$3-$ For the illustrated edge dislocation with $G=27$GPa,$|vec(b)|=0\mathrm{.}286nm,$ shear translation between two atomic rows $(x=0\mathrm{.}5nm),$ interplanar spacing of $0\mathrm{.}405$ nm $,$ and var$=0\mathrm{.}33.$ Determine:

$(40)$

$($a$)$ The Burgers vector assuming that the dislocation line is running out of the paper. $($You may need to re sketch similar schematic in your answer book$)$

$($b$)$ The theoretical critical shear stress.

$($c$)$ The Peierls$-$Nabarro stress.

$($d$)$ Why the calculated Peierls$-$Nabarro Stress is smaller than the theoretical value?