Type-II superconductors

Properties of type II superconductors (pure metals) 

Metal Crystal lattice structure (Strukturbericht, Pearson, space group) Critical temperature (.TJK) Critical magnetic field (HyA.m- ) Debye temperature (VK) Electronic molar heat capacity (ymJ.mof. K ) 

Material Crystal lattice structure Critical Experiment Critical magnetic fields  

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High performance sealants, 22 28 High phosphorus alloys, corrosion performance of, 9 710-711 High pinning Type II superconductors, 23 High pressure apparatus, 13 413 High pressure applications, 13 436-448 in commercial products, 13 436-438 in inorganic chemistry reactions, 13 440—448... 

Metallic taste, 11 565 Metallic tungsten, 25 374 Metallic Type II superconductors, critical current density value in, 23 822 Metallic vanadates, 25 513 Metalliding, 15 251 Metalliferous oxides deposits of, 17 689-690 in ocean basins, 17 693 Metalliferous sulfide deposits, 17 690-691 Metalliferous sulfides, in ocean basins, 17 693-694... 

In addition to a critical temperature and critical field, all superconductors have a critical current density, Jc, above which they will no longer superconduct. This limitation has important consequences. A logical application of superconductors is as current-carrying media. However, there is a limit, often a low one, to how much current they can carry before losing their superconducting capabilities. The relationship between Jc, He, and Te for a Type II superconductor is shown in Figure 6.32. Notice that the Hc-Tc portion of this plot has already been presented in Figure 6.10 for a Type I superconductor. 

Figure 6.32 The relationship between temperature, magnetic field and current density in a Type II superconductor. Reprinted, by permission, from W. Callister, Materials Science and Engineering An Introduction, 5th ed., p. 699. Copyright 2000 by John Wiley Sons, Inc.

Figure 6.9 Properties of superconductors (a) resistivity-temperature curve for a pure (solid) and an impure (broken) superconductor (b) magnetization as a function of external field for type I superconductor (c) magnetization curve for a type II superconductor.

Here we will summarize, from the previous subsections as well as from literature, some typical properties and representative parameters (see table 6) of the superconducting state of YNi2B2C and LuNi2B2C where completeness is not attempted. These materials are usually clean-limit type II superconductors. However by substitutional disorder on the rare earth site in (Y,Lu)Ni2B2C or on the transition-metal site in Lu(Ni,Co)2B2C the residual resistance ratio RRR = p(300 K)/p(Tc), where p(T) is the normal state resistivity, and the mean free path / of the electrons in the normal state can be considerably reduced... 

The range of coherence follows naturally from the BCS theory, and we see now why it becomes short in alloys. The electron mean free path is much shorter in an alloy than in a pure metal, and electron scattering tends to break up the correlated pairs, so dial for very short mean free paths one would expect die coherence length to become comparable to the mean free path. Then the ratio k i/f (called the Ginzburg-Landau order parameter) becomes greater than unity, and the observed magnetic properties of alloy superconductors can be derived. The two kinds of superconductors, namely those with k < 1/-/(2T and those with k > l/,/(2j (the inequalities follow from the detailed theory) are called respectively type I and type II superconductors. 

Conductor-Superconductor Transition When some metals or compounds are cooled below a certain temperature, their electrical resistance drops abruptly to zero. This temperature is referred to as the superconducting transition temperature. These materials are classified into two categories, type I or type II superconductors, depending upon how a bulk sample behaves in an external magnetic field. In the absence of an external magnetic field, the (superconductor + normal) transition is continuous in both types of superconductors. When a magnetic field is applied, the transition becomes first order in type I superconductors, but remains continuous in the type II superconductors. 

The behavior of type II superconductors in an applied field is more complicated. This behavior is illustrated in Figure 13.16b. Below a certain field strength 2 c, i, the magnetic field lines are repelled, and the material is superconducting. From 2 c, i to a second critical field strength magnetic field lines are able to penetrate the type II material in its superconducting state... 

Figure 13.16 Magnetization verses applied magnetic field for (a) a type I superconductor and (b) a type II superconductor. For the type I superconductor, the magnetic flux does not penetrate the sample below 9 Cc where the sample is a superconductor. Above rMc, the sample is a normal conductor. For the type II superconductor, the magnetic field starts to penetrate the sample at 3Cc, 1, a magnetic field less than rXc, the thermodynamic critical field. Superconductivity remains in the so-called vortex state between 9 c and Ci2 until WCt2 is attained. At this magnetic field, complete penetration occurs, and the sample becomes a normal conductor.

Soft metallic elements such as Al, In, Pb, Hg, Sn, Zn, Tl, Ga, Cd, V and Nb are type I superconductors. Alloys and chemical compounds such as Nb3Sn, V3Ga, and lZa3In, and some transition elements, are type II superconductors. Type II substances generally have a higher Tc than do type I superconductors. The recently discovered transition metal oxide superconductors have generated intense interest because they are type II superconductors with very high transition temperatures. Table 13.1 summarizes Tc for selected superconductors. 

The response for low doping closely follows a two-fluid type behaviour for low hole doping but which deviates from this at higher doping levels. Schneider and Keller [26] analysed Muon spin relaxation rate o- data and noted universal trends in the reduced transition temperature T for a series of extreme type II superconductors which includes the cuprates and the reduced muon spin relation rate [Pg.300]

The neodymium based plumbides NdCuPb, NdAgPb, and NdAuPb (Oner et al., 1999) show antiferromagnetic ordering at Tn = 14.6,12.6, and 18.9 K, respectively. These samples revealed an additional transition to a superconducting state at transition temperatures of 7.25, 7.00, and 6.85 K, respectively. The nature of these transitions is still not clear. Due to hystereses behavior of the magnetization of NdAgPb at 5 K, the authors claimed that NdAgPb is a type II superconductor. 

Some controversy also exists whether ZrBi2 is actually a type-II superconductor (Daghero et al., 2004 Gasparov et al., 2006). Tsindlekht et al. (2004) conclude that it is an unusual marginal superconductor near the border between type-I and type-II, while Wang and coworkers (Wang et al., 2005) report that there is a crossover from type-I superconductivity near Tc to type-II/I (as defined by Auer and Ullmaier (1973)) below Tc/2. 

The non-local effects can result in an anisotropy of Hc2 microscopically due to the anisotropy of the pairing state (Shiraishi et al., 1999) or directly to the anisotropy in the shape of the Fermi surface (Metlushko et al., 1997). The anisotropy of the Fermi surface sheets (see Section 3.2) has been assumed to cause the mentioned basal anisotropy of Hc2 because the borocarbide superconductors are usually clean-limit type-II superconductors. In the clean limit for an anisotropic Fermi surface the non-local corrections to Hc2 are given by... 

Section 3 will close with a short summary of the important properties and parameters of the superconducting state of YNi2B2C and LuNi2B2C (see Table 6), including additional references to those cited in the previous subsections, but without an attempt of completeness. These best-studied non-magnetic borocarbides are type-II superconductors (as discovered by Schubnikow et al., 1936) in... 

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