Superconductors critical properties

The prospects for various applications depend, of course, on the materials properties of the superconductor. Many properties are important, including mechanical properties, interfacial interactions and contacts, high frequency loss, and so forth. Here we emphasize as an example the critical current density, which is one of the most vital properties for most applications. 

Online and off-line investigations are in progress to study the effects of fast neutrons in solids using fluences in the range 10 -10 /cm. Samples and physical properties to be studied are as follows metals and alloys (mechanical, microstructure, electrical resistivity), superconductors (critical current, temperature and field), and insulators (electrical and... 

Dimensions. Most coUoids have aU three dimensions within the size range - 100 nm to 5 nm. If only two dimensions (fibriUar geometry) or one dimension (laminar geometry) exist in this range, unique properties of the high surface area portion of the material may stiU be observed and even dominate the overaU character of a system (21). The non-Newtonian rheological behavior of fibriUar and laminar clay suspensions, the reactivity of catalysts, and the critical magnetic properties of multifilamentary superconductors are examples of the numerous systems that are ultimately controUed by such coUoidal materials. 

This should come as no surprise, since the physical behavior of materials is non-linear and unpredictable, especially when materials are formulated or in combination. Two examples will suffice high temperature ceramic superconductors and insulators above their critical temperatures or at non-ideal stoichiometries composite structures may show several times the strength or impact resistance than would be expected from their component materials. Materials discovery will always require a good deal of trial and error, factors that may be mitigated by techniques that permit the simultaneous synthesis of large numbers of materials, followed by rapid or parallel screening for desired properties. 

The amount and positions (atomic locations) of oxygen atoms in the superconductors are highly critical and determine the properties of the superconductor. The oxygen vacancies (or deficiency) can be ordered in these materials. Neutron-diffraction experiments were required to determine the population parameters and the atomic positions of oxygen in these structures. The superconducting transition temperature in these "ceramic" oxides is a critical balance between the oxygen content and a proper mix of Cu2+ and Cus+ ions generated in the anneal or post-heat treatment. 

Single crystals are of critical importance to the study of complex solids such as the new high temperature superconductors. Single crystals are free of grain boundary effects and allow measurements of physical properties as a function of crystal orientation. 

Golovashkin, A.I., Superconductors with Unusual Properties and Possibilities of Increasing the Critical Temperature. Sov. Phys. Usp. 29(2) 199 (1986). 

Figure 6.10 Temperature dependence of critical magnetic field for a superconductor. Reprinted, by permission, from L. Solymar and D. Walsh, Lectures on the Electrical Properties of Materials, 5th ed., p. 429. Copyright 1993 by Oxford University Press.

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. 

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. 

The high critical temperature superconductors show a strong anisotropy in different properties critical current density [1], resistivity [2, 3] and the upper critical field [2],... 

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