Section: 12 | Properties of Superconductors |

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PROPERTIES OF SUPERCONDUCTORS

L. I. Berger and B. W. Roberts

The following tables include superconductive properties of selected elements, compounds, and alloys. Individual tables are given for thin films, elements at high pressures, superconductors with high critical magnetic fields, and high critical temperature superconductors.

The historically first observed and most distinctive property of a superconductive body is the near total loss of resistance at a critical temperature (T_c) that is characteristic of each material. Figure 1(a) below illustrates schematically two types of possible transitions. The sharp vertical discontinuity in resistance is indicative of that found for a single crystal of a very pure element or one of a few well-annealed alloy compositions. The broad transition, illustrated by broken lines, suggests the transition shape seen for materials that are not homogeneous and contain unusual strain distributions. Careful testing of the resistivity limit for superconductors shows that it is less than 4 × 10^–23 ohm cm, while the lowest resistivity observed in metals is of the order of 10^–13 ohm cm. If one compares the resistivity of a superconductive body to that of copper at room temperature, the superconductive body is at least 10¹⁷ times less resistive.

figure 1 described below

FIGURE 1. Physical properties of superconductors. (a) Resistivity vs. temperature for a pure and perfect lattice (solid line); impure and/or imperfect lattice (broken line). (b) Magnetic-field temperature dependence for Type I or “soft” superconductors. (c) Schematic magnetization curve for Type II or "hard" superconductors.

The temperature interval ΔT_c, over which the transition between the normal and superconductive states takes place, may be of the order of as little as 2 × 10^–5 K or several K in width, depending on the material state. The narrow transition width was attained in 99.9999% pure gallium single crystals.

A Type I superconductor below T_c, as exemplified by a pure metal, exhibits perfect diamagnetism and excludes a magnetic field up to some critical field H_c, whereupon it reverts to the normal state as shown in the H-T diagram of Figure 1(b).

The magnetization of a typical high-field superconductor is shown in Figure 1(c). The discovery of the large current-carrying capability of Nb₃Sn and other similar alloys has led to an extensive study of the physical properties of these alloys. In brief, a high-field superconductor, or Type II superconductor, passes from the perfect diamagnetic state at low-magnetic fields to a mixed state and finally to a sheathed state before attaining the normal resistive state of the metal. The magnetic-field values separating the four stages are given as H_c1, H_c2, and H_c3. The superconductive state below H_c1 is perfectly diamagnetic, identical to the state of most pure metals of the Type I or “soft” superconductor. Between H_c1 and H_c2 a “mixed superconductive state” is found in which fluxons (a minimal unit of magnetic flux) create lines of normal flux in a superconductive matrix. The volume of the normal state is proportional to –4πM in the “mixed state” region. Thus, at H_c2 the fluxon density has become so great as to drive the interior volume of the superconductive body completely normal. Between H_c2 and H_c3 the superconductor has a sheath of current-carrying superconductive material at the body surface, and above H _c3 the normal state exists. With several types of careful measurement, it is possible to determine H_c1, H_c2, and H_c3. Table 6 contains some of the available data on high-field superconductive materials.

High-field superconductive phenomena are also related to specimen dimension and configuration. For example, the Type I superconductor, Hg, has entirely different magnetization behavior in high-magnetic fields when contained in the very fine sets of filamentary tunnels found in an unprocessed Vycor glass. The great majority of superconductive materials are Type II. The elements in very pure form and a very few precisely stoichiometric and well annealed compounds are Type I with the possible exceptions of vanadium and niobium.

Metallurgical Aspects. The sensitivity of superconductive properties to the material state is most pronounced and has been used in a reverse sense to study and specify the detailed state of alloys. The mechanical state, the homogeneity, and the presence of impurity atoms and other electron-scattering centers are all capable of controlling the critical temperature and the current-carrying capabilities in high-magnetic fields. Well-annealed specimens tend to show sharper transitions than those that are strained or inhomogeneous. This sensitivity to mechanical state underlines a general problem in the tabulation of properties for superconductive materials. The occasional divergent values of the critical temperature and of the critical fields quoted for a Type II superconductor may lie in the variation in sample preparation. Critical temperatures of materials studied early in the history of superconductivity must be evaluated in light of the probable metallurgical state of the material, as well as the availability of less pure starting elements. It has been noted that recent work has given extended consideration to the metallurgical aspects of sample preparation.

Symbols in tables: T_c: Critical temperature; H_o: Critical magnetic field in the T = 0 limit; θ_D: Debye temperature; and γ: Electronic specific heat.

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TABLE 1. Selective Properties of Superconductive Elements

Element	T_c/K	H_o/Oe	θ_D/K	γ/mJ mol^–1K^–1
Continued on next page...
Al	1.175 ± 0.002	104.9 ± 0.3	420	1.35
Am* (α,?)	0.6
Am* (β,?)	1.0
Be	0.026			0.21
Cd	0.517 ± 0.002	28 ± 1	209	0.69
Ga	1.083 ± 0.001	58.3 ± 0.2	325	0.60
Ga (β)	5.9, 6.2	560
Ga (γ)	7	950, HF^a
Ga (Δ)	7.85	815, HF
Hf	0.128	12.7		2.21
Hg (α)	4.154 ± 0.001	411 ± 2	87, 71.9	1.81
Hg (β)	3.949	339	93	1.37
In	3.408 ± 0.001	281.5 ± 2	109	1.672
Ir	0.1125 ± 0.001	16 ± 0.05	425	3.19
La (α)	4.88 ± 0.02	800 ± 10	151	9.8
La (β)	6.00 ± 0.1	1096, 1600	139	11.3
Lu	0.1 ± 0.03	350 ± 50
Mo	0.915 ± 0.005	96 ± 3	460	1.83
Nb	9.25 ± 0.02	2060 ± 50, HF	276	7.80

^aHF denotes high-magnetic field superconductive properties.

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