(a) Briefly describe a twin and a twin boundary. (b) Cite the difference between mechanical and

A twin is a type of defect in crystalline materials where a mirror-image region is created by applying a shear force on the crystal lattice. This results in two adjacent, but differently oriented, regions that share the same lattice structure but have a specific orientation relationship. These two regions are known as the twin and the matrix. A twin boundary is the planar interface separating the twin and the matrix. It's characterized by a specific crystallographic plane, which acts as a mirror plane. The atoms at the twin boundary have different nearest neighbors that cause a coherent interface between the twin and the matrix.

Mechanical twinning occurs when an external force, like mechanical stress, acts on the crystal lattice, causing a sudden change in its orientation and creating the twin boundary. This happens as the material tries to accommodate the applied force, and the crystal lattice reorders through a shear process. An example of mechanical twinning is seen in metals like titanium and zirconium, where deformation twins are formed under high mechanical loads. On the other hand, chemical twinning or growth twinning occurs during the crystal growth process. In this case, the twin boundary is formed because of variations in the local environment like impurities, stresses, or temperature changes that affect the growth conditions. The crystal growth continues in a different orientation without any applied external force, producing the twin structure. An example of chemical twinning is seen in minerals like quartz, where twinned crystal structures form due to variations in their growth environment.