Page 64 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

It should be noted that the Miessner effect does not completely repel H; that is, the
field is able to penetrate the surface of the superconductor to a depth known as the
London penetration depth, l. For most superconductors, l is on the order of 100 nm
decaying exponentially beyond this region toward the bulk of the superconductor
structure.
The Meissner effect should be distinguished from the diamagnetism exhibited by
a perfect electrical conductor (Figure 2.28b). According to Lenz’s Law, when a
magnetic field is applied to a conductor, it will induce an electrical current in the
conductor that creates an opposing magnetic field. In a perfect conductor, a large
current can be induced; however, the resulting magnetic field will exactly cancel
the applied field. In contrast, the Meissner effect is the spontaneous repulsion
of the applied magnetic field that occurs only once the transition to superconductiv-
ity has been achieved.
Many pure transition metals (e.g., Ti, Zr, Hf, Mo, W, Ru, Os, Ir, Zn, Cd, Hg) and
main group metals (e.g., Al, Ga, In, Sn, Pb) exhibit superconductivity, many only
when exposed to high-pressure conditions. These materials are referred to as Type I
or soft superconductors.
Binary and ternary alloys and oxides of these elements, as well as pure V, Nb, Gd,
and T c are referred to as Type II or high-field superconductors. In contrast to Type I,
these materials exhibit conductive characteristics varying from normal metallic to
superconductive, depending on the magnitude of the external magnetic field. It is
noteworthy to point out that metals with the highest electrical conductivity (e.g., Cu,
Au) do not naturally possess superconductivity.
Although superconductivity was first discovered in 1911 for supercooled liquid
mercury, it was not until 1957 that a theory was developed for this phenomenon. [26]
Proposed by Bardeen, Cooper and Schrieffer, the BCS theory purports that at a
certain critical temperature, T c , the electrons within thermal energy (kT c ) of the
Fermi level are able to correlate their motion in pairs, referred to as Cooper pairs.
It is not readily apparent why this should occur, since electrons are mutually
repulsive due to like negative charges. The formation of Cooper pairs is thought to
result from electron–phonon (i.e., lattice vibration) coupling. That is, an electron
moving through the lattice attracts the positively-charged nuclei of the lattice atoms,
causing them to be distorted from their original position. This creates a small
attractive force toward another electron of opposite spin, whose motion becomes
correlated with that of the original electron (Figure 2.29a). The primary experimen-
tal evidence that supports the concept of phonon-facilitated Cooper pair formation is
known as the isotope effect (Figure 2.29b). That is, the linear inverse relationship of
critical temperature and mass of lattice atoms suggests that electron/lattice coupling
interactions are a key component to superconductivity.
Whereas individual electrons are fermions (1/2 spin) and must obey the Pauli
exclusion principle, Cooper pairs exhibit boson-like properties and are hence able
to condense into the same energy level. At absolute zero, the condensed Cooper
pairs form a single energy state that lies kT c below the Fermi level (Figure 2.30).
As a consequence of condensation, a number of forbidden energy levels appear