Anomalous Electrical Resistivity in Titanium-Molybdenum Alloys

Abstract

The results of resistivity measurements on Ti-Mo alloys of concentrations 5-20 at.% Mo are discussed. The experimentally determined resistivity concentration dependence, which exhibits a pronounced local maximum near 8 at.% Mo, is compared with some calculated curves, derived with the aid of previously determined Fermi-density-of-states [$n\left(E_F\right)$] and Debye-temperature (${\Theta }_D$) data. On the assumption that the total resistivity is the sum of contributions due to thermal scattering (the ideal resistivity ${\rho }_i$) and solute scattering (${\rho }_s$), the measured resistivity in the concentration range 5-15 at.% Mo is shown to be anomalously high. For a quenched alloy of composition near the middle of the above range, viz., Ti-Mo (10 at.%), the temperature dependence of resistivity ($\frac{d\rho }{\mathrm{dT}}$) is negative between 4 and 480 K. But at higher temperatures $\frac{d\rho }{\mathrm{dT}}$ is positive, and after being aged at 620 K the alloy assumes a normal positive $\frac{d\rho }{\mathrm{dT}}$ over the full temperature range of 4-620 K. As a result of this investigation it is deduced that the anomalous magnitude, composition dependence, and temperature dependence are all associated in one way or another with an $\omega$-phase precipitate (a small fraction of which is reversible or "athermal") occurring in the brine-quenched alloys within the composition range 5-15 at.% Mo. It is concluded, however, that the observed resistivity effects do not derive from intrinsic physical properties of the $\omega$ phase itself, but are due instead to electronic scattering from the interfaces between the precipitate particles and the matrix. Interfacial scattering associated with the irreversible (isothermal) $\omega$ phase is responsible for the anomalous isothermal resistivity, while the relatively small athermal $\omega$-phase component gives rise to the negative $\frac{d\rho }{\mathrm{dT}}$ exhibited by Ti-Mo (10 at.%).