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Superconductivity 2012
Demonstration What did we see? High-Tc
materials (How to make superconductors) Some
applications and important properties

Department of Physics, Umeå University, Sweden
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How do we show superconductivity?
Superconductors 1. have an electrical
resistivity that is exactly zero, 2. refuse
magnetic fields to enter the superconducting
volume.
(Lab experiment) Let's try!
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Meissner-Ochsenfeld effect
Perfect metal Superconductor
Room temperature Room temperature, with magnetic
field At low temperature (TltTc), after cooling
in a constant magnetic field
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"Perfect conductor" effect
Perfect metal Superconductor
Room temperature Low temperature (TltTc)without
magnetic field After applying a magnetic field
at low temperature (TltTc)
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Why is the levitation stable?
When you balance things on soft springs the
situation is usually unstable. So why doesn't the
magnet simply fall off? Because the field can
penetrate! Take a ceramic
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Why is the levitation stable?
Although the grains are superconducting, the
boundaries are effectively thin "normal" films.
Some field lines can find ways to penetrate the
ceramic, but then get "locked" in place - they
cannot move without crossing grains!
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Two types of superconductors Types I and II
Different behaviours in magnetic fields
(red) Weak B-fields are always repelled, by
both types strong fields destroy the
superconductivity in type I, but penetrate type
II in "vortex tubes" containing one flux quantum
each!
Type I Type II
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Superconducting materials
"Classical" superconductors Metals and
alloys! Hg 4.2 K Discovered by Heike Kammerling
Onnes in 1911 (Nobel Prize 1913) Pb 7.2
K Nb 9.2 K (0.2 T - type II element!) NbTi 9.8
K 14 T (The "standard" superconductor) NbN 16.1
K 16 T (used in thin film applications) Nb3Sn
18 K 24 T (expensive and difficult to use)
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High Transition Temperature Superconductors
(HiTcs)

MgB2
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High Transition Temperature Superconductors
(HiTcs)

Some representative heads of families of
HiTcs La2-xSrxCuO4 38 K (Bednorz
Müller, 1986) YBa2Cu3O7-d
92 K (Wu Chu, 1987) Bi2Ca2Sr2Cu3O10
110 K Tl2Ba2Ca2Cu3O10 125 K HgBa2Ca2Cu3O8
135 K
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High Transition Temperature Superconductors
(HiTcs)
Quite complicated structures! One of the simplest
is YBa2Cu3Ox, "Y-1-2-3"

The basic structure is tetragonal, with copper
and oxygen forming a framework into which we
insert Ba and Y. The formula is now YBa2Cu3O6,
and this material is NOT superconducting!
Department of Physics, Umeå University, Sweden
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High Transition Temperature Superconductors
(HiTcs)
Quite complicated structures! One of the simplest
is YBa2Cu3Ox, "Y-1-2-3"

The basic structure is tetragonal, with copper
and oxygen forming a framework into which we
insert Ba and Y. To get a superconducting
material we must add more oxygen, to obtain
YBa2Cu3O7!
Department of Physics, Umeå University, Sweden
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High Transition Temperature Superconductors
(HiTcs)
Quite complicated structures! One of the simplest
is YBa2Cu3Ox, "Y-1-2-3"

CuO chain Ba spacer CuO plane Y spacer CuO
plane Ba spacer CuO chain
These are the metallic, superconducting parts!
To some extent, more CuO planes mean higher Tc!
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High Transition Temperature Superconductors
(HiTcs)

How to make YBa2Cu3Ox, "Y-1-2-3" 1. Mix and
grind Y2O3, BaCO3 and CuO for a long time. 2.
Heat in an oven at 900-925 oC for at least 1
hour. 3. Crush, re-grind, and repeat 2. a few
times. 4. Press into a cake, then heat in pure
oxygen gas at 450 oC for at least 24 hours. 5.
Time to test for superconductivity!
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High Transition Temperature Superconductors
(HiTcs)

Higher values for Tc can be found for other
materials, based on Bi, Hg or Tl. These are also
layered, often with many parallel internal layers
of CuO Tl2Ba2CuO6 Tl-2201 (single CuO) 85
K Tl2Ba2CaCu2O8 Tl-2212 2 layers 105
K Tl2Ba2Ca2Cu3O10 Tl-2223 3 layers 125 K (Bi-2223
? 110 K, Hg-1223 ? 135 K)
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A new star MgB2
Superconductivity in MgB2 was discovered in 2001
with Tc 39 K, the highest for any "classical"
superconductor.

