Superconductivity

Superconductivity

---

In the age of technology, with smaller and smaller electronic components being used in a growing number of applications, one pertinent application of mathematics and physics is the study of superconductivity. All elements and compounds possess intrinsic physical properties including a melting and boiling point, malleability , and conductivity. Conductivity is the measure of a substance's ability to allow an electrical current to pass from one end of a sample to the other. The measurement of resistivity (the inverse of conductivity) is called resistance and is measured in the unit ohms (Ω).

Ohm's Law

An important and useful formula in science is called Ohm's Law, E = IR. E is voltage in volts, I is current in amperes, and R is resistance in ohms. To visualize this, imagine a wire conducting electrons along its length, like a river flowing on the surface of the wire. The resistance acts like rocks in the river, slowing the flow. Current is equivalent to the amount of water flowing (or the number of electrons per unit time), and voltage is equivalent to the slope of the river. As the water hits the rocks, it splashes up and away. This is equivalent to resistance generating heat in a circuit. All normal materials have some sort of resistance, thus all circuits generate heat to a greater or lesser degree.

An interesting thing happens as the temperature of the wire changes. As the temperature elevates, the resistance increases; as the temperature lowers, the resistance decreases, but only to a point, then it goes back up again. In 1911 Kamerlingh Onnes discovered that mercury cooled to 4 kelvin (4K) (that is −269.15°C , about −453° F) suddenly loses all resistance. He called this phenomenon superconductivity. Superconductivity is the ability of a substance to conduct electricity without resistance. If applied to Ohm's Law, a voltage (E ) is applied, the current (I ) should continue on its own if the voltage is then removed and the resistance is zero. This makes sense in terms of Ohm's Law, as E (0) = I (X ) ×R (0). When tested, it was found that this does indeed take place, with the current value (X ) dropping over time as a function of the voltage applied, with this current being referred to as a Josephson current.

At the time Onnes discovered superconduction , it was believed that superconductivity was simply an intrinsic property of a given material.* However, Onnes soon learned that he could turn superconduction on and off with the application of a large current, or strong magnetic field. Other than a lack of resistance, it was believed for many years that superconducting materials possessed the same properties as their normal counterparts. Then in 1933, it was discovered that superconducting materials are highly diamagnetic (that is, highly repelled by and exerting a great influence on magnetic fields), even if their normal counterparts were not. This led one of the discoverers, W. Meissner, to make scientific predictions regarding the electromagnetic properties of superconductors and have his name assigned to the effect, the Meissner effect.

*The zero point of the kelvin scale is the temperature at which all molecular motion theoretically stops, sometimes called absolute zero.

Meissner's predictions were confirmed in 1939, paving the way for further discoveries. In 1950 it was demonstrated for the first time that the movement of electrons in a superconductor must take atomic vibrational effects into account. Finally in 1957 a fundamental theory presented by physicists J. Bardeen, Leon Cooper, and J. R. Schrieffer, called BCS theory, allowed predictions of possible superconducting materials, and the behavior of these materials.

BCS Theory

BCS theory explains superconductivity in a manner similar to the river of electrons example. When the material becomes superconducting, the electrons become grouped into pairs called Cooper pairs. These pairs dance around the rocks (resistance), like two people holding hands around a pole. This symmetry of movement allows the electrons to move without resistance.

The first superconductors were experimental rarities, for research only. During the first 75 years of research, the temperature at which materials could be made to superconduct did not rise very much. Before 1986 the highest temperature superconductor worked at a temperature of 23 K. Karl Muller and Johannes Bednorz found a material that had a transition temperature (the temperature where a material becomes superconducting) of nearly 30 K, in 1986. Their research and discovery allowed even higher temperature superconductors to be made of ceramics containing various ratios of, usually, barium or strontium, copper, and oxygen. These ceramics allowed superconductivity to be done at liquid nitrogen temperatures (77 K)— a much more obtainable temperature than 4.2 K for liquid helium. However, ceramics are difficult to produce, break easily, and do not readily lend themselves to mass production. The newest generation of superconductors are nearing −148°C (125 K), which is the high temperature record as of 1998.

Superconductivity already touches the world, with its use in MRI (magnetic resonance imaging) magnets, chemical analytical tools such as NMR (nuclear magnetic resonance) spectroscopy, and unlimited electrical and electronic uses. If a high temperature superconductor could be mass produced cheaply, it would revolutionize the electronics industry. For example, one battery could be made to last years. In the future, people may look back at this basic research and compare it to the first discovery of fire.

see also Absolute Zero; Temperature, Measurement of.

Brook E. Hall

Bibliography

Mendelssohn, K. The Quest for Absolute Zero: The Meaning of Low Temperature Physics, 2nd ed. Boca Raton, FL: CRC Press, 1977.

Shachtman, T. Absolute Zero and the Conquest of Cold. New York: Houghton Mifflin Co., 1999.