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Plastic Deformation
Dislocation Reactions in FCC Crystal Structures

· In Face Centered Cubic (fcc) crystals, dislocation reactions can occur that make important contributions to work hardening. These reactions involve partial dislocations rather than the unit dislocations that have so far been considered.
· The elastic energy per unit length for a dislocation in a material with a shear modulus, G, is G b2. Energy considerations favor the formation of dislocations with the smallest possible Burgers vector.
· For the fcc lattice, the unit dislocation have Burgers vectors given by:
b= (a/2)<110> , where a is the length of the side of the cubic unit cell.
· For the cubic FCC structure the magnitude of the Burgers vector is given in terms of the Miller index (h k l) of its direction: 
b = (a/2) (h2+ k2+l2)0.5 = (a / 20.5 )