For each of edge, screw, and mixed dislocations, cite the relationship between the direction of the applied shear stress and the direction of dislocation line motion.

In an edge dislocation, the extra half plane of atoms is perpendicular to the dislocation line. When an applied shear stress is acting on the material, it will cause the dislocation line to move in the direction of the applied stress. Therefore, the direction of dislocation line-motion is the same as the direction of applied shear stress.

In a screw dislocation, the extra half plane of atoms is parallel to the dislocation line. When applied shear stress is acting on the material, it will cause the dislocation line to move in the direction that is perpendicular to both the dislocation line and the applied shear stress. Thus, the direction of dislocation line-motion is perpendicular to the direction of applied shear stress.

A mixed dislocation consists of both edge and screw dislocation components. The motion of the dislocation line is influenced by both the edge and screw dislocation components. When applied shear stress is acting on the material, the motion of the dislocation line can be decomposed into two parts: one parallel to the direction of applied shear stress (edge dislocation component) and one perpendicular to the direction of applied shear stress (screw dislocation component). In summary, for each type of dislocation: 1. Edge dislocation: The direction of dislocation line-motion is the same as the direction of applied shear stress. 2. Screw dislocation: The direction of dislocation line-motion is perpendicular to the direction of applied shear stress. 3. Mixed dislocation: The motion of the dislocation line can be decomposed into two parts, one parallel to the direction of applied shear stress (edge component) and one perpendicular to the direction of applied shear stress (screw component).