Irreversibility line

Martin et al. [126] have made single-phase TlBaSrCa2Cu309 8 with a Tc value of 103 K. On annealing in a reducing atmosphere, the Tc value has been shown to increase up to 116 K. It has also been proven that the irreversibility line does not depend on Tc (i.e., oxygen nonstoichiometry does not influence the nature of the irreversibility line in this phase). The TlSrCa2Cu309 phase has not been made in a pure phase yet since the Tl-1223 structure needs all Cu to be 2.33 +. But it is possible to stabilize this... 

For strong type-II superconductors a difference may exist between B 2 obtained from ac-susceptibility data and the thermodynamically relevant upper critical field, 5c2, for which (2.13) and (2.14) were derived originally. Prom extensive work on high-Tc cuprates it is known that B 2 is related to the so-called irreversibility line [196]. The basic idea of a semiquantitative flux-creep theory [197] is that pinned vortices can be activated thermally over an energy barrier Uq resulting in a reduced critical current of the form [196]... 

Therefore, a large number of published phase diagrams suffer from the drawback that the phase boundary lines have to be extracted from data wiiich are clearly affected by flux pinning, or even worse, that phase boundaries are added, which are not related to the thermodynamic state at all, but exclusively determined by the strength of the pinning potential ( irreversibility line , Malozemoff et al. 1988). 

In conclusion, as pointed out in the introduction, the results to be presented in sects. 5—8 are not aimed at a detailed discussion of these fundamental aspects of flux pinning and flux dynamics, but rather at possibilities to improve 7c in the 123 superconductors. We must be aware of the fact, however, that the Jc s quoted in the literature often do not refer to the true critical current densities, since the data are affected by creep and relaxation, and should rather be quoted as shielding current densities 7s- Furthermore, we will refiain from judgements of the nature of the boundary line, where 7s goes to zero, and will refer to it as the irreversibility line. This characteristic parameter is subject to the same restrictions as mentioned above i.e., sensitive to the resolution of the experiment and its time scale. It is useful to note that the shape of this curve (// c) follows a power law (with an exponent of 1.5) for more three-dimensional HTS, as predicted by Malozemoff et al. (1988) on the basis of a depiiming argument, but an exponential law for two-dimensional systems, as shown schematically in fig. 6. 

Fig. 6. Schematic representation of the irreversibility lines in HTS. The 3D case corresponds to a power-law dependence of on temperature, the 2D case to an exponential dependence.

To conclude this section, a few words on the experimental assessment of the irreversibility lines seem to be appropriate. As pointed out in much detail above, the timing ( time window ) of the experiment represents a deeisive factor for the apparent magnitude of J. Since we are now looking for methods to determine the exact location in the //.r plane, where becomes zero, the timing will again play a crucial role. In addition, the criterion Jc = 0 is extremely ill defined, since it entirely depends on the resolution of the experimental technique employed. I will choose two examples (SQUID magnetometry and ac susceptibility) to demonstrate the salient features of the problem. 

In conclusion, sufficient control of the experimental parameters and a critical assessment of the characteristics of each techniques will in general lead to reliable data both on the current densities and the irreversibility lines. Direct comparisons of published data are still difficult, in particular when the experimental parameters are not explicitly specified. 

The nature and, if available, the most likely pinning mechanisms of these defects will be reviewed in this section, while the impact of these defects on the critical current densities and the location of the irreversibility line will be mostly presented in sect. 7. 

This interplay between new and as-grown defect structures also plays a major role when critical current densities and irreversibility lines are analysed and related to flux-... 

The first conjecture is ruled out by all data on all forms of 123 superconductors, i.e., it turns out that decreases immediately if d starts to deviate from its optimum value. This is illustrated in fig. 32, where is plotted as a function of magnetic field in melt-textured Y-123 superconductors H c) with transition temperatures between 92.4 and 45.8 K (Wisniewski et al. 1996). The data deliberately refer to very low temperatures (5 K in this case), in order to minimise the influence of variations in Tc- A very similar behaviour is found for the irreversibility lines (IL s) as shown in fig. 33 for H c, i.e.. 

Fig. 33. Irreversibility lines in melt-textured Y-123 bulk superconductors (H c) with various degrees of oxygen deficiency (Wisniewski et al. 1996) (a) versus temperature (b) normalised versus [1 -(T/T )].

Fig. 38. Fast neutron irradiation of a Nd-123 melt-textured superconductor (Kem 1997) (a) critical current density (H 1 c) versus field at 77 K (prior to and following irradiation to a fluence of 2 x 10 m", >0.1 MeV) (b) irreversibility lines for ti c, same conditions as above.

Fig. 42. Shift of the irreversibility line H c) in an Y-123 single crystal following 1.08 GeV Au ion irradiation to various fluences (Civale and Krusin-Elbaum 1997).

Upper critical field and irreversibility line of vicinity of 7 . 263... 

The performance of high-temperature superconductors in magnetic fields is intimately related to the upper critical field H (T), the irreversibility line and the critical... 

It was previously suggested that positive curvature of the resistively determined Ha T) curve may be a general property of high-Ti cuprate superconductors (Cooper, Loram and Wade 1995, Ovchinnikov and Kresin 1995, 1996, Abrikosov 1997). However, the T-dependence of the resistively determined H 2 T) curve was interpreted as a measure of the T-dependence of the irreversibility line (Almasan et al. 1992a). Indeed, the irreversibility line extracted from zero-field-cooled and field-cooled... 

Schilling et al. (1993) observed a cross-over in the irreversibility line measured with // II c on single-crystal specimens of a Bi2Sr2CaCu20g superconductor Irom a parabolic temperature dependence, //=/fo(l - T /T c). near to an exponential dependence, exp(const/7 ), at larger H and TIT < 0.5. They argued that the two regimes reflect a cross-over from essentially three-dimensional (3D) vortex fluctuations near Tc to quasi-two-dimensional (2D) vortex fluctuations for H >Ha ols y and low temperatures, where s is the interlayer distance, y=Ac/Aab is the anisotropy parameter, and 0o is the magnetic flux quantum. 

Assuming that dominates possible quantum fluctuations, Schilling et al. (1993) used the phenomenological Lindemann melting criterion (Lindemann 1910) to describe the experimentally observed irreversibility line in terms of vortex-lattice melting i.e.. 

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