A diffusion couple including inert tungsten wire markers was made by plating pure copper onto a block of $-$brass with $x_{Zn}=0\mathrm{.}3,$ as shown in the Figure on the left. After $56$ days at $785C,$ the wire marker velocity was $2\mathrm{.}6{10}^{-9}m\frac{m}{s},$ with a composition at the markers of $x_{Zn}=0\mathrm{.}22.$ The composition gradient at the markers $d\frac{x_{zn}}{d}x$ is $0\mathrm{.}089m{m}^{-1}.$ A detailed analysis of the data using the Boltmann$-$Matano solution gives an interdiffusion coefficient:

$D=4\mathrm{.}5{10}^{-13}\frac{m^2}{s}$ at $x_{zn}=0\mathrm{.}22.$

The schematic in the middle shows the set$-$up$.$

$D=x_{Cu}{D}_{Zn}+x_{Zn}{D}_{Cu}$

$v=\frac{x_{\text{m}\text{a}\text{r}\text{k}\text{e}\text{r}}}{2}t$

$v=(D_{Zn}-D_{Cu})d\frac{x_{Zn}}{d}x$

a$.$ Use this information to calculate $D_{Zn}$ and $D_{Cu}$ at $x_{Zn}=0\mathrm{.}22.$

b$.$ Using arrows, show the direction of the fluxes $J_{Zn},J_{Cu}$ and the flux of vacancies $J_V,$ on the schematic.

c$.$ The melting point of $Zn$ is $419\mathrm{.}5C$ and the melting point of copper is $1084.6C.$ Does this fit with your calculation of the intrinsic diffusivities $D_{Zn}$ and $D_{Cu}?$ Explain. Which one is larger and why?

d$.$ Describe what the schematic on the right is trying to show.

According to the information in this problem, which element is A and which is B$?$