PHY_10_51_V2_TG_Supercond

RECOMMENDATIONS

 on lesson “SUPERCONDUCTIVITY AND ITS APPLICATION”

For teacher it might be useful go through the physics of superconductors:

Theory of superconductors

A successful theory of superconductivity was developed in the 1950s by John Bardeen, Leon Cooper, and J. Robert Schrieffer, for which they received the Nobel Prize in 1972. This theory is known as the BCS theory. BCS theory is complex, so we summarize it qualitatively below.

In a normal conductor, the electrical properties of the material are due to the most energetic electrons near the Fermi energy. In 1956, Cooper showed that if there is any attractive interaction between two electrons at the Fermi level, then the electrons can form a bound state in which their total energy is less than 2EF. Two such electrons are known as a Cooper pair.

It is hard to imagine two electrons attracting each other, since they have like charge and should repel. However, the proposed interaction occurs only in the context of an atomic lattice. A depiction of the attraction is shown in Figure 

 Electron 1 slightly displaces the positively charged atomic nuclei toward itself as it travels past because of the Coulomb attraction. Electron 2 “sees” a region with a higher density of positive charge relative to the surroundings and is therefore attracted into this region and, therefore indirectly, to electron 1. Because of the exclusion principle, the two electrons of a Cooper pair must have opposite spin.

The BCS theory extends Cooper’s ideas, which are for a single pair of electrons, to the entire free electron gas. When the transition to the superconducting state occurs, all the electrons pair up to form Cooper pairs. On an atomic scale, the distance between the two electrons making up a Cooper pair is quite large. Between these electrons are typically about 10^6 other electrons, each also pairs with a distant electron. Hence, there is considerable overlap between the wave functions of the individual Cooper pairs, resulting in a strong correlation among the motions of the pairs. They all move together “in step,” like the members of a marching band. In the superconducting transition, the density of states becomes drastically changed near the Fermi level. As shown in an energy gap appears around E_F because the collection of Cooper pairs has lower ground state energy than the Fermi gas of no interacting electrons. The appearance of this gap characterizes the superconducting state. If this state is destroyed, then the gap disappears, and the density of states reverts to that of the free electron gas.

Figure A relatively large energy gap is formed around the Fermi energy when a material becomes superconducting. If this state is destroyed, then the gap disappears, and the density of states reverts to that of the free electron gas.

The BCS theory is able to predict many of the properties observed in superconductors. Examples include the Meissner effect, the critical temperature, the critical field, and, perhaps most importantly, the resistivity becoming zero at a critical temperature. We can think about this last phenomenon qualitatively as follows. In a normal conductor, resistivity results from the interaction of the conduction electrons with the lattice. In this interaction, the energy exchanged is on the order of k_BT, the thermal energy. In a superconductor, electric current is carried by the Cooper pairs. The only way for a lattice to scatter a Cooper pair is to break it up. The destruction of one pair then destroys the collective motion of all the pairs. This destruction requires energy on the order of 10^{-3}eV, which is the size of the energy gap. Below the critical temperature, there is not enough thermal energy available for this process, so the Cooper pairs travel unimpeded throughout the superconductor.

Finally, it is interesting to note that no evidence of superconductivity has been found in the best normal conductors, such as copper and silver. This is not unexpected, given the BCS theory. The basis for the formation of the superconducting state is an interaction between the electrons and the lattice. In the best conductors, the electron-lattice interaction is weakest, as evident from their minimal resistivity. We might expect then that in these materials, the interaction is so weak that Cooper pairs cannot be formed, and superconductivity is therefore precluded.

Additional multiple-choice questions: Superconductors

1.    A solid that offers no _________ passage of electricity is called super conductors.
a) Conductance
b) Inductance
c) Resistance
d) Impedance

2.     The phenomena of super conductors was first discovered by ___________
a) Kammerlingh Onnes
b) Neils bohr
c) Richard Smalley
d) Otto lehman

3.     Super conductors are discovered in the year _______
a) 1900
b) 1991
c) 1911
d) 1905

4.    The earliest superconductors to be studied elaborately is ________
a) Niobium alloy
b) Copper alloys
c) Steel alloys
d) Iron alloy

5.     The shifting of electrons in super conductors is prevented by _________
a) Quantum effect
b) Threshold energy level
c) Energy barrier
d) Orbitals

