‫‪2019‬‬

‫‪Superconductors‬‬
‫‪By Sina Ehsanzadeh‬‬ ‫ﺳ!ﻨﺎ اﺣﺴﺎن زادە‬
‫ﭘﺎﻳﻪ ﻫﺷﺗﻡ‬ ‫ﻣﺩﺭﺳﻪ ﻧﻣﻭﻧﻪ ﺩﻭﻟﺗﯽ ﺑﺎﻗﺭﺍﻟﻌﻠﻭﻡ‬
 Introduction
“What’s A Conductor?”
A conductor is an object that allows electricity (or electrons to be more
precise) to pass through it easily.
The conductivity of an object is defined using a variable called
“resistance”. Resistance dictates that how much energy does electricity
lose while passing the conductor (how many electrons get held back
and stay in the object). Resistance can be based on many variables like
the objects form (electricity travels weakly through liquid metals like
mercury and such). But the important one is the movement of the
atoms in the object, because if the atoms of an object move fast, they
will usually get in the way of the electrons and slow down the current
(actually the hotter the object gets, the more the atoms move. meaning
that electrical resistance is highly dependent on temperature). If the
conductor is cold, it will conduct electricity better, meaning that the
resistance of the conductor will decrease. However, if a conductor
reaches very low temperatures, depending on the conductor’s material,
it might alter into superconductive form. Superconductors are
conductors with zero electrical resistance. That means if we make an
electrical circuit using superconductors, it will not lose (or exchange)
any electrical energy.
Chapter 1
“How Is a Superconductor Made?”
To make a superconductor we must find a way to make the object
reach critical temperatures. Critical temperatures are temperatures
extremely low and can create chemical changes in the objects that
reach that temperature. Critical temperatures are different depending
on what you use. A cheap and efficient but less remaining way to make
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superconductors is using coolant liquids like liquid nitrogen-the cheaper
choice-or liquid helium-more efficient, but more expensive. Another
more advanced but extremely expensive way that is done more in
scientific research is to use light rays (in lasers and such) to slow down
the moving atoms in the object, thereby lowering the temperature of
the object. The materials are also important, since different materials
have different critical temperatures. some of the materials that have
been used to make superconductors are the following (the
temperatures in these materials are their critical temperatures in both
Kelvin and Celsius): Aluminum (1.20K = -271.95°C), Mercury (4.15K = -
269°C), Niobium (9.26K = -263.89°C), Titanium (0.39 = -272.76°C), Tin
(3.72K = -269.43°C) and Lead. Most alloy superconductors are type II
superconductors (this will be explained further).
The most commonly used superconductor is the niobium-titanium alloy
superconductor. In the year 1986, it was discovered that some cuprate-
perovskite ceramic materials have much higher critical temperatures,
around 90K. These superconductors are termed high-temperature
superconductors. Beware though, despite their name, they still have
freezing cold temperatures (90K=-183°C).
Chapter 2
“Superconductors Classifications”
There are a few variables that dictate weather an object is a
superconductor or not. These are the following classifications:
1- Response to magnetic fields: superconductors can have two types
according to this:
Type I: This type has one critical field, causing the superconductor
to have a diamagnetic effect, meaning that it expulses magnetic
fields approaching it. This means that if we have a superconductor

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 and put it on top of a permanent magnet, it will float above the
magnet! This will only remain while the material is in
superconductive form.
Type II: this type of superconductor has two critical fields. This
allows magnetic fields to partially penetrate the super conductor
through isolated points called vortices, causing it to get attracted
to the magnet.
Furthermore, multicomponent superconductors have similarities
between both types of superconductors that creates a new group
called type I-5.
2- If a superconductor is conventional (low- temperature) it can be
explained by the BCS (Bardeen-Cooper-Schrieffer) theory, or its
derivatives, or unconventional (high-temperature), otherwise.
3- Superconductors can be compared by their critical temperatures.
A superconductor is termed high temperature if it can reach
superconductive state with a coolant liquid like liquid nitrogen
(around 77K or 196.15°C), otherwise it is known as a low
temperature superconductor.
4- Materials are also used as superconductors’ classifiers.
Superconductor materials have many classes like chemical
elements (e.g. mercury or lead), alloys (such as niobium-titanium,
germanium-niobium, and niobium nitride), ceramics (YBCO and
magnesium diboride), superconducting pnictides (like fluorine-
doped LaOFeAs) or organic superconductors (fullerenes and
carbon nanotubes; though perhaps these examples should be
included among the chemical elements, as they are composed
entirely of carbon).
Chapter 3
“Superconductor Properties”

