Please provide an explanation for each problem, explaining (1) the critical phenomenon that is operating in the problem, (2) the equations needed and any limitations associated with this equation, and (3) the importance of this behavior for real materials response (i.e., why is this important?)

Problem 1 A pure screw dislocation in an FCC crystal will tend to dissociate into two partial dislocations. To cross- slip, these partials must recombine. Determine the total work needed to recombine the two partials. To answer this problem, assume both an equilibrium separation distance that is based on the crystal's stacking fault energy and a minimum separation distance that is equal to the Burgers vector of a full dislocation. When calculating the work for recombination, consider the edge and screw components of the partials and the stacking fault that lies between them. How does the total work vary with the stacking fault energy? Let G = 60 GPa, bperfect = 2 10-10 m, ? = 0.33, and let ? vary from 0.01 to 0.2 J/m2.

Problem 1 What F ba 1 Z 8 = are What F5 = 2,1 ba "yzl Work = -1 bea 20 are Force I apply is resisting the forces from the defects points b SF ds Start w/ RHS which dissociates into J two partials, bel is + E, bea is - E, and bs, and bea are RHS character, the Forces? xy, 1 Keep Partial #1 stationary and apply stress Partial #2 into #1, |61|= 3 | Bposent | = b more ba a Gba 21 (1-1) + Gbs 217 (attractive) be and bs ? $ = 30 (for FCC) be= b sin b, bs = b cos = b, 1 = insert for (5a = 6 [3+ & 6 - +5] Sea 21 S Force in neg. Those spacing b attractive! (repulsive) are all per unit length! b De [ $ (B-) hus - 13] " -1 217 b 2 -8]ds ( [- - 25) + - 8]J = -1 211 (1-1) San 662 16 17 8 SF) y = 1/3 6 [(1-1)-() -8 (-6) (1) 2 (1-1) X Since: -Gh I Che 2w6-904 -XF = 0 Gb n (06) - 8 (612-6) 161