Dislocation thermal resistivity in concentrated alloys

The thermal conductivity was measured in the temperature range 0.4 - 4.0 K of concentrated alloys of copper, nickel, and aluminum in both a well-annealed and a heavily deformed state. The alloys are Cu + 10-at.% Al, Cu + 4-at.% Ni, and two commercial alloys, Evanohm and Al-2024. The lattice component of the thermal conductivity was deduced. Strong departures were observed in all cases from the $T^2$ dependence of the lattice thermal conductivity expected when phonons are scattered only by electrons and by sessile dislocations. With one exception (Evanohm), it was not possible to explain the observed lattice thermal conductivity in terms of nonrandomly arranged sessile dislocations, because the lattice component decreased with increasing $T$ in the range 0.55-0.8 K. It is suggested that the anomaly is due to mobile vibrating dislocations with a resonance frequency. Various resonance models of dislocations are discussed. The magnitude of the lattice thermal conductivity below 0.55 K of the annealed alloys seems to be independent of solute content and consistent with theoretical estimates of phonon-electron scattering.