Critical field thermodynamical

The free energies for the respective states can be determined from heat capacity data, and the thermodynamic critical field can be determined from a plot of free energy versus applied field for the two states, as illustrated in Figure 6.65. 

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.

From the specific-heat data the thermodynamical critical field Beth can be estimated [102, 194]. For K-(ET)2l3 this results in Beth 17mT. Be can also be calculated from the upper and lower critical fields via... 

X./. 247i2o nm. These values are compared in Table I with values obtained for K3C6o- for the Rb compound is somewhat smaller than obtained in the case of K3C60 but still larger than the nearest-neighbor C60 distance d (ca. I nm). We also estimate the thermodynamic critical field from //. (O)-7/H(0)//,2(0)/lnic (Ref. [14]) and compare it to K3C60 in Table I. 

First we review some typical materials parameters obtained from measurements on randomly oriented ceramics (6-7). Since the YBaCuO structure (5) and electronic properties 81 are highly anisotropic, the orientationally-averaged values obtained from studies of ceramics are only an initial indication until more complete experimental results on single crystals and oriented films and ceramics become available. For material with a resistivity just above the transition of 400 /xficm, a Hall carrier density of 4xl021cm , and dHc2/dT of 2 T/K (6-7). one deduces a BCS coherence length (0) of 1-4 nm, a London penetration depth A(0) of 200 nm, a mean free path t of 1.2 nm, a thermodynamic critical field Hc(0) of 1 T (10000 Oe) and an upper critical... 

Figure 2-4. Magnetization versus applied magnetic field for a type II superconductor. The flux starts to penetrate the specimen at a field Wei lower than the thermodynamic critical field The specimen is in a vortex state between Wei and Wc2 and it has superconducting electrical properties up to We2. (From Kittel [18].)...

Be = thermodynamic critical field Bc2 = upper critical field Bdc = stationary magnetic field crit = rf critical magnetic field Ep = peak electric field at the cavity surface / = frequency Fp = volume pinning force jc = critical current density k = Boltzmann constant / = mean free path R(T) = measured surface resistance Bcs = surface resistance, as described by the BCS theory Rres = residual surface resistance Tc = transition temperature... 

Of the seventeen rare earth metals only lanthanum is superconducting at atmospheric pressure. Lanthanum is one of the better elemental superconductors - its 6.1 K transformation ()3-La, fee) is only exceeded by those of lead (7.2 K) and niobium (9.2 K), and its thermodynamic critical field, H 0) = 1600 Oe is second to that of niobium s 1980 Oe. When the pressure dependence of the superconducting transition temperatures is taken into account lanthanum has the highest known elemental transition temperature, 13K, see fig. 12a. 

For niobium and its compounds at T< 0.5 Tc, where for the mean free path of an electron and the coherence length the ratio 4 L is true, these bonds may be written in a simple form [4]. Thus for the thermodynamic critical field He and for the field of magnetic breakdown Hmb they have the form ... 

The penetration depth X. is given at zero temperature, as are the coherence length the thermodynamic critical field H , and the energy gap A . 

The thermodynamic critical field Hc(T) is directly related to the free energy difference Fs between superconducting and normal state via... 

Fig. 17.24, Thermodynamic critical field HJ.T) for La,, Pr,Snj, The theoretical results are due to Keller et al. (1977) while the experimental data are from McCallum et al. (1975).

The thermodynamic critical field above with the SmA phase becomes globally unstable to the N phase at some temperature N -smA lower than To follows from Eq. 

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