Elementary excitations of Burger's model for a junction between grains

A theory is presented of the elementary excitations of Burgers' dislocation model for a symmetrical pure tilt boundary. Within the framework of isotropic elasticity we calculate the effective force constants of harmonic springs that hold together interfacial dislocations. Interactions between further neighbour dislocations are taken into account, and it is shown that the sum rule for the force constants is satisfied exactly. We discuss the peculiarities of the excitation spectrum and introduce a concept of a characteristic frequency associated with a tilt boundary.