6.     The electrons head in ___________ direction.
a) Same
b) Different
c) Opposite to one another
d) Random

7.     The normal metal passes into super conducting state at ___________
a) High temperature
b) Low temperature
c) Critical temperature
d) No temperature

8.     Based on magnetic response super conductors are of __________ types.
a) 1
b) 2
c) 3
d) 4

9.     Ideal super conductors completely become __________ at super conducting state.
a) Diamagnetic
b) Ferro magnetic
c) Ferri magnetic
d) Para magnetic

10.          The ideal super conductors exhibit __________
a) Meissner effect
b) Mesmeric effect
c) Mesomeric effect
d) Monomeric effect

11.          The hard super conductors are those in which the ideal behaviour is seen up to a ________ critical magnetic field.
a) Higher
b) Lower
c) Moderate
d) Zero

12.          This functions as a super conductor at a critical temperature of ________
a) 30^oK
b) 60^oK
c) 90^oK
d) 120^oK

13.         The constituents of this material that is yttrium, barium and copper are in ____________
a) 1:1:1
b) 1:2:2
c) 1:2:3
d) 1:2:1

14.         Preparation of super conductors by ceramic method by homogeneous mixture of the oxides __________ in their molar ratios.
a) Y₂O₃, BaCO₃, CuO
b) Y₂O₃, BaCO₃, Cu₂O
c) Y₂O₄, BaCO₃, CuO
d) YO₃, BaCO₃, CuO

15.         Annealing the homogeneous mixture to room temperature to retain its __________
a) Composition
b) Structure
c) Its properties
d) Composition, structure and its properties

Answers with explanations:

1.    Answer: c
Explanation: A solid that offers no resistance passage of electricity is called super conductors. They are very good conductors of electricity.

2.    Answer: a
Explanation: The phenomena of super conductors were first discovered by Kammerlingh Onnes. Neils bohr given about atomic structure. Richard Smalley discovered the fullerene by laser ablation method. Otto lehman coined the name liquid crystal.

3.    Answer: c
Explanation: Super conductors are discovered in the year 1911 by Kammerlingh Onnes. He is a Dutch physicist. When he was measuring the resistivity of the mercury below 4.2K he found the super conductors.

4.    Answer: a
Explanation: The earliest superconductors to be studied elaborately are niobium alloy. The super conductivity can be understood with the help of quantum physics.

5.    Answer: a
Explanation: The shifting of electrons in super conductors is prevented by quantum energy. Electrons in normal metals shift from one energy level to another.

6.    Answer: a
Explanation: The electrons head in same direction and continue to carry current endlessly. As they are in same direction, they do not collide with each other.

7.    Answer: c
Explanation: The normal metal passes into super conducting state at critical temperature. Most of the metals act as super conductors at low temperatures.

8.    Answer: b
Explanation: Based on the magnetic response super conductors are of two types. They are ideal super conductors or hard super conductors.

9.    Answer: a
Explanation: Ideal super conductors become diamagnetic at super conducting state. The permeability is less than that of permeability in Vaccum.

10.              Answer: a
Explanation: The ideal super conductors exhibit meissner effect. The expulsion of magnetic flux from the interior of a piece of super conducting material as the material undergoes transition to super conducting phase.

11.              Answer: b
Explanation: The hard super conductors are those in which the ideal behaviour is seen up to a lower critical magnetic field beyond which the magnetization gradually changes and attains zero.

12.              Answer: c
Explanation: This functions as a super conductor at a critical temperature of 900K. Charged particles in solids can travel only in fixed directions or levels.

13.              Answer: c
Explanation: The constituents of this material that yttrium, barium and copper are in 1:2:3 molar stoichiometric ratios and hence are called as 1:2:3 super conductors.

14.              Answer: a
Explanation: Preparation of super conductors by ceramic method by homogeneous mixture of the oxides Y₂O₃, BaCO₃, CuO in their molar ratios.

15.              Answer: d
Explanation: Annealing the homogeneous mixture to room temperature to retain its composition, structure and its properties. Heating them to obtain an oxygen deficient super conductors.

Useful resources:

https://www.sanfoundry.com/applied-chemistry-questions-answers-super-conductors/

https://play.howstuffworks.com/quiz/superconductivity-quiz

https://www.brainkart.com/article/Important-Questions-and-Answers--Super-Conducting-Materials_6812/

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