The material is cheap, easy to handle,
non-poisonous, and easily formed into wires or
films/tapes. Problem The practical critical
field seems to be limited to 3.5 T.
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An even newer star iron arsenides
In 2008, another type of layered, exotic
superconductors, based on iron and arsenic, was
discovered.

Takahashi et al., Nature 453, 376 (2008)
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An even newer star iron arsenides
In 2008, another type of layered, exotic
superconductors, based on iron and arsenic, was
discovered. Another family

is BaxKyFe2As2. Critical temperatures up to above
55 K have been reported when changing the La to
heavier rare earths. Again, the material is cheap
and fairly easy to handle, but As is clearly
poisonous!
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Applications for superconductors
There are basically two types of
applications Power circuits and
electronics/measurements. Most practical
applications use type II superconductors. Existing
and future commercial devices Power
transmission components, power storage devices,
electric motors and generators, frictionless
bearings, permanent magnets and electromagnets,
voltage standards, fast computers and
electronics, microwave filters, .........
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Applications for superconductors
In electronics, one possible application is in
fast computers. Clock pulses must be synchronized
in a computer, but at 3 GHz light travels only 10
cm
during one clock pulse! Shrinking a computer
means more concentrated heating, killing the CPU.
The obvious solution is a cool superconducting
computer!
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Electronics and measurements tunnelling
Tunneling between two superconductors (SIS) can
be used as the basis for many devices. In
principle, both electrons and pairs can tunnel
through a Josephson junction, so the real
behaviour can be either bistable (logic 1/0!) or
continuous.

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Electronics and measurements the SQUID
A particularly useful device is the SQUID
Superconducting QUantum Interference Device or
With a SQUID it is possible to routinely measure
magnetic fields down to well below 10-16 T!
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Electronics and measurements the SQUID

The SQUID can be used for measurements (as a
sensor). Superconducting loop Josephson
junctions, called weak links External
connections
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Electronics and measurements the SQUID

Each Josephson junction has a maximum
supercurrent I I0 sin g, so the maximum
current that can run through the device is 2I0.
2I0
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Electronics and measurements the SQUID

If we apply a very weak external magnetic field,
a circulating shielding current will appear and
no field will exist inside the loop! The external
current must decrease to avoid exceeding the
maximum supercurrents in the junctions.
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Electronics and measurements the SQUID

When the magnetic field corresponds to exactly ½
magnetic flux quantum inside the ring, the
circulating current has its maximum and the
external current its minimum value.
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Electronics and measurements the SQUID

