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 a type of defect in a crystal lattice where an extra half-plane of atoms is inserted. A screw dislocation, on the other hand, is a defect caused by shear forces that twist the lattice such that lattice planes spiral around the dislocation. Mixed dislocations possess characteristics of both edge and screw dislocations.

For an edge dislocation, the direction of dislocation line motion is perpendicular to both the dislocation line and the applied shear stress direction. The motion of the dislocation line will cause the extra half-plane of atoms to advance through the lattice, resulting in the material being deformed.

In the case of a screw dislocation, the dislocation line motion is parallel to the applied shear stress direction. The motion of the dislocation line occurs by the sliding of one part of the crystal lattice relative to the other, resulting in a twisting effect in the lattice structure.

For mixed dislocations, the motion of the dislocation line will have components along both the edge and screw dislocation directions. The direction of dislocation line motion will depend on the applied shear stress direction, and the angle between the applied shear stress direction and the dislocation line determines the proportion of edge and screw character in the mixed dislocation. In conclusion, the direction of dislocation line motion is influenced by the type of dislocation as well as the direction of the applied shear stress. For edge dislocations, the motion is perpendicular to the applied shear stress direction, for screw dislocations it is parallel, and for mixed dislocations, it is determined by the angle between the applied shear stress direction and the dislocation line.