The many unusual properties of the ternary molybdenum chalcogenides of the type MMo6X8 (M=Metal, X=Chalcogen) are reviewed. Special emphasis is put on the superconducting properties like critical temperature, critical field and the problem of coexistence of magnetism and superconductivity.

Chevrel phases: Superconducting and normal state properties

The specific heat C of a sintered polycrystalline sample of MgB 2 with a bulk superconducting transition temperature T c =36.7 K is measured as a function of the temperature (2–300 K) and magnetic field (0–16 T), together with magnetic properties (normal-state susceptibility, superconducting-state magnetization, etc.). The Sommerfeld constant γ =0.89±0.05 mJ/K 2 /gat (2.7 mJ/K 2 /mol) is determined in the normal state above H c2 . The normal- and superconducting-state entropies are equal at T c . Several moments of the PDOS are obtained from the lattice specific heat. We report bulk values for: the thermodynamic critical field, B c (0)=0.26 T; the slope of the upper critical field, (d B c2 /d T ) T c =0.56 T/K; the Ginzburg–Landau parameter, κ =38; the coherence length, ξ ≅5 nm; the lower critical field, B c1 ≅0.018 T; the London penetration depth, λ (0)≅180 nm. These results characterize MgB 2 as a type-II superconductor. The nearly quadratic dependence of C ( T ) versus T at T ≪ T c , its non-linear field dependence, and the discrepancy between the electron–phonon coupling constant λ ep as determined by the renormalization of the electron density of states ( λ ep ≅0.6) and by McMillan's equation for isotropic superconductors ( λ ep ≅1.1), are inconsistent with a single isotropic gap. In addition to high phonon frequencies, anisotropy or two-band gap structure may explain why the critical temperature of this superconductor is high in spite of its low condensation energy, which does not exceed 1/16 of that of YBa 2 Cu 3 O 7 and 1/4 of that of Nb 3 Sn.

Specific heat in the superconducting and normal state (2–300 K, 0–16 T), and magnetic susceptibility of the 38 K superconductor MgB2: evidence for a multicomponent gap

Significant efforts can be found throughout the literature to optimize the current-carrying capacity of Nb3Sn superconducting wires. The achievable transport current density in wires depends on the A15 composition, morphology and strain state. The A15 sections in wires contain, due to compositional inhomogeneities resulting from solid-state diffusion A15 formation reactions, a distribution of superconducting properties. The A15 grain size can be different from wire to wire, and is also not necessarily homogeneous across the A15 regions. Strain is always present in composite wires, and the strain state changes as a result of thermal contraction differences and Lorentz forces in magnet systems. To optimize the transport properties, it is thus required to identify how composition, grain size and strain state influence the superconducting properties. This is not possible accurately in inhomogeneous and spatially complex systems such as wires. This article therefore gives an overview of the available literature on simplified, well-defined (quasi-)homogeneous laboratory samples. After more than 50 years of research on superconductivity in Nb3Sn, a significant amount of results are available, but these are scattered over a multitude of publications. Two reviews exist on the basic properties of A15 materials in general, but no specific review for Nb3Sn is available. This article is intended to provide such an overview. It starts with a basic description of the niobium–tin intermetallic. After that, it maps the influence of Sn content on the electron–phonon interaction strength and on the field–temperature phase boundary. The literature on the influence of Cu, Ti and Ta additions will then be summarized briefly. This is followed by a review of the effects of grain size and strain. The article concludes with a summary of the main results.

/pdf/a-review-of-the-properties-of-nb3sn-and-their-variation-with-55dz895yba.pdf

A Review of the Properties of Nb3Sn and Their Variation with A15 Composition, Morphology and Strain State

Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by , with t = T/Tc. Knowing Hc2*(T) implies that Jc(T) is also known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from T up to about 80% of the maximum Hc2 can be described with Kramer's flux shear model, if nonlinearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain () dependence is introduced through a temperature and strain dependent Hc2*(T,) and Ginzburg–Landau (GL) parameter κ1(T,) and a strain dependent critical temperature Tc(). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependences on Hc2*(T) and Hc2*(). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkably simple relation , where C is a constant, s() represents the normalized strain dependence of Hc2*(0) and h = H/Hc2*(T,). Finally, a new relation for s() is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues with respect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyse magnet performance from wire results.

