The vibrational spectra of straight screw and edge dislocations in several body-centered cubic (Mo and Fe) and face-centered cubic (Cu and Al) metals were calculated within the harmonic approximation. Advantage was taken of the translational symmetry of straight dislocations to calculate efficiently their phonon eigenstates in the harmonic limit. This allowed calculation of the low-temperature contribution of straight screw and edge dislocations to the heat capacity of each respective metal, and showed that the dominant temperature dependence below 5K was linear. Comparison with heat capacity measurements of heavily cold-worked Cu reveals very good agreement with the present calculations. At higher temperatures, the contribution from the non-linear terms becomes significant. As a result, maxima in the straight dislocation heat capacities were observed in the temperature range from 9% to 16% of the Debye temperature. The appearance of localized and resonance peaks in the vibrational spectra induced by dislocations was investigated, and their spatial spread around the dislocation cores were studied in detail by projecting vibrational eigenstates onto individual atoms. The deviation of these atomic-level vibrational free energies from that of the perfect crystal was studied as a function of distance to the dislocation cores, and it was establish that, similar to the dislocation energy, the vibrational free energy of an isolated dislocation behaves logarithmically in the long-range limit. Finally, vibrational spectra were obtained for propagating waves along the dislocation line and it was found that the dispersion for these waves was consistent with the notion of kink formation and motion for screw dislocations.

Vibrational Properties of Straight Dislocations in BCC and FCC Metals within the Harmonic Approximation. P.C.Schuck, J.Marian, J.B.Adams, B.Sadigh: Philosophical Magazine, 2009, 89[31], 2861-82