Peierls stress is the force (first discovered by Rudolph Peierls and modified by Frank Nabarro

Frank Nabarro

Frank Reginald Nunes Nabarro MBE OMS FRS was an English-born South African physicist and one of the pioneers of solid-state physics, which underpins much of 21st century technology.-Education:...

) needed to move a dislocation

Dislocation

In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...

 within a plane of atoms in the unit cell. The magnitude varies periodically as the dislocation

Dislocation

In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...

 moves within the plane. Peierls stress depends on the size and width of a dislocation

Dislocation

In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...

 and the distance between planes. Because of this, Peierls stress decreases with increasing distance between atomic planes. Yet since the distance between planes increases with planar density, slip

Slip (materials science)

In materials science, Slip is the process by which plastic deformation is produced by a dislocation motion. By an external force, parts of the crystal lattice glide along each other, resulting in a changed geometry of the material. Depending on the type of lattice, different slip systems are...

 of the dislocation is preferred on closely packed planes.

Peierls–Nabarro stress proportionality

Where: the dislocation width = shear modulus = Poisson's ratio

Poisson's ratio

Poisson's ratio , named after Siméon Poisson, is the ratio, when a sample object is stretched, of the contraction or transverse strain , to the extension or axial strain ....

= interatomic spacing = interplanar spacing

The Peierls stress and yield strength temperature sensitivity

The Peierls stress also relates to the temperature sensitivity of the yield strength of a material because it too depends on both short range atomic order and atomic bond strength. As temperature increases, the vibration of atoms increases and thus both peierls stress and yield strength decrease as a result of weaker atomic bond strength at high temperatures.