of the explanation. Add a image of the step in the box, and the details in the table below the box. You can use any images for reference, but mention about it's copyright status The animator will have to re-draw / re-create the drawings Add more slides as per the requirement of the animation 17

Step 1: 1 A 1: ”At temperature T 1 =4. 4 K” Gas flow control 2 5 75 T=4. 4 K means µV Temperature controller 3 4 . . Box below is not to be shown on screen in 0. 50 Liquid helium reservoir Heat exchanger Zoomed means m. A Click to go to higher temperature(T) Click to go to lower temperature(T) Constant current supply Fig 1 Description of the action/ interactivity • Initial screen should display T=4. 4 K and appropriate values for the voltmeter and ammeter as shown in Fig 1. • Show Fig 1 with the readings in the data boxes as indicated. • The temperature meter will read T=4. 4 K as shown. • when the learner clicks on ‘click to go to lower temperature', go to step 2. • Do not allow the user to click on the action button to go to higher temperature. • show the 3 slides with heading A 1, B 1, C 1 together as shown in master layout. 18

1 Step 1 contd: B 1: ”At temperature T 1 =4. 4 K” : electrons 2 3 4 : atoms of the lattice. Fig 2 Description of the action/ interactivity • Always keep the size of the atoms of the lattice a lot larger than the size of the electrons. • Move the electrons along the path shown by the arrows in the above figure. • Do not let the electrons pass through the atoms of the lattice or through each other while moving in their respective paths indicated by arrows. • The arrows show the direction of motion and the entire motion of one electron is depicted in one color. • The electrons hit the atoms of the lattice and move along the path shown by the respective arrows. • Show the movement of the electrons along the different colored arrows simultaneously. • Different coloured lines for paths are given for the benefit of the animator and they should not be retained. • REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES. • Include + and – signs on the gray and blue balls respectively. . 5 19

1 Step 1 contd: C 1: ”At temperature T 1 =4. 4 K” 2 3 4 5 Fig 3 Description of the action/ interactivity • Show the graph as given above. • Show the red spot at the place shown in the graph above. • The red spot appears at the temperature of this slide, at T 1 =4. 4 K. • Make the red dot blink to indicate that it is the current value of resistance. • Show gridlines on the graph and plot these values according to the table given on slide 35. Text to be displayed (if any) (DT) 20

1 Step 2: A 2: ”At temperature T 2 =4. 3 K” Gas flow control 2 . . Box below is not to be shown on screen 60 T=4. 3 K means µV Temperature controller 3 in 0. 50 Liquid helium reservoir Heat exchanger Zoomed means m. A Click to go to higher temperature(T) Click to go to lower temperature(T) Constant current supply Fig 4 4 5 Description of the action/ interactivity • Show Fig 4 with the readings in the data boxes as indicated. • The temperature meter will read T=4. 3 K as shown. • when the learner clicks on ‘click to go to lower temperature', go to step 3. • If the user clicks on ‘click here to go to higher temperature’ then go to step 1. • show the 3 slides with heading A 2, B 2, C 2 together as shown in master layout. Text to be displayed (if any) 21

1 Step 2 contd: B 2: ”At temperature T 2 =4. 3 K” : electrons 2 3 4 5 : atoms of the lattice. Fig 5 Description of the action/ interactivity • Always keep the size of the atoms of the lattice a lot larger than the size of the electrons. • Move the electrons along the path shown by the arrows in the above figure. • Do not let the electrons pass through the atoms of the lattice or through each other while moving in their respective paths indicated by arrows. • Compared to Fig 2 show less number of collisions(as the temperature is lower) • Keep the speed of the electrons lesser as compared to their speed in Fig 2. • The arrows show the direction of motion and the entire motion of one electron is depicted in one color. • The electrons hit the atoms of the lattice and move along the path shown by the respective arrows. • Show the movement of the electrons along the different colored arrows simultaneously • Different coloured lines for paths are given for the benefit of the animator and they should not be retained. • REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES. • Include + and – signs on the gray and blue balls respectively. 22

1 Step 2 contd: C 2: ”At temperature T 2 =4. 3 K” 2 3 4 5 Fig 6 Description of the action/ interactivity • Show the graph as given above. • Show the red spot at the place shown in the graph above. • Let it get joined to the blue spot by means of the dotted line. • The red spot appears at the temperature of this slide, at T 2 =4. 3 K • Make the red dot blink to indicate that it is the current value of resistance. • Show gridlines on the graph and plot these values according to the table given on slide 35. Text to be displayed (if any) (DT) 23

