With the aid of diagrams, describe what dislocations are and what role theyplay in yielding.

Dislocations are defects in the crystal structure of materials. They are essentially 'extra' planes of atoms that have been inserted into the regular atomic array.

There are two basic types of dislocations, edge and screw dislocations, which differ by the way the atoms are displaced around them.

1. Edge Dislocations: An edge dislocation is caused by the termination of a plane of atoms in the middle of a crystal. In such a case, an extra half-plane of atoms is introduced. Here is a simple diagram to illustrate this:

    A A A A A
    A A A A A
    A A A A
    A A A A A
    A A A A A

In this diagram, each 'A' represents an atom in the crystal. The third row has one fewer atom than the others, representing an edge dislocation.

2. Screw Dislocations: A screw dislocation is formed by a shear stress that is applied to the crystal resulting in the lattice being distorted. The atoms move from their regular positions. Here is a simple diagram to illustrate this:

    A A A A A
      A A A A A
        A A A A A
          A A A A A
            A A A A A

In this diagram, each 'A' represents an atom in the crystal. The rows of atoms are displaced from their regular positions, representing a screw dislocation.

Dislocations play a key role in the process of yielding, or plastic deformation. When a material is subjected to stress, the dislocations move, allowing the material to deform without breaking. This is because the movement of dislocations requires less energy than breaking and forming new atomic bonds. The movement of dislocations allows the material to accommodate the stress and deform plastically, rather than breaking. This is why materials with high dislocation densities are typically more ductile.

In summary, dislocations are defects in the crystal structure of materials that play a key role in plastic deformation. They allow materials to deform under stress by moving, which requires less energy than breaking and forming new atomic bonds.