Vibrational properties of straight dislocations in bcc and fcc metals within the harmonic approximation

Abstract

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