Deviation from Matthiessen's rule at high temperatures: Theoretical interpretation

Abstract

Theoretical interpretation is given for the deviation from Matthiessen's rule (DMR) at high temperatures on dilute alloy systems Au in Cu, Cu in Au, and Ni in Cu, and Cu, Ag, and Ge in Al, measured with the use of the new experimental techniques developed by Fujita and others. The measured deviation from this rule, $\ensuremath{\Delta}(c, T)$, can be fitted to curves of $Y+AT$ ($Y\ensuremath{\approx}0$), where $T$ is the absolute temperature, and the numerical constant $A(Y)$ can be calculated using a standard lowest-order (higher-order) variational scheme. $Y$ is always positive and gives a measure of the anisotropy of the scattering at high temperatures. For most of the Al-based and noble-metal-based dilute alloys, $Y$ is small and the anisotropy scattering is unimportant. The proportionality factor $A$ has been evaluated, within the standard variational formalism, using an atomistic model calculation for the electron-phonon spectral function. It is shown that the leading contribution to the high-temperature DMR is due to the change in the phonon spectral function $F(\ensuremath{\omega})$ for Cu in Al, Ge in Al, Cu in Au, and Au in Cu alloys, while it comes from the change in the electron-phonon coupling function ${\ensuremath{\alpha}}_{\mathrm{tr}}^{2}(\ensuremath{\omega})$ (electron-mass-enhancement parameter ${\ensuremath{\lambda}}_{\mathrm{tr}}$) for the Ag in Al alloy.