Exponential temperature dependence of the electrical resistivity ofV3Si

Abstract

We report the results and interpretation of precision measurements of the electrical resistivity of ${\mathrm{V}}_3$Si in the temperature range $T_c\le T\le 77$ K. Four samples of a wide range in residual resistance ratio (RRR) and with $15.1\le T_c\le 16.8$ K have been investigated. We find that the resistivity of all the samples is well described by a temperature dependence of the form $\rho \mathrm{}\left(T\right)={\rho }_0+b{T}^n+d\exp (-\frac{T_0}{T})$, where $n$ falls within the range $1\le n\le 2$. The parameter $d$ is sensitive to the RRR of the sample, whereas $b$ and $T_0$ are relatively insensitive. The characteristic temperature $T_0\approx 175$ K is essentially independent of the choice of $n$ within the stated range. A similar exponential term in $\rho \mathrm{}\left(T\right)\mathrm{}$ of ${\mathrm{Nb}}_3$Sn with $T_0\approx 85$ K has previously been identified by Woodard and Cody. Nothing that in both ${\mathrm{V}}_3$Si and ${\mathrm{Nb}}_3$Sn the value of $T_0$ corresponds to the energy of [100] TA phonons near the zone boundary, we argue that the exponential term is due either to phonon-assisted interband scattering or intraband umklapp scattering. The reasons for the scattering effectiveness of this phonon will be discussed in light of recent band-structure calculations by Mattheiss and previous band models proposed to explain the anomalous normal-state properties of $A-15$ compounds. The nonexponential term in the resistivity is more difficult to characterize empirically and its origin is correspondingly more uncertain. We suggest it arises from intraband electron-electron scattering. The temperature dependence of the resistivity will be discussed with respect to anomalies observed in the low-temperature elastic constants, magnetic susceptibility, and specific heat of ${\mathrm{V}}_3$Si.