Oscillations of the elastic superstructure formed by a lattice of screw dislocations

The equations of small oscillations of a dislocation lattice formed by a periodic system of parallel rectilinear screw dislocations are formulated. The stability of such a lattice is discussed, and it is shown that it brings about a corresponding spontaneous twisting of a crystalline sample. The long-wavelength collective oscillations of an isotropic elastic medium containing a dislocation lattice are described, among which are some which resemble plasma oscillations in a system of electric charges. The dispersion relations are obtained for five branches of oscillations, corresponding to the five degrees of freedom of the system under study (three degrees of freedom for displacements of the medium and two corresponding to bending oscillations of the dislocations). The possibility of observing the resonance frequency in the oscillation spectrum near the analog of the plasma frequency is pointed out.