Dislocations in a simple cubic lattice

The properties of dislocations are calculated by an approximate method due to Peierls. The width of a dislocation is small, displacements comparable with the interatomic distance being confined to a few atoms. The shear stress required to move a dislocation in an otherwise perfect lattice is of the order of a thousandth of the "theoretical" shear strength. The energy and effective mass of a single dislocation increase logarithmically with the size of the specimen. A pair of dislocations of opposite sign in the same glide plane cannot be in stable equilibrium unless they are separated by a distance of the order of 10 000 lattice spacings. If an external shear stress is applied there is a critical separation of the pair of dislocations at which they are in unstable equilibrium. The energy of this unstable state is the activation energy for the formation of a pair of dislocations. It depends on the external shear, and for practical stresses is of the order of 7 electron volts per atomic plane. The size and energy of dislocations in real crystals are unlikely to differ greatly from those calculated: the stress required to move a dislocation and the critical separation of two dislocations may be seriously in error.