Problem $4$

Nitrogen from a gaseous phase is to be diffused into pure $(-$phase$)$ FCC iron.

$(25$ Points$)$

The diffusion coefficient for nitrogen in $-$phase iron at $675C$ is $2\mathrm{.}8{10}^{-11}\frac{m^2}{s}.$

What is the diffusion pre$-$exponential $(D_0)$ if the diffusion activation energy $(Q_d)$ is

empirically measured to be $0\mathrm{.}8e\frac{V}{?}$ atom.

If the surface concentration is maintained at $0\mathrm{.}3wt\%N,$ what will be the concentra$-$

tion $100m$ deep into the iron after $30$ minutes of exposure at $750C.$

The Gaussian Error Function table is given below:

$\backslash$table$[[$z$,$erf$($z$),$z$,$erf$($z$),$z$,$erf$($z$)],[0,0,0\mathrm{.}55,0\mathrm{.}5633,1\mathrm{.}3,0\mathrm{.}9340],[0\mathrm{.}025,0\mathrm{.}0282,0\mathrm{.}60,0\mathrm{.}6039,1\mathrm{.}4,0\mathrm{.}9523],[0\mathrm{.}05,0\mathrm{.}0564,0\mathrm{.}65,0\mathrm{.}6420,1\mathrm{.}5,0\mathrm{.}9661],[0\mathrm{.}10,0\mathrm{.}1125,0\mathrm{.}70,0\mathrm{.}6778,1\mathrm{.}6,0\mathrm{.}9763],[0\mathrm{.}15,0\mathrm{.}1680,0\mathrm{.}75,0\mathrm{.}7112,1\mathrm{.}7,0\mathrm{.}9838],[0\mathrm{.}20,0\mathrm{.}2227,0\mathrm{.}80,0\mathrm{.}7421,1\mathrm{.}8,0\mathrm{.}9891],[0\mathrm{.}25,0\mathrm{.}2763,0\mathrm{.}85,0\mathrm{.}7707,1\mathrm{.}9,0\mathrm{.}9928],[0\mathrm{.}30,0\mathrm{.}3286,0\mathrm{.}90,0\mathrm{.}7970,2\mathrm{.}0,0\mathrm{.}9953],[0\mathrm{.}35,0\mathrm{.}3794,0\mathrm{.}95,0\mathrm{.}8209,2\mathrm{.}2,0\mathrm{.}9981],[0\mathrm{.}40,0\mathrm{.}4284,1\mathrm{.}0,0\mathrm{.}8427,2\mathrm{.}4,0\mathrm{.}9993],[0\mathrm{.}45,0\mathrm{.}4755,1\mathrm{.}1,0\mathrm{.}8802,2\mathrm{.}6,0\mathrm{.}9998],[0\mathrm{.}50,0\mathrm{.}5205,1\mathrm{.}2,0\mathrm{.}9103,2\mathrm{.}8,0\mathrm{.}9999]]$