Construction of the Peierls–Nabarro potential of a dislocation from interatomic potentials

In a molecular dynamics simulation the Peierls–Nabarro potential felt by a screw dislocation in a primitive cubic lattice is determined by monitoring the potential energy of the dislocated crystal as a function of the position of the dislocation. In the absence of an external stress, the dislocation, if placed off the equilibrium position, moves towards it. In the quasistatic limit the potential energy of the crystal is the Peierls–Nabarro potential experienced by the dislocation. As the defect moves, it converts potential energy into kinetic energy until all atoms vibrate and the dislocation assumes a position that ensures equipartition between the potential and kinetic energy of the lattice. From the movement towards equilibrium the effective mass of the dislocation per lattice parameter a is determined as 0.1 times the atomic mass. It resists movement with a Newtonian friction coefficient B=0.016Gb/c t , where G is the shear modulus and ct the shear wave velocity.