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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]
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.
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.
This repulsion is a consequence of stress fields around each partial dislocation affecting the other. The force of repulsion depends on factors such as shear modulus, burger’s vector, Poisson’s ratio, and distance between the dislocations. [4] As the partial dislocations repel, stacking fault is created in between.
Position vector r is a point to calculate the electric field; r′ is a point in the charged object. Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues. [citation needed] Electric transport
If a shear stress is exerted on the slip plane then a force =, where b is the Burgers vector of the dislocation and x is the distance between the pinning sites A and B, is exerted on the dislocation line as a result of the shear stress.