Diffusion mechanisms and their relation to the Arrhenius temperature dependence of the diffusivity: $D=D_0$exp$(-\frac{Q_d}{R}T).$ Ideal gas constant $R$ : $8\mathrm{.}314\frac{J}{K}*mol.$

a$.$ Interstitial diffusion. In class, we discussed the interstitial mechanism of diffusion in a solid, whereby an interstitial impurity atom "hops" through the lattice. The activation energy for diffusion $Q_d$ is related to the energy barrier $(Q_m)$ that the interstitial atom must overcome as it moves from one interstitial site to another. Given this, why would you expect that interstitial carbon atoms diffuse slightly more slowly than interstitial nitrogen atoms in fcc iron $($hint: consider the atomic radii of $C$ and $N)?$ The atomic radii of $C$ and $N$ are $70pm$ and $65pm,$ respectively.

b$.$ Substitutional diffusion. For impurities $($or solutes$)$ that form substitutionally in a solid, the dominant mechanism for diffusion is the vacancy diffusion mechanism discussed in class. In this case, the activation energy for diffusion $(Q_d),$ is the sum of the vacancy formation energy $(Q_v)$ and the migration energy barrier $)=(Q_v+Q_m.$ Given this information, complete the table below for diffusion of $Ni$ in $Cu.$ Recall that the vacancy fraction is given as $x_v=$exp$(-\frac{Q_v}{R}T).$

$\backslash$table$[[T(C),D(\frac{m^2}{s}),x_v$