q

9.4.D - Superconductors


Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in Leiden and like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon.

It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood using the principles of classical physics.

In this unit you will:

  • Explain the methods used by the Bragg's to determine the crytal structure of materials
  • Describe those factors that cause resistance and affect conductivity in metals
  • Describe superconductivty and explain how it occurs
  • Describe the Meissner effect
  • Discuss some potential applications of superconductivity


Crystal Structure of Metals

The results obtained from the Bragg
spectrometer.

X-ray diffraction is a technique that was pionered by Bragg and Bragg, a father and son team, who used it to determine the distance between atoms and hence the crystal structures of NaCl, ZnS and diamond. This work was extended to include metals whose crystal structures were previously unknown. William Lawrence Bragg and his father, Sir William Henry Bragg, were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures. They are the only father-son team to jointly win. W. L. Bragg was 25 years old, making him the youngest Nobel laureate.

They designed a modified spectrometer and used it to have a parallel beam of monochromatic X-rays directed at a sodium chloride crystal. Their equipment called a Bragg X-ray spectrometer is shown in the diagram on the right. An ionisation chamber served to detect the intensity of the X-rays entering it. The prism table could be rotated through different angles to change the angle of incidence of the incoming monochromatic X-rays.

When they measured the intensity of the diffracted X-rays with respect to their incident angle, the diffracted beam was always diffacted as expected, however, it would not always be equally bright. For certain specific angles of incidence the diffracted beam was intensely bright. They obtained a graphshown on the right that indicated that:

Since a beam of X-rays consists of a bundle of separate waves, the waves can interact with one another. Such interaction is termed interference. If all the waves in the bundle are in phase, their crests and troughs occur at exactly the same position. This means that the phase difference for the two waves will be a whole number multiple of the wavelength equal to nλ where n = 1, 2, 3, 4, etc. The waves will interfere with one another under these conditions so that their amplitudes add together to produce a resultant wave that is has a larger amplitude. This is known as constructive interference.

Constructive and destructive interference.

If the waves are out of phase by a fraction rather than a whole number then destructive interference will occur and the amplitude of the waves will be reduced. In an extreme case, if the waves are out of phase by a multiple of half of a wavelngth (n/2λ), the resultant wave will have no amplitude and thus be completely cancelled.

The atoms in crystals interact with X-ray waves in such a way as to produce interference. The interaction can be thought of as if the atoms in a crystal structure reflect the waves. But, because a crystal structure consists of an orderly arrangement of atoms, the reflections occur from what appears to be planes of atoms. Let's imagine a beam of X-rays entering a crystal with one of these planes of atoms oriented at an angle of θ to the incoming beam of monochromatic X-rays (monochromatic means one colour, or in this case one discreet wavelength as produced by the characteristic spectra of the X-ray tube).

Two such X-rays are shown below, where the spacing between the atomic planes occurs over the distance, d. Ray 1 reflects off of the upper atomic plane at an angle θ equal to its angle of incidence. Similarly, Ray 2 reflects off the lower atomic plane at the same angle θ. While Ray 2 is in the crystal, however, it travels a distance of 2a further than Ray 1. If this distance 2a is equal to a whole number of wavelengths (nλ), then Rays 1 and 2 will be in phase on their exit from the crystal and constructive interference will occur.

The geometry of the interatomic spacing in a crystal. Atoms
are lined up horizontally along each of the layers.

If the distance 2a is not an integral number of wavelengths, then destructive interference will occur and the waves will not be as strong as when they entered the crystal.

Thus, the condition for constructive interference to occur is:

nλ = 2a

But, from trigonometry, we can figure out what the distance 2a is in terms of the spacing, d, between the atomic planes.

a = dsinθ

or

2a = 2dsinθ1

thus

nλ = 2dsinθn

This is known as Bragg's Law for X-ray diffraction.

What it says is that if we know the wavelength, λ, of the X-rays going in to the crystal, and we can measure the angle θ of the diffracted X-rays coming out of the crystal, then we know the spacing (referred to as d-spacing) between the atomic planes. The wavelength is determined from the results of the spectrometer. If n=1 then the wavelength is the value that produces the first spike or peak intensity in the graph of the results shown above. If n=2 then it is the wavelength to produce the second peak intensity, and so on.

d = nλ/2sinθn

Again it is important to point out that this diffraction will only occur if the rays are in phase when they emerge, and this will only occur at the appropriate value of n (1, 2, 3, etc.) and θ.

In theory, then we could re-orient the crystal so that another atomic plane is exposed and measure the d-spacing between all atomic planes in the crystal, eventually leading us to determine the crystal structure and the size of the unit cell. X-ray diffraction has allowed us to understand the structure of the crystal lattice in metals.

Click here to find out more about interference, Bragg's law and X-ray diffraction.