1 Step 3: A 3: ”At temperature T 3 =4. 2 K” Gas flow control . . Box below is not to be shown on screen 50 T=4. 2 K 3 4 5 0. 50 Liquid helium reservoir Heat exchanger means µV Temperature controller m. A Zoomed Click to go to higher temperature(T) in means Click to go to lower temperature(T) Constant current supply Fig 7 Description of the action/ interactivity Text to be displayed (if any) (DT) • Show Fig 7 with the readings in the data boxes as indicated. • The temperature meter will read T=4. 2 K as shown. • when the learner clicks on ‘click to go to lower temperature', go to step 4. • If the user clicks on ‘click here to go to higher temperature’ then go to step 2. • show the 3 slides with heading A 3, B 3, C 3 together as shown in master layout. 24

1 Step 3 contd: B 3: ”At temperature T 3 =4. 2 K” : electrons 2 3 4 5 : atoms of the lattice. Fig 8 Description of the action/ interactivity • Always keep the size of the atoms of the lattice a lot larger than the size of the electrons. • Move the electrons along the path shown by the arrows in the above figure. • Do not let the electrons pass through the atoms of the lattice or through each other while moving in their respective paths indicated by arrows. • Compared to Fig 5 show less number of collisions(as the temperature is lower) • Keep the speed of the electrons very much less as compared to their speed in Fig 5. • The arrows show the direction of motion and the entire motion of one electron is depicted in one color. • The electrons hit the atoms of the lattice and move along the path shown by the respective arrows. • Show the movement of the electrons along the different colored arrows simultaneously • Different coloured lines for paths are given for the benefit of the animator and they should not be retained. • REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES. • Include + and – signs on the gray and blue balls respectively. 25

1 Step 3 contd: C 3: ”At temperature T 3 =4. 2 K” 2 3 4 5 Fig 9 Description of the action/ interactivity • Show the graph as given above. • Show the red spot at the place shown in the graph above. • Let it get joined to the blue spots by means of the dotted line. • The red spot appears at the temperature of this slide, at T 3 =4. 2 K • Make the red dot blink to indicate that it is the current value of resistance. • Show gridlines on the graph and plot these values according to the table given on slide 35. Text to be displayed (if any) (DT) 26

1 Step 4: A 4: ”At temperature T 4 =4. 15 K” Gas flow control 2 3 4 . . Box below is not to be shown on screen 0. 00 T=4. 15 K µV Temperature controller in means 0. 50 Liquid helium reservoir Heat exchanger Zoomed m. A means Click to go to higher temperature(T) Click to go to lower temperature(T) Constant current supply Fig 10 Description of the action/ interactivity Text to be displayed (if any) (DT) • Show Fig 10 with the readings in the data boxes as 5 indicated. • The temperature meter will read T=4. 15 K as shown. • when the learner clicks on ‘click to go to lower temperature', go to step 5. • If the user clicks on ‘click here to go to higher temperature’ then go to step 3. • show the 3 slides with heading A 4, B 4, C 4 together as shown in master layout. 27

1 Step 4 contd: B 4: ”At temperature T 4 =4. 15 K” : electrons 2 3 4 5 : atoms of the lattice. Fig 11 Description of the action/ interactivity • Always keep the size of the atoms of the lattice a lot larger than the size of the electrons. • Show the two electrons(two dark blue balls surrounded by the light blue ring) moving together(paired in 2) along the path shown by the red arrow(do not show the red arrow on screen). • The lattice should bend when the cooper pairs pass through it. this effect is shown on the next slide. But in the animation on the next slide, the electrons are shown to be moving separately. . In our animation, remember to show the dark blue balls surrounded by the light blue cloud. when the electron move through the lattice, the way in which the lattice should bend is shown in the animation on the next slide. • The paired blue balls should not touch the atoms of the lattice while moving along the black arrow. • Different coloured lines for paths are given for the benefit of the animator and they should not be retained. • REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES. 28 • Include + and – signs on the gray and blue balls respectively.

Watch this link to view the source from where this animation is taken: http: //www. superconductors. org/bcs_anim. GIF 29

1 Step 4 contd: C 4: ”At temperature T 4 =4. 15 K” 2 3 4 5 Fig 12 Description of the action/ interactivity • Show the graph as given above. • Show the red spot at the place shown in the graph above. • Let it get joined to the blue spots by means of the dotted line. • The red spot appears at the temperature of this slide, at T 4=4. 15 K • Make the red dot blink to indicate that it is the current value of resistance. • Show gridlines on the graph and plot these values according to the table given on slide 35. Text to be displayed (if any) (DT) 30

1 Step 5: A 5: At temperature T 5 =4. 10 K” Gas flow control 2 3 . . Box below is not to be shown on screen 0. 00 T=4. 10 K means µV Temperature controller Zoomed in 0. 50 Liquid helium reservoir means m. A Heat exchanger Click to go to higher temperature(T) Click to go to lower temperature(T) Constant current supply Fig 13 4 Description of the action/ interactivity Text to be displayed (if any) (DT) • Show Fig 13 with the readings in the data boxes as indicated. • The temperature meter will read T=4. 10 K as shown. • Do not allow the learner to click on ‘click to go to lower 5 temperature' • If the user clicks on ‘click here to go to higher temperature’ then go to step 4. • show the 3 slides with heading A 5, B 5, C 5 together as shown in master layout. 31

