Burgers vector

Burgers vector
In physics, the Burgers vector, named after Dutch physicist Jan Burgers,
is a vector, often denoted b, that represents the magnitude and direction
of the lattice distortion resulting from a dislocation in a crystal lattice.
Burgers vectors
The vector s magnitude and direction is best understood when the
dislocation-bearing crystal structure is first visualized without the
dislocation, that is, the perfect crystal structure. 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. Once this encompassing rectangle is drawn,
the dislocation can be introduced. This dislocation will have the effect of
deforming, not only the perfect crystal structure, but the rectangle as well.
The said rectangle could have one of its sides disjoined from the
perpendicular side, severing the connection of the length and width line
segments of the rectangle at one of the rectangle s corners, and displacing
each line segment from each other. What was once a rectangle before the
dislocation was introduced is now an open geometric figure, whose
opening defines the direction and magnitude of the Burgers vector.
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.
The direction of the vector depends on the plane of dislocation, which is
usually on one of the closest-packed crystallographic planes. The
magnitude is usually represented by the equation:
where a is the unit cell edge length of the crystal, ||b|| is the magnitude of
Burgers vector and h, k, and l are the components of the Burgers vector, b
= . 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.
In edge dislocations, the Burgers vector and dislocation line are at right
angles to one another. In screw dislocations, they are parallel.
The Burgers vector is significant in determining the yield strength of a
material by affecting solute hardening, precipitation hardening and work
hardening.
Frank-Read Source
Animation illustrating how stress on a Frank-Read Source (center) can
generate multiple dislocation lines in a crystal.
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In materials science, a Frank-Read source is a mechanism explaining
the generation of multiple dislocations in specific well-spaced slip planes
in crystals when they are deformed. When a crystal is deformed, in order
for slip to occur, dislocations must be generated in the material. This
implies that, during deformation, dislocations must be primarily
generated in these planes. Cold working of metal increases the number of
dislocations by the Frank-Read mechanism. Higher dislocation density
increases yield strength and causes work hardening of metals.
It was proposed by and named after British physicist Charles Frank and
Thornton Read.