 

Conduction in Metals

X-ray diffraction has shown that the atoms of most metals exist in very ordered arrangements of called crystals. The crystal structure of metals can be viewed as a highly ordered lattice of positive ions surrounded by a "sea" of nearly free (delocalised) electrons and it is this that makes metals such good electrical conductors. The electrons are bound to the nucleus by the attractive force between the positive ions and the electrons. Quantum physics predicts that in pure perfectly crytalline metals there should be little or no resistance to the motion of electrons since electrons behave like waves propagating through it. That is, the perfect regularity of the crystal enables the electrons to travel unimpeded, as a wave through the crystal.

Anything that disturbs the regularity of the crytal lattice will cause electrons to collide with the positive ions and give the crystal electrical resistance. As you know, metals do show electrical resistance because they get hot after current flows through them. The resistance of metals originates from collisions of electrons with the irregularities in the crystal lattice. These irregularities usually occur in three ways:

  • Vibrations of the positive ions in the lattice

  • Impurities when foreign atoms are substituted for a metal atom in the crystal lattice

  • Defects in the crystalline structure of the lattice such as a missing atom

The crystal lattice of all metals above a temperature of 0 K consists of waves of lattice vibrations known as phonons. A phonon colliding with an electron causes it to lose energy and thus contributes to electrical resistance. Real metal wires consist of many small crystals joined together and separated by irregular boundaries. The boundaries also serve as places where electron collisions take place and thus contribute to electrical resistance.

 

Superconductivity

The relationship between resistance and temperature
for a normal conductor and a superconductor.

Superconductors are materials that have no resistance to the flow of electricity below a specific temperature. Not only have the limits of superconductivity not yet been reached but the theories that explain superconductor behavior seem to be constantly under review. In 1911, superconductivity was first observed by Dutch physicist Heike Kamerlingh Onnes of Leiden University. When he cooled mercury to the temperature of liquid helium, 4 K (-269°C), its resistance suddenly disappeared. It was necessary for Onnes to come within 4 K of the coldest temperature that is theoretically attainable to witness the phenomenon of superconductivity. Later, in 1913, he won a Nobel Prize in physics for his research in this area.

A great deal of research is still being carried out into the nature of superconductors because of their ability to conduct electricity without significant losses in energy.



A video from the BBC that provides a good introduction to superconductivity. You should watch this before you
read the rest of the material on this page.

 

Type 1 Superconductors

The Type 1 category of superconductors is mainly comprised of metals and metalloids that show some conductivity at room temperature. They require incredibye cold temperatures to slow down molecular vibrations sufficiently to facilitate unimpeded electron flow in accordance with what is known as BCS theory. BCS theory suggests that electrons team up in Cooper pairs in order to help each other overcome molecular obstacles - much like race cars on a track drafting each other in order to go faster. Scientists call this process phonon-mediated coupling because of the energy packets generated by the flexing of the crystal lattice.

Type 1 superconductors - characterized as the "soft" superconductors - were discovered first and require the coldest temperatures to become superconductive. They exhibit a very sharp transition to a superconducting state (see graph above) and "perfect" diamagnetism - the ability to repel a magnetic field completely.

Many additional elements can be coaxed into a superconductive state with the application of high pressure. For example, phosphorus appears to be the Type 1 element with the highest critical temperature but it requires compression pressures of 2.5 Mbar to reach a a critical temperature of 14-22 K.

Type 2 Superconductors

The planar layering structure of a
Type 2 superconductor.

Except for the elements vanadium, technetium and niobium, the Type 2 category of superconductors is comprised of metallic compounds and alloys. The recently discovered superconducting "perovskites" (metal-oxide ceramics that normally have a ratio of 2 metal atoms to every 3 oxygen atoms) belong to this Type 2 group. They achieve higher critical temperatures than Type 1 superconductors by a mechanism that is still not completely understood. Conventional wisdom holds that it relates to the planar layering within the crystalline structure. Although, other recent research suggests the holes of hypocharged oxygen in the charge reservoirs are responsible (holes are positively-charged vacancies within the lattice). The superconducting cuprates (copper-oxides) have achieved astonishingly high critical temperatures when you consider that in 1985 23 K was the highest known critical temperature. To date, the highest Tc attained at ambient pressure has been 138 K. One theory predicts an upper limit of about 200 K for the layered cuprate. Others assert there is no limit. Either way, it is almost certain that other, more synergistic compounds still await discovery among the high-temperature superconductors.

Type 2 superconductors, known as the "hard" superconductors, differ from Type 1 in that their transition from a normal to a superconducting state is more gradual and occurs at higher temperatures that Type 1 superconductors.

How is Superconductivity Explained?

In 1957, Bardeen, Cooper and Schrieffer (BCS) proposed a theory that explained the microscopic origins of superconductivity, and could quantitatively predict the properties of superconductors.

