QUESTION THREE

$($a$)$ What is diffusion?

$($b$)$ Why is the diffusion rate in solids slower than that in liquids and gasses?

$($c$)$ State two mechanisms of diffusion in solids.

$\backslash$table$[[,2],[$ marks$],3],[$ marks$],2]]$

$($d$)$ A diffusion couple was formed between pure copper and a Copper:Nickel alloy. After heating the couple to $1000C$ for $30$ days, the concentration of nickel in the pure copper was found to be $\frac{10\mathrm{.}0}{b}ar(wt)\%$ at a position $0\mathrm{.}5$ mm from the pure copper$-$Copper:Nickel interface. What is the original composition of nickel in the Copper:Nickel alloy? The preexponential, $D_0,$ is $2\mathrm{.}7{10}^{-4}\frac{m^2}{s}$ and the activation energy for the diffusion of Nickel in Copper is $236,000\frac{J}{m}ol.$ Take the Universal gas constant, R $,$ to be $8\mathrm{.}314\frac{J}{m}o\frac{l}{K}$ and the Avogadro's constant, N $,$ to be $6\mathrm{.}022\frac{{10}^{23}}{m}ol.$ Use the error function values given in Table $1.$

$\backslash$table$[[,z,$ef$($z$),z,$eff$($z$),z,$eff$($z$)],[,0,0,0\mathrm{.}55,0\mathrm{.}5633,13,0\mathrm{.}9340],[,0\mathrm{.}025,0\mathrm{.}0282,0\mathrm{.}60,0\mathrm{.}6039,1\mathrm{.}4,0\mathrm{.}9523],[,0\mathrm{.}05,0\mathrm{.}0564,0\mathrm{.}65,0\mathrm{.}6420,1\mathrm{.}5,0\mathrm{.}9661],[,0\mathrm{.}10,0\mathrm{.}1125,0\mathrm{.}70,0\mathrm{.}6778,1\mathrm{.}6,0\mathrm{.}9763],[,0\mathrm{.}15,0\mathrm{.}1680,0\mathrm{.}75,0\mathrm{.}7112,1\mathrm{.}7,0\mathrm{.}0838],[,0\mathrm{.}20,0\mathrm{.}2227,0\mathrm{.}80,0\mathrm{.}7421,1\mathrm{.}8,0\mathrm{.}8891],[,0\mathrm{.}25,0\mathrm{.}2763,0\mathrm{.}85,0\mathrm{.}7707,1\mathrm{.}8,0\mathrm{.}9891],[,0\mathrm{.}30,0\mathrm{.}3286,0\mathrm{.}90,0\mathrm{.}7970,1\mathrm{.}9,0\mathrm{.}9028],[,035,03794,0\mathrm{.}95,0\mathrm{.}8209,20,0\mathrm{.}9953],[,0\mathrm{.}40,0\mathrm{.}4284,1\mathrm{.}0,0\mathrm{.}427,2\mathrm{.}2,0\mathrm{.}9981],[,,0\mathrm{.}4755,1\mathrm{.}1,0\mathrm{.}8802,2\mathrm{.}4,0\mathrm{.}9993],[,0\mathrm{.}50,0\mathrm{.}5205,1\mathrm{.}2,0\mathrm{.}9103,2\mathrm{.}6,09998],[,,,,,28,0\mathrm{.}9999]]$