Page 66 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

Figure 2.30. Schematic of Cooper pair formation for a metallic superconductor. 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 (Cooper pairs). This process is referred to as condensation. At absolute zero, the condensed
Cooper pairs form a single energy state that lies kT c below the Fermi level. As a consequence of
condensation, a number of forbidden energy levels (bandgap, E g ) appear within the conduction band,
centered about the Fermi level. The energy of this bandgap corresponds to the minimum energy required
to break up a Cooper pair and release the electrons into the vacant quantum levels. At 0 < T < T c ,the
superconductor metal is in an excited state, wherein a number of electrons, primarily from broken Cooper
pairs, have been promoted across the bandgap into vacant energy states. Reproduced with permission from
Hurd, C. M. Electrons in Metals, Wiley: New York, 1975. Copyright John Wiley & Sons Limited.

vibrations and impurities cannot disrupt by scattering in the same manner as
individual conduction electrons.
In order to exhibit superconductive behavior, early Type I and II materials needed
to be cooled below a critical temperature (T c ) ranging from 0.015 (for W) to 23 K
(for Nb 3 Ge). An intriguing goal of current research is to increase the T c to room
temperature (high-temperature superconductors, HTS), which would trivialize
resistance-free applications such as power grid lines and widespread levitated trains.
In 1986, Muller and Bednorz at IBM made an important discovery toward this goal –
the first high-temperature superconductor, La 2 x Sr x CuO 4 (LSCO), with a critical
temperature of 35 K. A year later, the first material with a critical point above the
boiling point of nitrogen (77 K) was discovered, known as YBa 2 Cu 3 O 7 d (YBCO),
with a critical point of 92 K. In more recent years, the highest-temperature cuprate
based superconductors have been synthesized with a general formula M u N w Ca x-
Cu y O z (where M ¼ Y, Bi, Tl, or Hg; N ¼ Ba or Sr; u ¼ 1or2; w ¼ 2or4; x ¼ 0,
1, or 2; y ¼ 1, 2, or 3; z ¼ 3, 4, 6, 7, 9, 10, or 15). To date, the highest-temperature
superconductive materials are thallium (e.g., TlBa 2 Ca 2 Cu 3 O 9 , T c ¼ 133 K),