If the field increases further, one flux quantum
is admitted through a weak link, and the
circulating current reverses! It can easily be
shown that the external current is a periodic
function Imax 2I0cos(pF/F0)
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But how do you make ceramic "wires"?
There are two ways 1. Thin films on a metal or
ceramic substrate 2. "Powder-in-tube" technology
Stainless Deposition of
Oxygen treatment Storage steel
band ceramic film
in hot oven
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But how do you make ceramic "wires"?
There are two ways 1. Thin films on a metal or
ceramic substrate 2. "Powder-in-tube" technology
Fill a silver tube with superconductor powder,
then draw to desired shape, then heat treat
("anneal").
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But how do you make ceramic "wires"?
The "powder-in-tube" method is simlar to what you
do to "classical" superconductors
Basic procedure - Make a Cu cylinder, - make a
lot of holes along axis, - fill the holes with
superconducting rods, - draw the whole cylinder
to wire, as if it were massive Cu! This procedure
works well with Nb-Ti, which is soft and ductile
like copper!
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But how do you make ceramic "wires"?
All superconductor wires have similar internal
"multi-strand" structures!
NbTi wire
High-Tc (BiSSC) wires
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Using type II superconductors
An obvious application for a superconductor is to
transport electric current. What happens to
electrons in a B-field ?
Let us remember two laws Fm qv ? B
("Maxwell") ? F 0 ("Newton")
B-field
There will be a force on the magnetic field lines!
Current
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Using type II superconductors
Is this a problem ? A moving field ? changing
flux but - d?/dt E !
This gives two problems 1. A voltage appears
along the current flow "resistance"! 2. This
causes dissipation of heat, since P U?I
B-field
Current
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Using type II superconductors
Is this a problem ? A moving field ? changing
flux but - d?/dt E !
This gives two problems 1. A voltage appears
along the current flow "resistance"! 2. This
causes dissipation of heat, since P U?I
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Using type II superconductors
Or, if we measure voltage as a function of
applied current at constant temperature
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Using type II superconductors
Conclusion We want to keep the flux lattice
fixed in space! How do we do this? Flux lines
prefer to go through non-superconducting regions,
because it requires energy to create a vortex
tube! So, we should insert impurity particles
into the superconductor!
This method is called flux pinning.
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Using type II superconductors
You have already seen a magnet fly ! You can also
make a really good magnetic bearing, or freeze
in a field to make a permanent magnet with a
field which you can shape exactly as you want it!
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Using type II superconductors
BUT Flux pinning also gives problems There is
afriction force that keeps them in place, and
because J ? ? X B, dBz/dx ? Jc everywhere inside
a type II superconductor! Increasing external
field
Department of Physics, Umeå University, Sweden
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Using type II superconductors
BUT Flux pinning also gives problems There is
afriction force that keeps them in place, and
because J ? ? X B, dBz/dx ? Jc everywhere inside
a type II superconductor! Increasing external
field
Department of Physics, Umeå University, Sweden
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Using type II superconductors
BUT Flux pinning also gives problems There is
afriction force that keeps them in place, and
because J ? ? X B, dBz/dx ? Jc everywhere inside
a type II superconductor! Decreasing external
field
Department of Physics, Umeå University, Sweden
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Using type II superconductors
BUT Flux pinning also gives problems There is
afriction force that keeps them in place, and
because J ? ? X B, dBz/dx ? Jc everywhere inside
a type II superconductor!
This leads to a magnetic hysteresis, and to
energy loss ( heating!). It can be shown that
the loss is proportional to the thickness a of
the superconductor!
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A possible novel application
The first practical application for high-Tc
materials in power circuits is likely to be
something that cannot be made without
superconductivity. One such example is the
superconducting current limiter
Consider a standard transformer (which you can
find in any electronic device, at home or
here) U1/U2 N1/N2 I2/I1, where 1 means
"input" side, 2 "output" side, and N is the
number of wire turns!
http//www.yourdictionary.com
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A possible novel application
The first practical application for high-Tc
materials in power circuits is likely to be
something that cannot be made without
superconductivity. One such example is the
superconducting current limiter
Suppose we make a transformer with N2 1 (a
single turn). If we short-circuit the output,
U20, then U1 NU2 0, for all
currents! Usually this is just stupid, but what
if we make the secondary one turn of
superconducting wire?
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A possible novel application
Superconducting current limiter
Primary current I1
I2 N I1 if the coil superconducts
U1 U2 0, and P UI 0 ! However, whenever
I2 gt Ic the secondary turns normal and R1
U1/I1 N2U2/I2 N2R2 ! Because N can be made
large and high-Tc materials have very large
normal resistivities, this works as a "fuse"!
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A possible novel application
Superconducting current limiter
N1 500 N2 1 Ic 85 A at 77 K (measured!) Tc
110 K (Bi-2223)
Department of Physics, Umeå University, Sweden