The vector giving the closure failure of a circuit taken around a dislocation. For a perfect dislocation in FCC it is (a/2)<110>. It determines the type and energy of the dislocation.
Japanese name: バーガースベクトル
Burgers vector appears in 2 practice questions across 1 topic, including Crystal defects and diffusion.
Make a closed circuit around a dislocation, stepping the same number of atoms in each direction, and then follow the same steps in a perfect crystal without the dislocation: the circuit fails to close and a gap remains. The vector representing this gap is the Burgers vector b. Its sign depends on the conventions for the direction of the circuit and whether the vector runs from start to finish or finish to start (such as the FS/RH rule), so calculations must stick to one convention. The vector b corresponds to the amount and direction of slip when the dislocation passes, and many dislocation properties are determined by it.
The energy of a dislocation per unit length is about Gb²/2, proportional to |b|², so b is chosen as the shortest lattice translation vector. Typical choices are (a/2)<110> in FCC (magnitude a/√2), (a/2)<111> in BCC (√3a/2) and (a/3)<11-20> in HCP (magnitude a). This gives about 0.256 nm for copper and about 0.248 nm for α-iron. The guideline that a dislocation lowers its energy by splitting into two whose Burgers vectors satisfy b₁² > b₂² + b₃² is Frank's rule, and it also explains the dissociation into partial dislocations in FCC.
Even where the dislocation line curves, the Burgers vector of a single dislocation is the same everywhere. Where b is perpendicular to the line the dislocation is edge, where parallel it is screw, and in between it has mixed character. A dislocation therefore cannot end inside a crystal; it must exit at a surface, form a loop or join other dislocations at a node. The sum of Burgers vectors flowing into a node equals the sum flowing out. Note also that an edge dislocation moves in the direction of b, whereas a screw dislocation moves perpendicular to b.
In TEM, dislocation contrast almost vanishes under the condition g·b = 0, where g is the diffraction vector. Finding this invisibility condition for two different g vectors fixes the direction of b. In addition, the rate of plastic shear strain produced by moving dislocations is γ̇ = ρ_m b v (ρ_m is the density of mobile dislocations and v their average velocity), so b is the quantity linking dislocation motion to macroscopic deformation. The force on a dislocation is also estimated as τb per unit length, the product of the shear stress τ and b.
Answer: A. They are perpendicular to each other
An edge dislocation has the form of an extra half-plane of atoms inserted into the crystal, and its Burgers vector b is perpendicular to the dislocation line. An edge dislocation glides in the direction of b, and its slip plane is uniquely defined as the plane containing both b and the line. b is parallel to the line in a screw dislocation; because a screw dislocation has no unique slip plane, it can cross-slip onto another slip plane. Most real dislocations are mixed dislocations in between, with the proportions of edge and screw character changing continuously along the line, so there is no fixed 45°.
Answer: C. About 0.286 nm
The magnitude of (a/2)<110> is (a/2) × √(1² + 1² + 0²) = a/√2, so 0.405/1.414 ≈ 0.286 nm. This equals the nearest-neighbor distance in FCC; dislocations take the shortest lattice translation vector along the close-packed direction as their Burgers vector. About 0.405 nm is the lattice parameter itself (a translation along <100>), which is unfavorable because the dislocation energy is proportional to b². About 0.351 nm applies the BCC (a/2)<111>, that is, √3a/2. The elastic energy per unit length of a dislocation is about Gb²/2, so dislocations with smaller b are more stable.
For a vector of the form (a/n)<uvw>, the magnitude is (a/n)√(u² + v² + w²). For example, (a/2)<110> in FCC copper (a = 0.3615 nm) is 0.3615/√2 ≈ 0.256 nm, equal to the nearest-neighbor distance.
A partial dislocation has a short vector that is not a lattice translation vector. The Shockley partial in FCC is (a/6)<112>; because it leaves a stacking fault behind it, partials exist not singly but as pairs with a stacking fault between them.
Its sign is reversed. Even for the same dislocation, the sign of b is set by the choice of line direction and the circuit convention, so when adding dislocations or considering reactions, the same convention must be used throughout.
An edge dislocation has the form of an extra half-plane of atoms inserted into the crystal, and its Burgers vector b is perpendicular to the dislocation line.
Which correctly describes the relation between the Burgers …This equals the nearest-neighbor distance in FCC; dislocations take the shortest lattice translation vector along the close-packed direction as their Burgers vector.
The Burgers vector of a perfect dislocation in an FCC metal…