PeierlsNabarro

The Peierls-Nabarro model describes the motion of dislocations in crystalline solids. A dislocation is a line defect in the crystal lattice, and its movement leads to plastic deformation. The model focuses on the energy associated with a dislocation line, particularly how this energy changes as the dislocation moves.

Rudolf Peierls and F.R.N. Nabarro independently developed this concept. They realized that a dislocation core, the region immediately surrounding the dislocation line, is not infinitely sharp. Instead, it has a finite width due to the discrete nature of the atomic lattice. As the dislocation moves, atoms must be rearranged across this core region.

The Peierls-Nabarro model calculates the energy required to move the dislocation from one equilibrium position to another. This energy barrier is known as the Peierls stress. The magnitude of the Peierls stress depends on factors such as the atomic spacing, the interatomic forces, and the width of the dislocation core. A wider core generally leads to a lower Peierls stress, meaning the dislocation can move more easily.

This model is fundamental in understanding the mechanical properties of materials, particularly their resistance to plastic deformation. It helps explain why different materials deform differently and how factors like temperature and alloying can affect their strength. While simplified, the Peierls-Nabarro model provides a crucial theoretical framework for studying dislocation mobility.