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The '''Burgers vector''', named after Dutch physicist [[Jan Burgers]], is a [[Vector (geometric)|vector]], often denoted '''b''', that represents the [[Magnitude (vector)|magnitude]] and direction of the lattice distortion of [[dislocation]] in a [[Crystal structure|crystal lattice]].<ref>Callister, William D. Jr. "Fundamentals of Materials Science and Engineering," [[John Wiley & Sons]], Inc. Danvers, MA. (2005)/</ref> | |||
[[Image:Vector de Burgers.PNG|250px|thumbnail|right|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 [[Crystal structure#Unit cell|unit cell]] 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 the closest-packed plane of unit cell. | |||
The magnitude is usually represented by the equation: | |||
::<math> | |||
\|\mathbf{b}\|\ = \textstyle\frac{a}{2}\sqrt{h^2+k^2+l^2} | |||
</math> | |||
where ''a'' is the unit cell length of the crystal, ||'''b'''|| is the magnitude of Burgers vector and h, k, and l are the components of the Burgers vector, '''b''' = <h k l>. 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 [[Dislocation#Edge dislocations|edge dislocations]], the Burgers vector and [[dislocation line]] are at right angles to one another. In [[Dislocation#Screw dislocations|screw dislocations]], they are parallel.<ref>Kittel, Charles, "Introduction to Solid State Physics," 7th edition, [[John Wiley & Sons]], Inc, (1996) pp 592-593.</ref> | |||
The Burgers vector is significant in determining the [[Yield (engineering)|yield strength]] of a material by affecting [[Solid solution strengthening|solute hardening]], [[precipitation hardening]] and [[work hardening]]. | |||
==See also== | |||
* [[Frank-Read Source]] | |||
==References== | |||
<references/> | |||
==External links== | |||
{{DEFAULTSORT:Burgers Vector}} | |||
[[Category:Crystallography]] | |||
[[Category:Materials science]] | |||
[[Category:Vectors]] | |||
[[de:Versetzung (Materialwissenschaft)#Der Burgersvektor]] | |||
Revision as of 05:55, 7 April 2013
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 of dislocation in a crystal lattice.[1]
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 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 the closest-packed plane of unit cell. The magnitude is usually represented by the equation:
where a is the unit cell length of the crystal, ||b|| is the magnitude of Burgers vector and h, k, and l are the components of the Burgers vector, b = <h k l>. 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.[2]
The Burgers vector is significant in determining the yield strength of a material by affecting solute hardening, precipitation hardening and work hardening.
See also
References
- ↑ Callister, William D. Jr. "Fundamentals of Materials Science and Engineering," John Wiley & Sons, Inc. Danvers, MA. (2005)/
- ↑ Kittel, Charles, "Introduction to Solid State Physics," 7th edition, John Wiley & Sons, Inc, (1996) pp 592-593.