Deformation twins are also able to form along the {111} planes of FCC crystals, as a result of the application of a shear stress across this type of plane. In twinning, the shear directions are < >. (a) Prove, using Eq. 5.4, that the [ ̅]and [ ̅] are directions that lie in the (111) plane. (b) Determine the Schmid factors for the (111)[ ̅],()[ ̅], and ()[ ̅] twinning systems if a tensile stress is applied along the [711] direction.