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Superconductivity and thePeriodic Table System |
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- Brent Matthias, "Superconductivity and the Periodic System," in
*The Proceedings of Progress in Low Temperature Physics*, Vol. 2, edited by C.J. Gorter (1957) pp.138-150.Matthias found that

- Superconductivity is observed only in metals.
- Superconductivity is found in elements for which the number of valence electrons Z is greater than or equal to 2 and lees than or equal to 8.
- Superconductivity is found in compounds for which 2≤Z≤8, but Z may slightly less than 2 or slightly greater than 8.
- Superconductivity is not found in ferromagnetic or antiferromagnetic substances.
- Superconductivity is found only substances which have a cener of inversion in their crystal structure.
- Superconductivity is not found in substances whose crystal structure has the space group Cd I.
- For superconducting substances such that 2<Z<8 a transition temperature
T
_{C}has a scaling law relationship to the interelectron spacing parameter (r/a_{0}) where r is the interelectron spacing and a_{0}is the Bohr radius; i.e.#### T

_{C}= A·(r/a_{0})^{α}where A and α are constants.

The interelectron spacing is given by

#### r = [(3/4)πN

_{e}]^{½}where N

_{e}is the density of electrons. -
There is a different relationship between transition temperature
T
_{C}and the number of valence electrons Z for superconducting substances than there is for nonsuperconducting substances.

- J. Bardeen, L.N. Cooper and J.R. Schrieffer, "Theory of Superconductivity,"
*Physical Review*, Vol. 108 (1957) pp. 1175-1204.- The authors' model starts with free electrons in a lattice. The interaction of an electron with the lattice results in vibrations
in the lattice, called
*phonons*. If ω is the rate vibration of a phonon then its energy is hω, where h is Planck's constant. One essential result is that if two electrons interact through phonons and the energy of the phonon, hω, is less than the energy increment for the state of an electron then there is an attraction between the two electrons that leads them to form a pair. The formation of such pairs is condusive to superconductivity. - The authors state in their conclusions
Although our calculations are based on a rather idealized model, they give reasonably good account of the equilibrium properties of superconductors. When the parameters of the theory are determined empirically, we find that we get agreement with observed specific heats and penetration depths within the order of 10%, Only the critical temperature involves the superconducting phase; the other two parameters required (density of states and average velocity at the Fermi surface) are determined from the normal phase. This quantitative agreement, as well as the fact that we can account for the main features of superconductivity is convincing evidence that our model is essentially correct.

- The authors' model starts with free electrons in a lattice. The interaction of an electron with the lattice results in vibrations
in the lattice, called
- David Pines, "Superconductivity and the Periodic System,"
*Physical Review*, Vol.109, (1958), pp. 280-287.- David Pines shows that the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity explains, at least qualitatively, the regularities for superconductivity in relation to the periodic system found by Matthias.

(To be continued.)

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