Superconductivity in Zr_xNb_1−2xMo_x alloys: Possible dominance of a soft phonon mode

Abstract

Normal-state specific heat and superconducting transition temperature measurements were performed on pure polycrystalline Nb and isoelectronic bcc Zr_xNb_1−2xMo_x alloys (x = 0.02, 0.05, and 0.10). Measured T _c, γ and θ _D all decline nearly linearly from the pure Nb values with increasing x. The changes are 15, 10, and 6%, respectively, for x = 0.1. T _cH calculated by Hopfield's theory, using data and linearly interpolated values of η and θ _D /〈θ²〉_linear ^1/2, increases with x by 28% for x = 0.1. By relaxing the linear interpolation of θ_D/〈θ²〉^1/2, Hopfield's theory can be used to evaluate an average phonon frequency 〈θ²〉_emp ^1/2 from data. It is found to be nearly constant at about 229 K, in contrast to 〈θ²〉_linear ^1/2, which declines by 8% at x = 0.1. We suggest that one possible explanation for this behavior is the dominance of incipient soft-phonon longitudinal modes which occur in Nb and presumably in the alloys. Miedema's method has been used to calculate the variation of both γ and T _c with alloying. The calculated γ is nearly constant, while the calculated T _c declines more quickly than the measured variation. The band-structure electron density of states calculated with the aid of McMillan's equation for these isoelectronic alloys is found to decline by 8% at x = 0.1, in contrast to the prediction of the rigid band model. Normal-state low-temperature specific heat measurements on a pure annealed polycrystalline sample of Nb yield γ = 7.80 ± 0.02 mJ mole⁻¹ K⁻² and θ_D = 276 ± 2 K, in excellent agreement with previous measurements. The break in slope of C _p/T vs. T ² at 3.2 K is discussed.