The energy of dislocation dipoles

In conventional dislocation theory based on the concept of Volterra dislocations, the energy of coplanar dislocation dipoles cannot be obtained without introducing an ill-defined ad hoc annihilation distance. When the dislocations are described more realistically by Peierls dislocations, absolute values for the dipole energy can be obtained from physical arguments. It is found that when dislocations in a dipole come close, they may not annihilate each other but the dipole can collapse when the dislocations have reached a critical separation of several lattice constants.