Stability transition conditions of dislocation cores and Peierls stress

At the atomic scale, a dislocation in a crystal possesses two equilibrium cores: One has its symmetric center at the lattice point and is referred to as the O-core; the other has its symmetric center at the middle between two neighboring lattice points and is referred to as the B-core. The possible positions (symmetric centers) of the B-core and the O-core are arrayed alternately, and the dislocation movement undergoes a sequential transformation between the two types of dislocation cores. The core with lower energy is stable, and the energy difference between the O-core and the B-core is the Peierls barrier. It is found that the stability of the core is not fixed. In some materials, the B-one core is stable, and in other materials, the O-core is stable. Furthermore, the core stability can be tuned by exerting pressure or changing the environmental temperature. Because at the stability transition point the energy difference is zero, the Peierls barrier disappears and the dislocation almost moves freely. As a consequence, material plasticity dominated by the dislocation mobility will undergo substantial change in the process of the stability transition. Therefore, it is important to understand under what condition the transition occurs. Using the variational method, the stability phase boundary in the model-parameter space is investigated and the transition condition is approximately described by an analytical equation. Furthermore, it is found that in addition to the disappearance of the Peierls barrier, the B-core and the O-core have the same width at the transition point.