$16\mathrm{.}2$ a$.$ Given that there is a regular solution between components A and B$,$ plot the Gibbs FIGURE $16\mathrm{.}4$ The same regular solution free energy versus composition diagram at $973K$ as in Figure $16\mathrm{.}3$ with an expanded free energy range. The two equilibrium compositions, $x_{{}_1}$ and $x_{{}_2}$ are at the minima in the curve and give two points on the two$-$phase boundary. The spinodal points, where $de{l}^2\frac{G}{d}el{x}_B^2=0,$ are shown. Point $x_1$ is within the spinodal and will phase separate along the line SD by spinodal decomposition. Point $x_2$ is outside the spinodal and will decompose by nucleation and growth because it requires an increase in free energy to separate into two phases along the line NG$.$ The horizontal dashed line shows the equal chemical potentials of A and $B$ for $x=0\mathrm{.}5,$ the curve maximum.

energy$-$composition curve $($Figure $16\mathrm{.}4)$ versus XB at $973$ K if $\backslash$Gamma $=20,000$ J$/$mol$.$

b$.$ Calculate the values of XB at the two equilibrium concentrations.

c$.$ Calculate the values of XB at the two spinodal points.

d$.$ Calculate the chemical potentials of A and B at XB $=0\mathrm{.}05.$

e$.$ Calculate the values of the spinodal points and the phase boundary from T $=800$ K to

the maximum temperature at $10$ K intervals