Superconducting transition temperature, lattice instability, and electron-to-atom ratio in transition-metal binary solid solutions

In a series of transition-metal binary alloys, as the average electron-to-atom ratio z decreases from 6.0 to 4.0, the measured electronic-specific-heat coefficient γ, and with it the average Fermi density of states $n\left(E_F\right)$ rises to a maximum near z=4.4. From an analysis of the coupled results of low-temperature calorimetric and magnetic susceptibility measurements it has been shown in a previous paper that, at least for the Ti-Mo system, the maximum in average $n\left(E_F\right)$ was induced through the influence of submicroscopic metallurgical inhomogeneities (clustering and second-phase precipitation) present in the as-quenched z≲4.3 material, and was not a property of the (hypothetical) single-phase bcc alloy. In addition, it was demonstrated that were it not for this precipitation, the effects of which became increasingly noticeable as z decreased below about 4.3, $n\left(E_F\right)$ would otherwise increase monotonically as z decreased from 6.0 to 4.0. In this paper, which is an extension of that work, the superconducting behavior of Ti-Mo is explored. The results of calorimetric measurements yield both a superconducting transition temperature T_c and a Debye temperature ${\Theta }_D$ which (through the elastic constants cᵢⱼ) may be related to lattice stability. Again, if we postulate the existence of single-phase bcc Ti-Mo alloys, in which precipitation for z≲4.3 has been inhibited, a semiquantitative argument shows that T_c should also increase monotonically with decreasing z. As a generalization of this result, it is suggested that in the well-known double-humped curve of T_c vs z for transition-metal binary alloys the local maximum near z=4.4 is induced (or at least strongly contributed to) by microstructural effects, rather than being a property of single-phase bcc alloys. Finally, a connection is made between the superconducting behaviors of transition-metal binary alloys, which might be regarded as low-perturbation systems, and the tightly bound transition-metal-nontransition-metal intermetallic compounds, for which the very opposite is true. The coupling parameter is "lattice stability" which decreases with decreasing z, in the range under consideration, for both the alloys as well as the compounds. The increase of T_c with decreasing z generally terminates at the edge of the regime of phase stability (e.g., at the low-concentration limit of the equilibrium single-phase bcc field, in the case of Ti-Mo alloys).