Superconductor thermodynamic properties

Not only do the thermodynamic properties follow similar power laws near the critical temperatures, but the exponents measured for a given property, such as heat capacity or the order parameter, are found to be the same within experimental error in a wide variety of substances. This can be seen in Table 13.3. It has been shown that the same set of exponents (a, (3, 7, v, etc.) are obtained for phase transitions that have the same spatial (d) and order parameter (n) dimensionalities. For example, (order + disorder) transitions, magnetic transitions with a single axis about which the magnetization orients, and the (liquid + gas) critical point have d= 3 and n — 1, and all have the same values for the critical exponents. Superconductors and the superfluid transition in 4He have d= 3 and n = 2, and they show different values for the set of exponents. Phase transitions are said to belong to different universality classes when their critical exponents belong to different sets. 

Early was proposed to used the functional integral methods for calculation the thermodynamic properties of high-Tc superconductors including antiferromagnetic spin fluctuations [5],... 

A = a material constant involving elastic and thermodynamic properties of the superconductor flo = fluxoid lattice parameter B = magnetic induction Bc2 = upper critical magnetic induction b = reduced magnetic induction B/Bc2 b = Burgers vector D = diameter of specimen (D) = average grain size... 

The privileged position of the extended Born-Handy formula can be seen also in the derivation of the main thermodynamical properties of superconductors. We need not know anything specific about superconductors the pure assumption of the J-T like solution of this formula is sufficient. 

The first role - removal of electron degeneracies - is fulfilled via the vibronic coupling. The second role - the symmetry breaking - is caused by the rotonic and transionic coupling. Finally the third role - forming of stmcture - is a result of optimalization where all three types of coupling participate. Only in the adiabatic limit the forming of molecular and crystallic stmcture reduces to the standard one, defined by the B-O approximation. Moreover, at finite temperatures the extended Born-Handy formula plays yet another role it defines all thermodynamic properties of the non-adiabatic systems, as was demonstrated on the derivation of the critical temperature of superconductors. 

Chapters 13 and 14 use thermodynamics to describe and predict phase equilibria. Chapter 13 limits the discussion to pure substances. Distinctions are made between first-order and continuous phase transitions, and examples are given of different types of continuous transitions, including the (liquid + gas) critical phase transition, order-disorder transitions involving position disorder, rotational disorder, and magnetic effects the helium normal-superfluid transition and conductor-superconductor transitions. Modem theories of phase transitions are described that show the parallel properties of the different types of continuous transitions, and demonstrate how these properties can be described with a general set of critical exponents. This discussion is an attempt to present to chemists the exciting advances made in the area of theories of phase transitions that is often relegated to physics tests. 

As we explore the interaction of cold-atom systems with microwave and terahertz radiation, we find that they have some unique properties as detectors. A comparison with superconductor-based detectors such as SQUlDs is instractive. Because of the third law of thermodynamics, i.e., a system in a single quantum state has zero entropy, the response of a SQUID is almost free of thermal noise. But an additional properly of SQUIDs is that they exhibit the phenomenon of coherence, i.e., wave interference, which leads to entirely new effects, e.g. the AC and DC Josephson effects. Cold atom clouds share this behavior, as we will discuss below. 

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].)...

In July, 2010, physicists at Rice University in Houston, Texas the Max Planck Instimte for Chemical Physics of Solids and the Max Planck Institute for the Physics of Complex Systems, both in Dresden, Germany and the Vienna University of Technology have reported that after seven years of research on high-temperature superconductors they have established quantum-critical scaling properties at work during the transition from one quantum phase to another. In experiments with a heavy-fermion metal containing ytterbium, rhodium, and silicon, researchers identified thermodynamic scaling properties as a result of a fermi-volume collapse. 

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