What is the Peierls stress?
The Peierls stress is the minimum shear stress required to move a single dislocation of unit length in a perfect crystal. The magnitude of the Peierls stress determines the ability of the lattice to resist dislocation motion – the lattice resistance in the absence of thermal activation.
Another way is to think about the resistive force to dislocation motion as the magnitude of the gradient of strain energy curve. This means that the Peierls stress is proportional to the maximum gradient of the misfit energy curve. If we use the continuum model, the energy of the dislocation is independent of position. Any stress, however small, would set the dislocation into motion, because the dislocation is always in neutral equilibrium and so will move under any force. We know this is not right. We need to take into account the crystal structure on an atomic level such that the energy of the dislocation depends on its exact position. The dislocation will have several stable equilibrium positions which persist up until a stress is applied that exceeds a certain magnitude (the Peierls stress), at which point the dislocation can move.