Problem $2$: Lomer Lock

Consider an FCC crystal with two

dislocations: $\frac{a}{2}[\frac{01}{b}ar(1)]$ dislocation on the $(111)$

slip plane, and $\frac{a}{2}[101]$ dislocation on the

$(\frac{11}{b}ar(1))$ slip plane, as shown to the right.

a$.)$ What is the line of intersection of the two planes?

b$.)$ Take this line of intersections as the line direction for the two dislocations. Is each

dislocation edge$-$type, screw$-$type, or mixed?

c$.)$ A tensile stress along the horizontal line $([110]$ direction$)$ resolves as shear stresses on each

plane to drive the two dislocations to the right. When they reach the plane intersection, the

dislocations react. What is the resulting Burgers vector from the reaction? Is the reaction

energetically favorable?

d$.)$ What is the slip plane of the new dislocation $($Hint: take the cross product from the results of

part $($a$)$ and the results of part $($c$))?$ Do you expect the dislocation to be mobile?