Lattice Thermal Conductivity of Plastically Deformed Copper plus 10 Atomic Percent Aluminum Specimens in the Temperature Range 1-4°K

Abstract

The total thermal and electrical conductivities of seven polycrystalline rods of copper plus 10 at.% aluminum, which were in a total of 25 different states of recovery from plastic deformation at 77 °K, and one commercially pure nickel single crystal were measured in the liquid-helium temperature range. The low-temperature lattice thermal conductivity of a specimen which had been plastically deformed 9% recovered slowly as it was annealed between 300 and 700 °K, and then rapidly recovered to its prestrain magnitude after being annealed between 700 and 800 °K. The recrystallization temperature was 725 °K. Metallographic grain-size studies supported these conclusions. An application of the theory of Klemens and Ackerman and Klemens to the variation of the dislocation lattice thermal resistivity with annealing temperature (below 700 °K) due to impurity atmospheres made it possible to determine the fractional atomic-volume difference $\alpha$ between the aluminum and copper atoms to be 0.23. When the same theory was compared with variation of the dislocation lattice thermal resistivity with aluminum concentration found by Charsley, Salter, and Leaver, it was found that $\alpha =0.\mathrm{}24$. From the experimental x-ray data, $\alpha$ is 0.20. A later theory of Klemens which treated the variation of dislocation resistivity with annealing time at fixed annealing temperature was found to be inconsistent with the data of this work, but the experimental error was large. The theory contained the assumption that a unique diffusion constant could be defined for the deformed alloys, but this may not have been true, since plastic deformation generates excess vacancies. An anomalous departure of the phonon-electron lattice thermal resistivity from a $T^{-2\mathrm{}}$ temperature dependence was thought to be an effect associated with the small electron mean free paths in these alloys. The theory of Lindenfeld and Pennebaker qualitatively explained the anomaly.