Limitation of the Phonon Heat Conductivity by Edge-Dislocation Dipoles, Single Dislocations, and Normal Processes

The scattering of phonons by edge-dislocation dipoles leads to deviations from the quadratic temperature dependence of the lattice thermal conductivity found when the latter is limited by the interaction of phonons with isolated dislocations. At temperatures where the dominant wavelength ${\lambda }_d$ of the phonons is large compared with the distance $R$ between the two dislocations of a dipole, it is found that the conductivity is almost independent of the absolute temperature $T$ and larger than the corresponding value for isolated dislocations. With increasing temperature ($R\gg {\lambda }_d$), the thermal conductivity due to dipoles approaches asymptotically the conductivity limited by isolated dislocations. The interaction of the phonons with the dipoles is treated by nonlinear continuum theory which includes also the normal three-phonon interaction. Numerical results, obtained with the material constants of copper, show that dipoles with distances $R$ smaller than $\left|\mathrm{b}\right|(370\mathrm{}°\mathrm{K}/T)$ (b=Burgers vector) can be distinguished from isolated dislocations by measuring the thermal conductivity.