The Burgers vector, named after Dutch physicist Jan Burgers, is a vector In elementary mathematics, physics, and engineering, a Euclidean vector is a geometric object that has both a magnitude (or length) and direction. A Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by, often denoted b, that represents the magnitude and direction of the lattice distortion of dislocation In materials science, a dislocation is a crystallographic defect or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials. The theory was originally developed by Vito Volterra in 1905. Some types of dislocations can be visualized as being caused by the termination of a plane in a crystal lattice In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry. Patterns are located upon the points of a lattice, which is an array.[1]
Burgers vectorsThe 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 In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry. Patterns are located upon the points of a lattice, which is an array 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. 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 In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square. More generally, when the end points are both vertices of a polygon, the line segment is either an edge if they are adjacent vertices, or 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 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 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 In materials science, a dislocation is a crystallographic defect or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials. The theory was originally developed by Vito Volterra in 1905. Some types of dislocations can be visualized as being caused by the termination of a plane, 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 The yield strength or yield point of a material is defined in engineering and materials science as the stress at which a material begins to deform plastically. Prior to the yield point the material will deform elastically and will return to its original shape when the applied stress is removed. Once the yield point is passed some fraction of the of a material by affecting solute hardening Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice another element (the base metal). The alloying element diffuses into the matrix, forming a solid solution. In most binary systems, when alloyed above a certain, precipitation hardening Precipitation hardening, also called age hardening, is a heat treatment technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium, magnesium, nickel and titanium, and some stainless steels. It relies on changes in solid solubility with temperature to produce fine particles of an impurity and work hardening Work hardening, also known as strain hardening, is the strengthening of a material by, macroscopically speaking, plastic deformation . As the material becomes increasingly saturated with new dislocations, more dislocations are prevented from nucleating (a resistance to dislocation-formation develops). This resistance to dislocation-formation.
See also
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References
- ^ Callister, William D. Jr. "Fundamentals of Materials Science and Engineering," John Wiley & Sons John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing and markets its products to professionals and consumers, students and instructors in higher education, and researchers and practitioners in scientific, technical, medical, and scholarly fields. The company produces books,, Inc. Danvers, MA. (2005)
- ^ Kittel, Charles, "Introduction to Solid State Physics," 7th edition, John Wiley & Sons John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing and markets its products to professionals and consumers, students and instructors in higher education, and researchers and practitioners in scientific, technical, medical, and scholarly fields. The company produces books,, Inc, (1996) pp 592-593.
External links
Categories: Crystallography Categories: Condensed matter physics | Mineralogy | Chemistry | Materials science Materials science includes those parts of chemistry, physics, geology, and even biology that deal with the physical, chemical or biological properties of materials. It is usually considered an applied science, in which the properties under study have some industrial purpose | Vectors In mathematics and physics, the concept of a vector is of fundamental importance and encompasses a variety of distinct but related notions