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Most of the physical properties of superconductors vary from material
to material, such as the heat capacity and the critical temperature,
critical field, and critical current density at which superconductivity is
destroyed.
On the other hand, there is a class of properties that are independent
of the underlying material. For instance, all superconductors have
exactly zero resistivity to low applied currents when there is no
magnetic field present or if the applied field does not exceed a critical
value. The existence of these "universal" properties implies that
superconductivity is a thermodynamic phase, and thus possesses
certain distinguishing properties which are largely independent of
microscopic details.
Some elementary properties of superconductors are the following:
1- Zero electrical DC resistance:
The simplest method to measure the electrical resistance of a
sample of some material is to place it in an electrical circuit in series
with a current source I and measure the resulting voltage V across
the sample. The resistance of the sample is given by Ohm's law as R
= V / I. If the voltage is zero, this means that the resistance is zero.
Superconductors are also able to maintain a current with no
applied voltage whatsoever, a property exploited in superconducting
electromagnets such as those found in MRI (Magnetic Resonance
Imaging) machines. Experiments have demonstrated that currents in
superconducting coils can persist for years without any measurable
degradation. Experimental evidence points to a current lifetime of at
least 100,000 years. Theoretical estimates for the lifetime of a
persistent current can exceed the estimated lifetime of the universe,
depending on the wire geometry and the temperature. In practice,

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 currents injected in superconducting coils have persisted for more
than 23 years (as in August 2018) in superconducting gravimeters. In
such instruments, the measurement principle is based on the
monitoring of the levitation of a superconducting niobium sphere of
mass 4 grams.
In a normal conductor, an electric current may be visualized as a
fluid of electrons moving across a heavy ionic lattice. The electrons
are constantly colliding with the ions in the lattice, and during each
collision, some of the energy carried by the current is absorbed by
the lattice and is converted into heat, which is essentially the
vibrational kinetic energy of the lattice ions. As a result, the energy
carried by the current is constantly being dissipated. This is the
phenomenon of electrical resistance and Joule heating.
The situation is different in a superconductor. In a conventional
superconductor, the electronic fluid cannot be resolved into
individual electrons. Instead, it consists of bound pairs of electrons
known as Cooper pairs. This pairing is caused by an attractive force
between electrons from the exchange of phonons. Due to quantum
mechanics, the energy spectrum of this Cooper pair fluid possesses
an energy gap, meaning that there is a minimum amount of energy
that must be supplied in order to excite the fluid. Therefore, if
energy is larger than the thermal energy of the lattice, given by kT,
where k is Boltzmann's constant and T is the temperature, the fluid
will not be scattered by the lattice. The Cooper pair fluid is thus a
superfluid, meaning it can flow without energy dissipation.
In a class of superconductors known as type II superconductors,
including all known high-temperature superconductors, an
extremely low but non-zero resistivity appears at temperatures not
too far below the nominal superconducting transition when an

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 electric current is applied in conjunction with a strong magnetic field,
which may be caused by the electric current. This is due to the
motion of magnetic vortices in the electronic superfluid, which
dissipates some of the energy carried by the current. If the current is
sufficiently small, the vortices are stationary, and the resistivity
vanishes. The resistance due to this effect is tiny compared with that
of non-superconducting materials, but must be taken into account in
sensitive experiments. However, as the temperature decreases far
enough below the nominal superconducting transition, these
vortices can become frozen into a disordered but stationary phase
known as a "vortex glass". Below this vortex glass transition
temperature, the resistance of the material becomes truly zero.
2- Meissner effect:
When a superconductor is placed in a weak external magnetic field,
and cooled below its transition temperature, the magnetic field is
ejected. The Meissner effect does not cause the field to be
completely ejected, but instead, the field penetrates the
superconductor, but only to a very small distance, characterized by a
parameter λ, called the London penetration depth, decaying
exponentially to zero within the bulk of the material. The Meissner
effect is a defining characteristic of superconductivity. For most
superconductors, the London penetration depth is on the order of
100 nm.

The Meissner effect is sometimes confused with the kind of

diamagnetism one would expect in a perfect electrical conductor:
according to Lenz's law, when a changing magnetic field is applied to
a conductor, it will induce an electric current in the conductor that
creates an opposing magnetic field. In a perfect conductor, an
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 arbitrarily large current can be induced, and the resulting magnetic
field exactly cancels the applied field.

