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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and Superfluidity 2 log Tc(calc) V 1 0 Ir Al Tl Zn Ru Re Ti CdOs Ga Mo Th Zr Nb Ta Pb HgLa InSn -1 Hf log Tc(measured) W -2 -2 -1 0 1 2 Figure 8.1 The comparison of the calculated values of critical temperatures of superconductors with measurement data. Circles relate to type-I superconductors, squares show type-II superconductors. On the abscissa, the measured values of critical temperatures are plotted, on ordinate, the calculated estimations are plotted. The calculations of critical temperatures for type-I superconductors were made by using Eq.(7.3) and the estimations for type-II superconductors was obtained by using Eq.(8.6). The comparison of the results of these calculations with the measurement data (Figure 8.1) shows that for the majority of type-II superconductors the estimation Eq.(8.6) can be considered quite satisfactory. 1 1 The lowest critical temperature was measured for Mg. It is approximately equal to 1mK. Mg-atoms in the metallic state are given two electrons into the electron gas of conductivity. It is confirmed by the fact that the pairing of these electrons, which manifests itself in the measured value of the flux quantum [42], is observed above T c. It would seem that in view of this metallic Mg-ion must have electron shell like the Ne-atom. Therefore it is logical to expect that the critical temperature of Mg can be calculated by the formula for I-type superconductors. But actually in order to get the value of T c ≈ 1mK, the critical temperature of Mg should be calculated by the formula (8.6), which is applicable to the description of metals with an unfilled inner shell. This suggests that the ionic core of magnesium metal apparently is not as simple as the completely filled Ne-shell. 94 Science Publishing Group

Chapter 8 Another Superconductors 8.2 Alloys and High-Temperature Superconductors In order to understand the mechanism of high temperature superconductivity, it is important to establish whether the high-T c ceramics are the I or II-type superconductors, or whether they are a special class of superconductors. In order to determine this, we need to look at the above established dependence of critical parameters from the electronic specific heat and also consider that the specific heat of superconductors I and II-types are differing considerably. There are some difficulties by determining the answer this way: as we do not precisely know the density of the electron gas in high-temperature superconductors. However, the densities of atoms in metals do not differ too much and we can use Eq.(7.3) for the solution of the problem of the I- and II-types superconductors distinguishing. If parameters of type-I superconductors are inserted into this equation, we obtain quite a satisfactory estimation of the critical temperature (as was done above, see Figure 8.1). For the type-II superconductors’ values, this assessment gives an overestimated value due to the fact that type-II superconductors’ specific heat has additional term associated with the magnetization of d-electrons. This analysis therefore, illustrates a possibility where we can divide all superconductors into two groups, as is evident from the Figure 8.2. It is generally assumed that we consider alloys Nb 3 Sn and V 3 Si as the type-II superconductors. This assumption seems quite normal because they are placed in close surroundings of Nb. Some excess of the calculated critical temperature over the experimentally measured value for ceramics T a 2 Ba 2 Ca 2 Cu 3 O 10 can be attributed to the measured heat capacity that may have been created by not only conductive electrons, but also non-superconducting elements (layers) of ceramics. It is already known that it, as well as ceramics Y Ba 2 Cu 3 O 7 , belongs to the type-II superconductors. However, ceramics (LaSr) 2 Cu 4 , Bi-2212 and Tl-2201, according to this figure should be regarded as type-I superconductors, which is unusual. Science Publishing Group 95

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