Anomalous electrical resistivity, bcc phase stability, and superconductivity in titanium-vanadium alloys

Precise measurements of the electrical resistivities $\rho$ of a series of Ti-V alloys have been made in the 77-300-K temperature range. The isothermal composition dependences are shown to be anomalously large (by an amount ${\rho }_{\mathrm{anom}}$) over a concentration range of from about 12-at.% to at least 70-at.% V. Throughout this range ${\rho }_{\mathrm{anom},77\mathrm{}}$ is larger than ${\rho }_{\mathrm{anom},300\mathrm{}}$. Furthermore, within the composition range of 20-33-at.% V, ${({\rho }_{77}-{\rho }_{300})}_{\mathrm{anom}}$ exceeds the decrease in ideal resistivity between 300 and 77 K, leading to a net negative temperature coefficient of resistivity for those alloys. The results are discussed in the context of transition-metal binary-alloy phase stability, expressed in terms of soft phonons which become more and more localized as the solute concentration increases in the average electron-to-atom ratio range 4.1 to 5.0. A connection is made with superconductivity in alloys formed between groups-IV and -V transition metals. It is pointed out that the phonons of instability, which are responsible for the anomalous resistivity, also favor superconductive coupling and consequently a relatively "high" $T_c$; but that at the same time, this effect must compete with a proximity-effect-induced lowering of the average $T_c$ by the product of the lattice instability (viz., $\omega$ phase), which itself has a very low $T_c$.