Class problem

Consider a diffusion couple

set up between pure tungsten

and a tungsten $-1$ at $\%$ thorium

alloy. After several minutes of

exposure at $2000C,$ a

transition zone of $0\mathrm{.}01cm$

thickness is established. What

is the flux of thorium atoms at

this time if diffusion is due to

$($a$)$ volume diffusion, $($b$)$ grain

boundary diffusion, and

$($c$)$

surface diffusion. Diffusion

coefficient D from thorium to

tungsten are:

$D_{\text{S}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}}=0\mathrm{.}47$exp$(-66,\frac{400}{k}T)$

$D_{\text{V}\text{o}\text{l}\text{u}\text{m}\text{e}}=$exp$(-120,\frac{000}{k}T)$

$D_{G.B.}=0\mathrm{.}74$exp$(-90,\frac{000}{k}T)$