The fomration of a Cooper pair in a
Type 1 superconductor.

Mathematically, BCS theory is complex and relies on the formation of Copper pairs which can only be explained fully using quantum theory. For our explanation we will use a classical model that treats electrons as particles rather than waves.

Electrons passing through the lattice attract the positive ions around them, causing a distortion in thestructure of the lattice. A second electron (the Cooper pair partner) is attracted by the positive charge of the displaced ions. This second electron can only be attracted to the lattice distortion if it comes close enough before the ions have had a chance to return to their equilibrium positions. The net effect is a weak delayed attractive force between the two electrons. This short-lived distortion of the lattice is sometimes called a virtual phonon because its lifetime is too short to propagate through the lattice like a wave, as a normal phonon would.

The Cooper pairs within the superconductor are what carry the supercurrent, but why do they experience such perfect conductivity? The Cooper pair is more stable than a single electron within the lattice and as such it experiences less resistance. You should remember that one of the causes of resistance is the electron-phonon interactions in the lattice caused by the vibration of postive ions. These vibrations are dependant on temperature and below the critical temperature they would be significantly reduced. Physically, the Cooper pair is more resistant to these vibrations (phonons) within the lattice as the attraction to its partner will keep it 'on course'. Therefore, Cooper pairs move through the lattice relatively unaffected by thermal vibrations (electron-phonon interactions) when a superconductor is below its critical temperature.

Cooper pairs are continually breaking up and reforming. As long as the superconductor is cooled to very low temperatures, the Cooper pairs are able to form and stay intact for periods of time due to the reduced vibrations in the lattice. As the superconductor gains heat energy, the vibrations in the lattice become more violent and the Cooper pairs are not able to form and stay intact causing the superconductivity to diminish.

 

Meissner Effect

In the Meissner effect, the field lines of a magnet are prevented from
entering a superconductor so the magnet hovers above the
superconductor.

When a superconductor material in its normal state is placed in a magentic field, the magetic field strength inside the conductor is almost the same as the magnetic field strength outside the conductor. This is shown in the first picture in the diagram on the right.

If the material is in its superconducting state, currents flow inside the superconductor which produce magnetic fields that cancel the magnetic fields flowing through the superconductor from the outside. The external magnetic field is effectively prevented from flowing through the superconductor. The expulsion of the magnetic field from the inside of a superconductor is called the Meisner effect and is illustrated in second picture in the diagram.

If a magnet is brought near a superconductor, the field lines around the magnet are prevented from flowing through the superconductor and the magnet is levitated above the superconductor. This application of the Meisner effect is shown in the diagram above.

 

Applications of Superconductivity

Maglev Train

The levitation and propulsion system in Maglev trains.

Magnetic-levitation is an application where superconductors perform extremely well. Transport vehicles such as trains can be made to "float" on strong superconducting magnets, virtually eliminating friction between the train and its tracks. Not only would conventional electromagnets waste much of the electrical energy as heat, they would have to be physically much larger than superconducting magnets. A landmark for the commercial use of MAGLEV technology occurred in 1990 when it gained the status of a nationally funded project in Japan. The Minister of Transport authorized construction of the Yamanashi Maglev Test Line that opened on April 3, 1997. In December 2003, the MLX01 test vehicle (shown above) attained an incredible speed of 581 kph.

Although the technology has now been proven, the wider use of MAGLEV vehicles has been constrained by political and environmental concerns (strong magnetic fields can create a bio-hazard). The world's first MAGLEV train to be adopted into commercial service, a shuttle in Birmingham, England, shut down in 1997 after operating for 11 years. A Sino-German maglev is currently operating over a 30-km course at Pudong International Airport in Shanghai, China. The USA plans to have its first (non-superconducting) Maglev train in operation by late 2004 on a Virginia college campus.



A short video from WOW Labs showing how superconductivity is used to levitate
and propel trains.

Running alongside the track are walls (see photo) with a continuous series of vertical coils of wire mounted inside. The wire in these coils is not a superconductor. As the train passes each coil, the motion of the superconducting magnet on the train induces a current in these coils, making them electromagnets. The electromagnets on the train and outside produce forces that levitate the train and keep it centered above the track. In addition, a wave of electric current sweeps down these outside coils and propels the train forward (see drawings).

There are presently two different Maglev systems:

  • The electromagnetic suspension system (EMS), currently used in Germany, uses conventional electromagnets mounted under the train on structures that wrap around the guideway to provide the lift and to create the frictionless running surface. This system is unstable because of the varying distances between the magnets and the guideway. This instability needs to be monitored closely and computers have provided the control system to correct the instability. The lifting force is produced by arrays of electromagnets of like polarity in the train and the guideway which repel each other to lift the train off the track.