The Meissner effect is distinct from this—it is the spontaneous

expulsion which occurs during transition to superconductivity.
Suppose we have a material in its normal state, containing a
constant internal magnetic field. When the material is cooled below
the critical temperature, we would observe the abrupt expulsion of
the internal magnetic field, which we would not expect based on
Lenz's law.
The Meissner effect was given a phenomenological explanation by
the brothers Fritz and Heinz London, who showed that the
electromagnetic free energy in a superconductor is minimized,
provided.
A superconductor with little or no magnetic field within it is said to
be in the Meissner state. The Meissner state breaks down when the
applied magnetic field is too large. Superconductors can be divided
into two classes according to how this breakdown occurs. In Type I
superconductors, superconductivity is abruptly destroyed when the
strength of the applied field rises above a critical value. Depending
on the geometry of the sample, one may obtain an intermediate
state consisting of a baroque pattern of regions of normal material
carrying a magnetic field mixed with regions of superconducting
material containing no field. In Type II superconductors, raising the
applied field past a critical value, leads to a mixed state (also known
as the vortex state), in which an increasing amount of magnetic flux
penetrates the material, but there remains no resistance to the flow
of electric current as long as the current is not too large. At a second
critical field strength, superconductivity is destroyed. The mixed
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 state is actually caused by vortices in the electronic superfluid,
sometimes called fluxions because the flux carried by these vortices
is quantized. Most pure elemental superconductors, except niobium
and carbon nanotubes, are Type I, while almost all impure and
compound superconductors are Type II.
London Moment:
Conversely, a spinning superconductor generates a magnetic field,
precisely aligned with the spin axis. The effect, the London moment,
was put to good use in Gravity Probe B. This experiment measured
the magnetic fields of four superconducting gyroscopes to determine
their spin axes. This was critical to the experiment, since it is one of
the few ways to accurately determine the spin axis of an otherwise
featureless sphere.
Chapter 4
“Superconductors Applications”
To give the most efficient answers to this category it’s best to divide
the application between the high and low temperature
superconductors:
1- Low temperature super conductors:
-Magnetic Resonance Imaging (MRI) and Nuclear Magnetic
Resonance (NMR):
The biggest application for superconductivity is in producing
the large-volume, stable, and high-intensity magnetic fields
required for MRI and NMR. This represents a multi-billion-
US$ market for companies such as Oxford Instruments and
Siemens. The magnets typically use low-temperature
superconductors (LTS), because high-temperature
superconductors are not yet cheap enough to cost-
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 effectively deliver the high, stable, and large-volume fields
required, notwithstanding the need to cool LTS instruments
to liquid helium temperatures. Superconductors are also
used in high field scientific magnets.
-Particle accelerators and magnetic fusion devices:
Particle accelerators such as the Large Hadron Collider can
include many high field electromagnets requiring large
quantities of LTS. To construct the LHC magnets required
more than 28 percent of the world's niobium-titanium wire
production for five years, with large quantities of Nb-Ti alloy
also used in the magnets for the LHC's huge experiment
detectors.
A small number of magnetic fusion devices (mostly -
tokamaks) have used SC coils. The current construction of
ITER has required unprecedented amounts of LTS (e.g. 500
tonnes, causing a 7-fold increase in the world's annual
production capacity).
-Electric power transmission:
Essen, Germany has the world's longest superconducting
power cable in production at 1 kilometer. It is a 10 kV liquid
nitrogen cooled cable. The cable is smaller than an
equivalent 110 kV regular cable and the lower voltage has
the additional benefit of smaller transformers.
2- High temperature superconductors:
-HTS-based systems:
Promising future industrial and commercial HTS applications
include Induction heaters, transformers, fault current

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 limiters, power storage, motors and generators, fusion
reactors (see ITER) and magnetic levitation devices.
-Holbrook Superconductor Project:
The Holbrook Superconductor Project is a project to design
and build the world's first production superconducting
transmission power cable. The cable was commissioned in
late June 2008. The suburban Long Island electrical
substation is fed by about 600-meter-long underground
cable system consists of about 99 miles of high-temperature
superconductor wire manufactured by American
Superconductor, installed underground and chilled with
liquid nitrogen greatly reducing the costly right-of-way
required to deliver additional power.
-Trapped field magnets:
Exposing superconducting materials to a brief magnetic field
can trap the field for use in machines such as generators. In
some applications they could replace traditional permanent
magnets.
Conclusion
The quantum phenomenon known as superconductors opened a new
field of science and allows us to reach new technology for clean energy,
saving energy by preventing electrical resistance to lower electrical
energy, healthcare and safety. This can help make a safer and cleaner
environment and protect earth from further pollution and more
catastrophic climate change that harms billions of people’s lives.

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