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.

An edge dislocation is characterized by a slip plane, a Burgers vector, and a dislocation line. In an edge dislocation, the Burgers vector is perpendicular to the dislocation line. When a shear stress is applied parallel to the slip plane and in the direction of the Burgers vector, the dislocation starts to move in the direction of the applied stress.

A screw dislocation can be characterized by a dislocation line and a Burgers vector, just like an edge dislocation. However, for a screw dislocation, the Burgers vector is parallel to the dislocation line. When a shear stress is applied along the Burgers vector direction, the dislocation moves parallel to the direction of the applied stress and in the opposite direction of the Burgers vector.

A mixed dislocation has characteristics of both edge and screw dislocations. The Burgers vector in a mixed dislocation has both edge and screw components, and thus it is neither parallel nor perpendicular to the dislocation line. The motion of a mixed dislocation depends on the configuration of the dislocation and the applied stress acting on the slip plane. It may move in different directions under stress, and the resultant motion signifies a combination of both edge and screw dislocations.

In summary, the relationship between the direction of the applied shear stress and the direction of dislocation line motion is as follows: 1. Edge dislocations: The applied shear stress must be parallel to the slip plane and in the direction of the Burgers vector for dislocation motion to occur. The direction of motion is in the direction of the applied stress. 2. Screw dislocations: The applied shear stress must be along the direction of the Burgers vector for dislocation motion to occur. The direction of motion is parallel to the applied stress and opposite to the Burgers vector. 3. Mixed dislocations: The motion of mixed dislocations depends on the configuration of the dislocation and the orientation of applied stress acting on the slip plane. It signifies a combination of edge and screw dislocation motion.