Editing Dislocation (section)

===Edge===
[[Image:Dislocation edge d2.svg|right|thumb|Schematic diagram (lattice planes) showing an edge dislocation. Burgers vector in black, dislocation line in blue.]]

A crystalline material consists of a regular array of atoms, arranged into lattice planes. An edge dislocation is a defect where an extra half-plane of atoms is introduced midway through the crystal, distorting nearby planes of atoms. When enough force is applied from one side of the crystal structure, this extra plane passes through planes of atoms breaking and joining bonds with them until it reaches the grain boundary.  The dislocation has two properties, a line direction, which is the direction running along the bottom of the extra half plane, and the [[Burgers vector]] which describes the magnitude and direction of distortion to the lattice. In an edge dislocation, the Burgers vector is perpendicular to the line direction.

The stresses caused by an edge dislocation are complex due to its inherent asymmetry. These stresses are described by three equations:<ref name="rhill">{{cite book|first1=R.E.|last1=Reed-Hill|first2=Reza|last2=Abbaschian|date=1994|title=Physical Metallurgy Principles|location=Boston|publisher=PWS Publishing Company|isbn=0-534-92173-6}}</ref>

::<math> \sigma_{xx} = \frac {-\mu \mathbf{b}} {2 \pi (1-\nu)} \frac {y(3x^2 +y^2)} {(x^2 +y^2)^2}</math>

::<math> \sigma_{yy} = \frac {\mu \mathbf{b}} {2 \pi (1-\nu)} \frac {y(x^2 -y^2)} {(x^2 +y^2)^2}</math>

::<math> \tau_{xy} = \frac {\mu \mathbf{b}} {2 \pi (1-\nu)} \frac {x(x^2 -y^2)} {(x^2 +y^2)^2}</math>

where <math>\mu</math> is the [[shear modulus]] of the material, <math>\mathbf{b}</math> is the [[Burgers vector]], <math>\nu</math> is [[Poisson's ratio]] and <math>x</math> and <math>y</math> are coordinates.

These equations suggest a vertically oriented dumbbell of stresses surrounding the dislocation, with compression experienced by the atoms near the "extra" plane, and tension experienced by those atoms near the "missing" plane.<ref name="rhill"/>