If sufficient force is applied to a crystal, it can be permanently deformed. Permanent deformation in metal crystals occurs due to atomic displacements on the planes that are most closely packed, and it happens in the most closely packed directions. Assume that a force is applied to a crystal of FCC copper that permanently stretches the crystal in the [001] direction. The (111) plane is one of the close-packed planes in FCC copper on which permanent deformation could occur.
(a) What is the angle between the [001] direction and the normal to the (111) plane?
(b) Atom displacements along which close-packed directions within the (111) plane could contribute to the permanent deformation of the crystal in the [001] direction?
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