Lattice dynamics of a solid with a screw dislocation

A Green function method is developed for the study of the perturbed vibrational modes of a solid containing a straight screw dislocation. The method takes into account the discrete structure of the lattice and makes direct use of the fact that at large distances from the dislocation axis the atomic displacements are correctly given by the continuum theory. An intermediate state is first constructed in which each atom is given a displacement appropriate to the static continuum theory and then the lattice is allowed to relax to its final state. The unperturbed Green function in the intermediate state is defined in terms of the harmonic force constants and the anharmonic terms in the crystal hamiltonian are treated as perturbations.

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