a$)$ Define diffusion, interdiffusion$/$impurity diffusion, and self$-$diffusion? $(6$ point$)$

b$)$ What are the diffusion mechanisms? Please explain them. Which one is more rapid and why? $(11$ point$)$

c$)$ Determine the carburizing time necessary to achieve a carbon concentration of $0\mathrm{.}45wt\%$ at a position $2$ mm into an iron$-$carbon alloy that initially contains $0\mathrm{.}20wt\%C.$ The surface concentration is to be maintained at $1\mathrm{.}30wt\%C,$ and the treatment is to be conducted at $1000C.($Diffusion coefficient of carbon in iron is $1\mathrm{.}93{10}^{-11}\frac{m^2}{s}$ at $1000C.)$ Use the table in lecture notes to determine the related $z$ or erf$(z)$ values. $(10$ point$)$