Dislocations and Grain Boundaries

A so$-$called symmetrical low$-$angle boundary can be described as an assembly of edge dislocations

$($see figure $1).$

Figure $1$: Schematic sketch of a low$-$angle boundary.

Estimate the specific grain boundary energy for copper with a $10$ tilt angle, $G=40$GPa, and

$|vec(b)|=4{10}^{-10}m.$ Note: Make use of the fact that the energy of a dislocation can be assumed to

be $E_D=\frac{1}{2}G{b}^2.$

Calculate the values for tilt angles of var${}_1=5$ and var${}_2=12.$

Why is there a limit for the tilt angle of low$-$angle boundaries at about $15?$