Superconductivity critical temperature

Phase transitions are involved in critical temperature thermistors. Vanadium, VO2, and vanadium trioxide [1314-34-7] V2O3, have semiconductors—metal transitions in which the conductivity decreases by several orders of magnitude on cooling. Electronic phase transitions are also observed in superconducting ceramics like YBa2Cu30y but here the conductivity increases sharply on cooling through the phase transition. 

Superconductivity. One potential future use of vanadium is in the field of superconductivity. The compound V Ga exhibits a critical current at 20 T (20 X lO" G), which is one of the highest of any known material. Although niobium—zirconium and Nb Sn have received more attention, especiahy in the United States, the vanadium compound is being studied for possible future appHcation in this field since V Ga exhibits a critical temperature of 15.4 K as opposed to 18.3 K for Nb Sn. 

Three important characteristics of the superconducting state are the critical temperature, the critical magnetic field, and the critical current. These parameters can be varied by using different materials or giving them special metallurgical treatments. 

Superconductivity exists within the boundaries of three limiting parameters which must not be exceeded the critical temperature (T ), the critical magnetic field (H ) and the critical current demsity (J ). 

The BCS theory leads to the following equation for the critical temperature, Tc, for superconductivity ... 

Fig. 3.—The curve represents the calculated values of the superconductivity critical temperature. The circles are the experimental values for the elements and for binary alloys between adjacent elements.

A material that displays superconductivity does so only below a critical temperature, Tc Above Tc, the material has normal resistivity, but as the temperature drops below Tc, its resistance abruptly disappears, as the graph shows. 

Gold is the only known dopant to YBa2Cu307, 5, which increases the critical temperature Tc of transition to the superconducting state. In this way, is enhanced from 97 K by 1.5 K. Eibschiitz et al. [401] observed by Mossbauer studies that the... 

Among various superconductors, compounds with the A15 (Cr3Si) crystal structure have the highest critical temperatures. This crystal structure has a simple relationship with the Ll2 structure (Ito and Fujiwara, 1994) as illustrated in Figure 8.9. When the unit cells are aggregated, the face-centered pairs of atoms form uniform chains of transition metal atoms along three orthogonal directions. This feature may be related to the relatively stable superconductivity in compounds with this structure. 

Materials that exhibit the phenomenon of superconductivity enter into a new state below a critical temperature Tc (see Table 8.11). 

We can conclude that the new behaviour of the superconducting material is due to a new state for the electrons in fact, at the critical temperature, there is a jump of the electronic specific heat. In no external magnetic field, it is a second-order transition, which does not involve latent heat. 

Superconducting only in thin films or under high pressure in a crystal modification not normally stable. Critical temperatures for those elements from [32, Chapter 12]. 

The temperature dependence of the pairing gap for the homogeneous, LOFF and DFS superconducting phases shows the phenomenon of reentrance the superconducting state is revived at finite temperatures. There exist two critical temperatures corresponding to phase transitions from the normal to the superconducting state and back as the temperature is increased from zero to finite values. 

In a superconducting system, when one increases the temperature at a given chemical potential, thermal motion will eventually break up the quark Cooper pairs. In the weakly interacting Bardeen-Copper-Schrieffer (BCS) theory, the transition between the superconducting and normal phases is usually of second order. The ratio of the critical temperature TcBCS to the zero temperature value of the gap AbGS is a universal value [18]... 

One expects the diquark condensate to dominate the physics at densities beyond the deconfinement/chiral restoration transition and below the critical temperature. Various phases are possible. E.g., the so called 2-color superconductivity (2SC) phase allows for unpaired quarks of one color. There may also exist a color-flavor locked (CFL) phase [7] for not too large value of the strange quark mass ms, for 2A > m2s/fiq, cf. [8], where the color superconductivity... 

The inset of Fig. 2 shows that the generalization of the BCS relation Tc 0.57 A(T = 0. fiq) g(pq), between the critical temperature Tc of the superconducting phase transition and the pairing gap A at T = 0 is satisfactorily fulfilled in the domain of the phase diagram relevant for compact stars. 

Figure 3. Phase diagrams for different form-factor models Gaussian (solid lines), Lorentzian a = 2 (dashed lines) and NJL (dash-dotted). In /3-equilibrium, the colorsuperconducting phase does not exist for Co Gi. In the inset we show for the Gaussian model the comparison of the numerical result with the modified BCS formula Tf = 0.57 A(T = 0, fiq) g(Hq) for the critical temperature of the superconducting phase transition.

We have investigated the influence of diquark condensation on the thermodynamics of quark matter under the conditions of /5-equilibrium and charge neutrality relevant for the discussion of compact stars. The EoS has been derived for a nonlocal chiral quark model in the mean field approximation, and the influence of different form-factors of the nonlocal, separable interaction (Gaussian, Lorentzian, NJL) has been studied. The model parameters are chosen such that the same set of hadronic vacuum observable is described. We have shown that the critical temperatures and chemical potentials for the onset of the chiral and the superconducting phase transition are the lower the smoother the momentum dependence of the interaction form-factor is. 

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