Thermal Properties of Mobile Defects

Using simplified models, calculations are made for the contribution of mobile dislocations and small-angle boundaries to the specific heat and thermal resistivity of crystals. The specific heat is found to be proportional to $T$ and $T^2$, and the lattice resistivity approximately to $T^{-n}$ (where $n$ lies between 3 and $\frac{7}{2}$ for the usual range of measurements) and $T^{-5\mathrm{}}$ for mobile dislocations and mobile small-angle boundaries, respectively, over a range of low temperatures, but eventually both go to zero in the limit as the temperature approaches zero. The magnitudes of the effects are such that although the contribution of dislocations to the specific heat of some pure cold-worked nonconductors and superconductors may be measurable, that from small-angle boundaries is not. The effect of dislocations on the thermal resistivity is large and should compete with boundary scattering for temperatures of the order of ${10}^{-2\mathrm{}}$ of the Debye temperature, with dislocation densities of the order of ${10}^7$ ${\mathrm{cm}}^{-2\mathrm{}}$ in specimens of a few millimeters in diameter. The predicted temperature dependence is in agreement with recent measurements on superconducting lead at low temperatures. At present a contribution from mobile boundaries to the thermal resistivity is not excluded as a possibility.