1 Step 5 contd: B 5: At temperature T 5 =4. 10 K” : electrons 2 3 4 5 : atoms of the lattice. Fig 14 Description of the action/ interactivity • Always keep the size of the atoms of the lattice a lot larger than the size of the electrons. • Show the two electrons(two dark blue balls surrounded by the light blue ring) moving together(paired in 2) along the path shown by the red arrow(do not show the red arrow on screen). • The lattice should bend when the cooper pairs pass through it. this effect is shown on the next slide. But in the animation on the next slide, the electrons are shown to be moving separately. . In our animation, remember to show the dark blue balls surrounded by the light blue cloud. when the electron move through the lattice, the way in which the lattice should bend is shown in the animation on the next slide. • The paired blue balls should not touch the atoms of the lattice while moving along the black arrow. • This image is identical to the image in Fig 11. • Different coloured lines for paths are given for the benefit of the animator and they should not be retained. • REPEAT THE ANIMATION TILL THE TEMPERATURE VALUE CHANGES. 32 • Include + and – signs on the gray and blue balls respectively.

Watch this link to view the source from where this animation is taken: http: //www. superconductors. org/bcs_anim. GIF 33

1 Step 5 contd: C 5: At temperature T 5 =4. 10 K” 2 3 4 5 Fig 15 Description of the action/ interactivity • Show the graph as given above. • Show the red spot at the place shown in the graph above. • Let it get joined to the blue spots by means of the dotted line. • The red spot appears at the temperature of this slide, at T 5 =4. 10 K • Make the red dot blink to indicate that it is the current value of resistance. • Show gridlines on the graph and plot these values according to the table given on slide 35. Text to be displayed (if any) (DT) 34

Table for plotting the graph: Resistance(R(Ω)) Temperature(T(K)) 0. 15 4. 4 0. 13 4. 3 0. 10 4. 2 0. 00 4. 15 0. 00 4. 10 35

1 Interactivity and Boundary limits 2 3 4 5 In this section, you will add the ‘Interactivity’ options to the animation. Use the template in the next slide to give the details. Insert the image of the step/s (explained earlier in the Section 3) in the box, and provide the details in the table below. The details of Interactivity could be: Types: Drop down, Slider bar, Data inputs etc. Options: Select one, Multiple selections etc Boundary Limits: Values of the parameters, which won’t show results after a particular point Results: Explain the effect of the interaction in this column Add more slides if necessary 36

1 Interactivity option 1: Step No: Same as slides 18 to 35. 2 3 4 5 Interactivity type (IO 1/IO 2. . ) • Clickable action buttons. Instruction to the learner • Vary temperature. Boundary limits • In graphical representation: Plot only those values given on slide 35. • In microscopic view, for electrons: Show only 6 electons. Instructions for the animator Results and Output Only in the initial slide show a pop up next to the action buttons giving the instructions to the user. 37

INSTRUCTIONS SLIDE Self- Assessment Questionnaire for Learners • Please provide a set of questions that a user can answer based on the LO. They can be of the following types: – These questions should be 5 in number and can be of objective type (like MCQ, Match the columns, Yes or No, Sequencing, Odd One Out). – The questions can also be open-ended. The user would be asked to think about the question. The author is requested to provide hints if possible, but a full answer is not necessary. – One can include questions, for which the user will need to interact with the LO (with certain parameters) in order to answer it. 38

INSTRUCTIONS SLIDE Questionnaire for users to test their understanding • Please make sure that the questions can be answered by interacting with the LO. It is better to avoid questions based purely on recall. 39

Questionnaire 1. At what temperature does the sample enter the superconducting state? Answers: a) d)4. 10 K 4. 4 K b) 4. 3 K c) 4. 15 K 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! ” 40

Questionnaire 2. What happens to the resistivity of the sample as the temperature decreases? Answers: a) same increases b) decreases d)becomes zero c) remains 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! ” 41

Questionnaire 3. What happens to the resistivity of the sample at the transition temperature? Answers: a)increases d)becomes zero b) decreases c) remains same 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! ” 42

Questionnaire 4. What happens to the resistivity of the sample below the transition temperature? Answers: a) returns to normal c)it is zero d)increases a lot. b) decreases further 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! ” 43

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 d)becomes zero. b) decreases c)remains constant 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! ” 44

1 Questionnaire 6. What happens to the electrons when the material enters the superconducting state? 2 Answers: a)each electron flows through the sample without any resistance b)each electron flows through the sample with lot of resistance 3 4 5 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!” 45

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) 46

INSTRUCTIONS SLIDE Summary • Please provide points to remember to understand the concept/ key terms of the animation • The summary will help the user in the quick review of the concept. 47

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. 48