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The Burgers vector will be the vector to complete the circuit, i.e., from the start to the end of the circuit. [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). [3]
A vector made from two Roman letters describes the Burgers vector of a perfect dislocation. If the vector is made from a Roman letter and a Greek letter, then it is a Frank partial if the letters are corresponding (Aα, Bβ,...) or a Shockley partial otherwise (Aβ, Aγ,...). Vectors made from two Greek letters describe stair-rod dislocations.
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation [1] occurring in various areas of applied mathematics, such as fluid mechanics, [2] nonlinear acoustics, [3] gas dynamics, and traffic flow. [4]
The contrast of a dislocation is scaled by a factor of the dot product of this vector and the Burgers vector (). As a result, if the Burgers vector and g → {\displaystyle {\vec {g}}} vector are perpendicular, there will be no signal from the dislocation and the dislocation will not appear at all in the image.
Nye has introduced a set of tensor (so-called Nye's tensor) to calculate the geometrically necessary dislocation density. [4] For a three dimension dislocations in a crystal, considering a region where the effects of dislocations is averaged (i.e. the crystal is large enough). The dislocations can be determined by Burgers vectors.
Lattice configuration of the slip plane in a bcc material. The arrow represents the Burgers vector in this dislocation glide system. Slip in body-centered cubic (bcc) crystals occurs along the plane of shortest Burgers vector as well; however, unlike fcc, there are no truly close-packed planes in the bcc crystal structure. Thus, a slip system ...
When the scalar field is the real numbers, the vector space is called a real vector space, and when the scalar field is the complex numbers, the vector space is called a complex vector space. [4] These two cases are the most common ones, but vector spaces with scalars in an arbitrary field F are also commonly considered.
the perturbation carried by the dislocation (Burgers vector) is along a dense direction: the shift of one node in a dense direction is a lesser distortion; the dislocation line tends to follow a dense direction, the dislocation line is often a straight line, a dislocation loop is often a polygon.