  • The electrodynamic suspension system (EDS), developed in Japan, uses superconducting magnets on the vehicle and electrically conductive strips or coils in the guideway to levitate the train. This does not require the same degree of computer monitoring and adjustment while travelling, but the requirement for very low temperatures means that, for the moment, this is not a practical system. The system for accelerating the train along the guideway is similar to the EMS system.

Electricity Generation and Transmission

Electric generators made with superconducting wire are far more efficient than conventional generators wound with copper wire. In fact, their efficiency is above 99% and their size about half that of conventional generators. These facts make them very lucrative ventures for power utilities. General Electric has estimated the potential worldwide market for superconducting generators in the next decade at around $20-30 billion dollars. Late in 2002 GE Power Systems received $12.3 million in funding from the U.S. Department of Energy to move high-temperature superconducting generator technology toward full commercialization.

Recently, power utilities have also begun to use superconductor-based transformers and "fault limiters". The Swiss-Swedish company ABB was the first to connect a superconducting transformer to a utility power network in March of 1997. ABB also recently announced the development of a 6.4MVA (mega-volt-ampere) fault current limiter - the most powerful in the world. This new generation of HTS superconducting fault limiters is being called upon due to their ability to respond in just thousandths of a second to limit tens of thousands of amperes of current. Advanced Ceramics Limited is another of several companies that makes BSCCO type fault limiters. Intermagnetics General recently completed tests on its largest (15kv class) power-utility-size fault limiter at a Southern California Edison (SCE) substation near Norwalk, California. And, both the US and Japan have plans to replace underground copper power cables with superconducting BSCCO cable-in-conduit cooled with liquid nitrogen. (See photo below.) By doing this, more current can be routed through existing cable tunnels. In one instance 250 pounds of superconducting wire replaced 18,000 pounds of vintage copper wire, making it over 7000% more space-efficient.

An idealised application for superconductors is to employ them in the transmission of commercial power to cities. However, due to the high cost and impracticality of cooling miles of superconducting wire to cryogenic temperatures, this has only happened with short "test runs". In May of 2001 some 150,000 residents of Copenhagen, Denmark, began receiving their electricity through HTS (high-temperature superconducting) material. That cable was only 30 meters long, but proved adequate for testing purposes. In the summer of 2001 Pirelli completed installation of three 400-foot HTS cables for Detroit Edison at the Frisbie Substation capable of delivering 100 million watts of power. This marked the first time commercial power has been delivered to customers of a US power utility through superconducting wire. Intermagnetics General has announced that its IGC-SuperPower subsidiary has joined with BOC and Sumitomo Electric in a $26 million project to install an underground, HTS power cable in Albany, New York, in Niagara Mohawk Power Corporation's power grid. The 350-meter cable, believed to be four times the length of any previously installed HTS cable, will be designed to provide more power and operate at significantly lower loss levels than other HTS installations.

Magnetic Resonance Imaging

An MRI through a human head.

An area where superconductors can perform a life-saving function is in the field of biomagnetism. Doctors need a non-invasive means of determining what's going on inside the human body. By impinging a strong superconductor-derived magnetic field into the body, hydrogen atoms that exist in the body's water and fat molecules are forced to accept energy from the magnetic field. They then release this energy at a frequency that can be detected and displayed graphically by a computer. Magnetic Resonance Imaging (MRI) was actually discovered in the mid 1940's. But, the first MRI exam on a human being was not performed until July 3, 1977. And, it took almost five hours to produce one image! Today's faster computers process the data in much less time.

Military Applications of Superconductors

Superconductors have also found widespread applications in the military. HTSC SQUIDS are being used by the US NAVY to detect mines and submarines and, significantly smaller motors are being built for NAVY ships using superconducting wire and "tape". In mid-July, 2001, American Superconductor unveiled a 5000-horsepower motor made with superconducting wire.

The military is also looking at using superconductive tape as a means of reducing the length of very low frequency antennas employed on submarines. Normally, the lower the frequency, the longer an antenna must be. However, inserting a coil of wire ahead of the antenna will make it function as if it were much longer. Unfortunately, this loading coil also increases system losses by adding the resistance in the coil's wire. Using superconductive materials can significantly reduce losses in this coil. The Electronic Materials and Devices Research Group at University of Birmingham (UK) is credited with creating the first superconducting microwave antenna. Applications engineers suggest that superconducting carbon nanotubes might be an ideal nano-antenna for high-gigahertz and terahertz frequencies, once a method of achieving zero "on tube" contact resistance is perfected.

The most ignominious military use of superconductors may come with the deployment of "E-bombs". These are devices that make use of strong, superconductor-derived magnetic fields to create a fast, high-intensity electro-magnetic pulse (EMP) to disable an enemy's electronic equipment. Such a device saw its first use in wartime in March 2003 when US Forces attacked an Iraqi broadcast facility.