Superconductors

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Superconductors

Presented by Onur KARAGÖZ

Content


Meissner Effect


Quantum Effects


Transition to Zero Resistivity


“Super” conductivity?


Superconductivity
, discovered in 1911 by
Heike Kamerlingh Onnes, is a phenomenon
occurring in certain materials at extremely low
temperatures.


It was not yet discovered whether the
resistance remains 0, or it is exactly 0 due to
experimental results. So we name it “super”
not perfect conductor.

Meissner Effect

Meissner Effect

http://www.superlife.info/en/book/index.html

http://www.superlife.info/en/book/index.html

The hallmark of superconductivity is expulsion of the
internal B field in an applied magnetic (H) field, unless the
applied field exceeds a critical level.


London Equation

A bulk superconductor is shielded completely from an
external magnetic field by a supercurrent that flows within
the penetration depth (
λ
) at the surface.

m=electron mass

e=electron charge

n
e
=concentration

μ
o
=permeability
in vacuum

London Equation


n
e
, the concentration is given by the following equation:

ρ
=conductor’s
mass density

N
A
=Avogadro’s
number

W
A
=Atomic
weight

Quantum Effects


Cooper Pairs


Flux Quantization

Cooper Pairs

Cooper pairs can have the same energy level.

The mediator that holds the two electrons is a
phonon.

Flux Quantization


Deaver and Fairbank did experiments with a
tiny superconducting cylinder made by
electroplating tin on a copper wire. They found
magnetic flux quantized in units of


such that the flux through the cylinder was
given by


Related with the Type II superconductors in
the mediated phase that creates vortices.

Transition to Zero Resistivity


Critical


Temperature


Magnetic Field


Current Density


Superconductor Types


Type I (soft)


Type II (hard)


Critical Temperature

Critical Magnetic Field H
c

http://hyperphysics.phy
-
astr.gsu.edu/hbase/solids/scbc.html#c2

Critical Current Density J
c

http://www.users.qwest.net/~csconductor/Experiment_Guide/Critical%20Current%2
0Density
-
1.htm

T
c

H
c

and J
c

of YBCO

BCS Theory


Bardeen, Cooper, and Schrieffer


A key conceptual element in this theory is the
pairing of electrons close to the
Fermi level

into
Cooper pairs

through interaction with the
crystal lattice.


This pairing results from a slight attraction
between the electrons related to lattice
vibrations; the coupling to the lattice is called a
phonon

interaction.


Bandgap


The BCS theory predicts a bandgap of


Ginzburg
-
Landau Theory


Coherence length

is a measure of the
shortest distance over which superconductivity
may be established or destroyed without
excessive cost in energy.


Penetration depth


Types of Superconductors


Type I : Metals and metalloids


Type II: Metal alloys, cuprates etc.

Type I


Always rather pure metallic elements


Easily quenched in magnetic fields less than
~1000 gauss


Must exclude virtually all of an applied
magnetic field to remain superconducting

Type I

http://www.superlife.info/en/book/victor/Image9.jpg

Type I


Nb3Sn


Niobium stannide,
Nb3Sn, is a well
-
established
superconductor of the
A15 (Cr3Si) structure.

A15 structure

http://alpha.mems.duke.edu/aiqin/sdarticle1.pdf

Type II


Alloys or compounds (Niobium and vanadium
are exceptions)


They are able to retaintheir superconductive
characteristics in rather intense magnetic
fields.


Rather than using the energy required to
completely expel magnetic fields, the fields are
confined to an internal array of normal
-
state
flux tubes called"vortices" since they are
surrounded by a circulating supercurrent.


They are capable of carrying relatively large
current densities.

Type II

Three
critical
magnetic
fields

H
c1

H
c2

H
c3

http://www.superlife.info/en/book/victor/Image10.jpg

YBCO


YBa
2
Cu
3
O
7
-
x

was discovered to have a Tc of
92

K in 1987.


This was the first time that superconductivity
had been observed at temperatures which
could be conveniently attained with liquid
nitrogen, and so created great excitement at
the prospect of low
-
cost applications of
superconductivity.


YBCO



There are two
CuO layers.



CuO
2
layers are
responsible for
the
superconductivity

http://cst
-
www.nrl.navy.mil/lattice/struk.picts/hightc/1212c.s.png

YBCO


The only known stable four
-
element compound with a
T
c
above 77 K.


Includes neither toxic
elements nor volatile
compounds


Easy to make single
-
phase
YBCO


Less anisotropic than other
HTS materials, carries higher
current densities at higher
magnetic fields


http://www.tkk.fi/Units/AES/projects/prlaser/ybco.jpg

BSCCO

(Bismuth strontium
calcium copper oxide)


Bi
2
Sr
2
CuO
x



BSCCO can have 1, 2, or
3 CuO planes, with
Tc

increasing with the
number of planes.


Bismuth can also be
replaced with thallium or
mercury, which results in
the highest
Tc

material
known (142K).

MgB
2

MgB
2


Magnesium diboride, MgB2, was first reported
to be superconducting in 2001.


It is superconducting at a temperature of 38
-
40

K and it is an intermetallic material.


Why MgB
2
?


Cost


Lower anisotropy unlike cuprates


Larger coherence lenghts


Transparency of the grain boundaries to current flow


References


Solid State Physics, J.R. Hook & H.E. Hall,Wiley,2000


Superconductivity, J.B. Ketterson & S.N. Song, Cambridge,1999


Superconductivity Fundamentals and Applications, W. Buckel & R.
Kleiner, Wiley,2004


http://alpha.mems.duke.edu/aiqin/sdarticle1.pdf


http://www.ewh.ieee.org/tc/csc/News/MgB2Feb2002.html


http://www.tkk.fi/Units/AES/projects/prlaser/material.htm


http://hyperphysics.phy
-
astr.gsu.edu/hbase/solids/supcon.html#c1


http://www.msm.cam.ac.uk/ascg/materials/mgb2.php


http://hoffman.physics.harvard.edu/research/SCmaterials.php


http://www.superconductors.org/INdex.htm


http://www.futurescience.com/manual/sc1000.html#C


http://www.superlife.info/en/book/index.html