Soft superconductors

One interesting application of the theory developed in the preceding sections involves the superconducting state. A transition from the normal to the superconducting state occurs in some materials at a fixed temperature Tc. Such a state is characterized not only by the complete disappearance of electrical resistivity, but also by the fact that, in type I, soft superconductors at least, the magnetic induction B is zero. Since B - H + 4irM, this means that for such superconductors M - - 4jtH. 

In addition to catalytic applications, the perovskite backbone is a key component in modern high-temperature superconductive materials. By definition, a superconductor exhibits no resistance to electrical conductivity, and will oppose an external magnetic field, a phenomenon referred to as the Meissner effect (Figure 2.19). 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. 

The preceding material may be used to characterize the thermodynamics of transitions from the normal to the superconducting state. This transformation takes place for a limited class of materials at a particular temperature Tc, currently below 140 K. For soft superconductors of type I this state is marked by a complete disappearance of electrical resistivity and by the fact that at moderate values the magnetic induction B = M. + AnH vanishes within the bulk of the sample, so that for such materials M = —AnH. However, as the field is increased a critical magnetic field He is reached beyond which the material reverts back to its normal state. In first approximation He depends only on temperature according to the relation... 

FIGURE 1. Physical properties of superconductors, (a) Resistivity vs. temperature for a pure and perfect lattice (solid line) impure and/or imperfect lattice (broken line), (b) Magnetic-field temperature dependence for Type-I or soft superconductors, (c) Schematic magnetization curve for hard" or Type-II superconductors. 

Fig. 3. Infinitely long soft-superconductor solenoid (ideal case).

It is of interest to apply the Chandrasekhar-Hulm model to these experiments. For the short-sample quenching current of a soft superconductor in a transverse homogeneous field, Silsbee s rule yields... 

Soft superconductors in general show an increase in critical temperature [ ] when strained in one direction. However, elastic torsion seems to have no influence on the critical field [ ]. Past work [ ] has shown that superconducting surface layers of NbsSn on niobium and core wires [ ] under pull, torsion, and uniaxial compression exhibit a decrease in critical... 

The magnetization curve expected for a superconductor under the conditions of the Meissner experiment is sketched in Fig. 3.25a. This applies quantitatively to a specimen in the form of a long solid cylinder placed in a longitudinal magnetic field. Pure specimens of many materials exhibit this behavior and are labeled Type I superconductors or, formerly, soft superconductors. The values of are too low for Type I superconductors to have any useful technical application in coils for superconducting magnets. 

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