Burgers vector

In materials science, the Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted as b, that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.

In this perfect crystal structure, a rectangle whose lengths and widths are integer multiples of a (the unit cell edge length) is drawn encompassing the site of the original dislocation's origin.

This dislocation will have the effect of deforming, not only the perfect crystal structure, but the rectangle as well.

Specifically, the breadth of the opening defines the magnitude of the Burgers vector, and, when a set of fixed coordinates is introduced, an angle between the termini of the dislocated rectangle's length line segment and width line segment may be specified.

[2] One can also use a counterclockwise Burgers circuit from a starting point to enclose the dislocation.

The Burgers vector will instead be from the end to the start of the circuit (see picture above).

The magnitude is usually represented by the equation (For BCC and FCC lattices only): where a is the unit cell edge length of the crystal,

and hence the magnitude is represented by Generally, the Burgers vector of a dislocation is defined by performing a line integral over the distortion field around the dislocation line where the integration path L is a Burgers circuit around the dislocation line, ui is the displacement field, and

In most metallic materials, the magnitude of the Burgers vector for a dislocation is of a magnitude equal to the interatomic spacing of the material, since a single dislocation will offset the crystal lattice by one close-packed crystallographic spacing unit.

The Burgers vector plays an important role in determining the direction of dislocation line.

Burgers vector in an edge dislocation (left) and in a screw dislocation (right). The edge dislocation can be imagined as the introduction of a half plane (gray boxes) that does not fit the crystal symmetry. The screw dislocation can be imagined as cut and shear operation along a half plane.