Dislocation character

For line tangent $\mathbf{t}$, a screw dislocation has Burgers vector parallel to $\mathbf{t}$, an edge dislocation has it perpendicular, and a mixed dislocation has both components.

A mixed dislocation has a line direction neither parallel nor perpendicular to its Burgers vector, combining screw and edge character. Along a curved dislocation line, the local character can change continuously while the Burgers vector remains fixed.

A dislocation loop therefore need not be assigned one character everywhere. Decomposing a local segment into edge and screw contributions helps analyze its stress field, mobility, and interaction with obstacles.

An edge dislocation is a crystal line defect whose Burgers vector is perpendicular to the dislocation line. It is often pictured as the termination of an extra half-plane of atoms inside the crystal.

Motion of the line allows a slip displacement to advance through the material without every bond across a whole plane changing simultaneously. Its surrounding elastic distortion includes compressive and tensile regions, connecting an atomic-scale defect with macroscopic plastic deformation.

A screw dislocation is a crystal line defect whose Burgers vector is parallel to the dislocation line. Atomic planes around it have a helical arrangement, rather than the extra-half-plane geometry associated with an edge dislocation.

Its motion permits crystal slip. Because several planes can contain the same line and Burgers vector, screw segments can sometimes change their glide plane by cross-slip, with the actual possibility depending on the crystal and defect structure.

The antiplane field $w=b\arg (x+iy)/(2\pi )$ has a smooth local gradient on the punctured plane and satisfies the differential strain compatibility condition there. Its circulation around the defect axis is nevertheless $b\ne 0$, excluding a globally single-valued displacement on that domain. A radial cut permits a branch with an axial jump $b$ between the two cut faces; joining faces with that mismatch is the Volterra construction of a screw dislocation with Burgers vector parallel to the axis. The stress has a singular core where linear elasticity requires microscopic or plastic regularization. This example separates a local differential integrability test from global closure around a hole.

Motion of a screw segment from one allowed glide plane to another containing the same Burgers vector.