/pdf/a-general-scaling-relation-for-the-critical-current-density-3o1ips6ain.pdf

A general scaling relation for the critical current density in Nb3Sn

We review the scaling relations for the critical current density (Jc) in Nb3Sn wires and include recent findings on the variation of the upper critical field (Hc2) with temperature (T) and A15 composition. Measurements of Hc2(T) in inevitably inhomogeneous wires, as well as analysis of literature results, have shown that all available Hc2(T) data can be accurately described by a single relation from the microscopic theory. This relation also holds for inhomogeneity averaged, effective, Hc2*(T) results and can be approximated by Hc2(t)=Hc2(0) = 1-t1.52, with t = T=Tc.Knowing Hc2*(T) implies that also Jc(T) is known. We highlight deficiencies in the Summers/Ekin relations, which are not able to account for the correct Jc(T) dependence. Available Jc(H) results indicate that the magnetic field dependence for all wires from mu0H = 1 T up to about 80 percent of the maximum Hc2 can be described with Kramer's flux shear model, if non-linearities in Kramer plots when approaching the maximum Hc2 are attributed to A15 inhomogeneities. The strain (e) dependence is introduced through a temperature and strain dependent Hc2*(T,e) and Ginzburg-Landau parameter kappa1(T,e) and a strain dependent critical temperature Tc(e). This is more consistent than the usual Ekin unification of strain and temperature dependence, which uses two separate and different dependencies on Hc2*(T) and Hc2*(e). Using a correct temperature dependence and accounting for the A15 inhomogeneities leads to the remarkable simple relation Jc(H,T,e)= (C/mu0H)s(e)(1-t1.52)(1-t2)h0.5(1-h)2, where C is a constant, s(e) represents the normalized strain dependence of Hc2*(0) andh = H/Hc2*(T,e). Finally, a new relation for s(e) is proposed, which is an asymmetric version of our earlier deviatoric strain model and based on the first, second and third strain invariants. The new scaling relation solves a number of much debated issues withrespect to Jc scaling in Nb3Sn and is therefore of importance to the applied community, who use scaling relations to analyze magnet performance from wire results.

Bulk samples covering the entire homogeneity range of the Nb-Sn A15-phase were prepared by a new method: levitation melting under high argon pressure. The variations of the lattice parameter, superconducting transition temperature, resistivity and critical field slope were measured as a function of composition. A low-temperature X-ray diffraction study was undertaken in order to fix the compositional limit of the tetragonal phase. The theoretical expectations for the critical field slopes at the transition temperature, Tc, based on actually-observed alloy parameters, were found to be in good agreeement with measured values.

The physical and structural properties of superconducting A15-type Nb-Sn alloys

The low temperature phase diagram of the system CuxMo6S8 in the range 1.5≤×≤3.55

The compounds M x Mo 6 X 8 (M=Pb, Sn, Cu, x =S, Se) crystallizing in the rhombohedral Chevrel phase have been prepared by melting under a pressure of 100 bars of argon and temperatures above 1700°C . The variation of the superconducting transition temperature as a function of the concentration x was studied in the systems Cu x Mo 6 S 8 and Cu x Mo 6 Se 8 . The microscope observation of these compounds leads to the conclusion that the phase forms congruently. Large single crystals have been prepared. The temperature at which the rhombohedral phase transforms to the orthorhombic structure decreases strongly if the Cu content increases.

H. Devantay

Papers

The physical and structural properties of superconducting A15-type Nb-Sn alloys

The low temperature phase diagram of the system CuxMo6S8 in the range 1.5≤×≤3.55

Metallurgical and physical properties of ternary Molybdenum Sulfides (M x Mo 3 S 4 ) as synthetized in the bulk state