Debye-Waller factor and multiphonon contributions to the phonon-limited resistivity of Na and K

Abstract

The recent first-principles calculation of the phonon-limited electrical resistivity ($\ensuremath{\rho}$) of sodium and potassium [R. C. Shukla and R. Taylor, J. Phys. F 6, 531 (1976)] is extended to include the effects of the Debye-Waller factor (DW) and the multiphonon series (MP) in the high-temperature limit. In this limit, the leading temperature dependence of the contribution to $\ensuremath{\rho}$, from the DW and the first term of the MP series, is found to vary as ${T}^{2}$. The individual contributions to $\ensuremath{\rho}$ from the DW and the first term of the MP series are found to be large but in opposite directions in the entire temperature range from the Debye temperature (${\ensuremath{\bigominus}}_{D}$) to the melting temperature (${T}_{M}$). For example, as the temperature increases from ${\ensuremath{\bigominus}}_{D}$ to ${T}_{M}$, the DW contribution decreases the value of $\ensuremath{\rho}$ for Na and K by 9-20% and 5-20%, respectively, whereas, the MP contribution increases the value of $\ensuremath{\rho}$ by 11-25% and 6-21%, respectively. The total DW and MP contribution to $\ensuremath{\rho}$ amounts to 5% in Na and 1% in K near ${T}_{M}$. It appears that there is no exact cancellation between the DW and MP contributions to $\ensuremath{\rho}$ although the cancellation is much stronger in K than in Na. The second and subsequent terms of the MP series make negligible contribution to $\ensuremath{\rho}$. Even better agreement between the calculated and experimental values of $\ensuremath{\rho}$ is achieved when these positive contributions from the DW and MP are added to the calculated resistivity in the harmonic approximation R. C. Shukla and R. Taylor, [J. Phys. F 6, 531 (1976)].