$(34$ pts$)$ Answer the following questions:

$($a$)(4$ pts$)$ Carbon diffuses in iron via an

interstitial mechanism $-$ for FCC iron from

one octahedral site to an adjacent one. In

figure, we assume the diffusion occurs from

$(0,\frac{1}{2},1)$ to $(\frac{1}{2},\frac{1}{2},\frac{1}{2}).$ Determine a

crystallographic direction in which this

diffusion of carbon in FCC iron takes place.

$($b$)(4$ pts$)$ Deep sea fish can survive without distortion under very high hydrostatic

pressure environment. Why?

$($c$)(6$ pts$)$ Schematically $($but accurately$)$ draw a typical stress$-$strain curve for $($i$)$

aluminum, $($ii$)$ alumina, and $($iii$)$ polyethylene. Draw these three cases in one plot for

the direct comparison.

$($d$)(6pts)$ The dislocation loop is located on a crystal slip plane with

its Burgers vector $($b$)$ as shown below. Identify the 'dislocation

character' at point A$,$ B$,$ and between A and B$?$