Q$)$ An approximate expression for the total driving force for precipitation in a regular solution

is

$G_0=RT[x_{0}In(\frac{x_0}{x_e})+(1-x_0)In(\frac{(1-x_0)}{(1-x_e)})]-(x_0-x_e{)}^2$

$($a$)$ Use this equation to estimate the total free energy

released when ${}^{\text{'}}+$ at $600K$ if $x_0=0\mathrm{.}1,x_e=0\mathrm{.}02$

and $=0($ideal solution$)(R=8\mathrm{.}31Jmo{l}^{-1}K{T}^{-1}).$

$($b$)$ Estimate the volume fraction of precipitate at equilibrium if $$ is pure solute $(x_B^{}=1).$

$($Assume the molar volume is constant.$)$

$($c$)$ If the alloy is heat treated to produce a precipitate dispersion with a spacing of $50nm$

estimate the total $\frac{}{}$ interfacial area, $m^{-3}$ of alloy. $($Assume a simple cubic array.$)$

$($d$)$ If ${}_{}=200mJ{m}^{-2}$ what is the total interfacial energy of alloy?.

$($e$)$ What fraction of the total driving force would remain as interfacial energy in the above

case?