Peierls stress (also known as the lattice friction stress
) is the force (first described by
Rudolf Peierls
Sir Rudolf Ernst Peierls, (; ; 5 June 1907 – 19 September 1995) was a German-born British physicist who played a major role in Tube Alloys, Britain's nuclear weapon programme, as well as the subsequent Manhattan Project, the combined Allied ...
and modified by
Frank Nabarro
Frank Reginald Nunes Nabarro MBE OMS FRS (7 March 1916 – 20 July 2006) was an English-born South African physicist and one of the pioneers of solid-state physics, which underpins much of 21st-century technology.
Education
Born 7 March 19 ...
) needed to move a
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
within a plane of atoms in the
unit cell
In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector, for example) does not necessaril ...
. The magnitude varies periodically as the
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
moves within the plane. Peierls stress depends on the size and width of a
dislocation
In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to sl ...
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 atomic density,
slip
Slip or SLIP may refer to:
Science and technology Biology
* Slip (fish), also known as Black Sole
* Slip (horticulture), a small cutting of a plant as a specimen or for grafting
* Muscle slip, a branching of a muscle, in anatomy
Computing and ...
of the dislocation is preferred on closely packed planes.
Peierls–Nabarro stress proportionality
:
Where:
:
the dislocation width
:
=
shear modulus
In materials science, shear modulus or modulus of rigidity, denoted by ''G'', or sometimes ''S'' or ''μ'', is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain:
:G \ \stackrel ...
:
=
Poisson's ratio
In materials science and solid mechanics, Poisson's ratio \nu ( nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Pois ...
:
= slip distance or
Burgers vector
In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as , that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.
The vecto ...
:
= interplanar spacing
The Peierls stress and yield strength temperature sensitivity
The Peierls stress also relates to the temperature sensitivity of the
yield strength
In materials science and engineering, the yield point is the point on a stress-strain curve that indicates the limit of elastic behavior and the beginning of plastic behavior. Below the yield point, a material will deform elastically and wi ...
of material because it very much 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.
References
{{Reflist
*Hertzberg, Richard W. ''Deformation and Fracture Mechanics of Engineering Materials 4th Edition''
Crystallographic defects