Experiments like Kirkendalls's are performed at elevated temperature. One such experiment using a 70:30 mole \(\%\) copper mixture on one side and pure zinc on the other, was conducted at \(785^{\circ} \mathrm{C}\) and yielded individual diffusion coefficients for copper and zinc in the alloy of:

\[D_{C u}=2.2 \times 10^{-13} \frac{\mathrm{m}^{2}}{\mathrm{~s}} \quad D_{Z n}=5.1 \times 10^{-13} \frac{\mathrm{m}^{2}}{\mathrm{~s}}\]

a. What is the nominal effective diffusivity in the alloy, \(D_{\text {eff }}\) ?

b. Where does the maximum molar velocity occur?

c. Given your answers to parts

(a) and (b), plot the molar velocity as a function of time.

d. If we define the front location, i.e., where the tracer particles lie, as the point where \(0.5=\exp \left[-\frac{y^{2}}{4 D_{\text {eff }} t}\right]\), how does that front progress as a function of time? Plot it.