Figure $1$ shows a$)$ the experimentally determined $In-Sn$ binary phase diagram

$($NB$.$ the dashed lines represent uncertain equilibria$)$ and b$)$ Gibbs energy $-$

composition diagram at $50C.$ Based on the diagrams please answer following

questions:

a$)$ What is the solubility of Tin in tetragonal Indium at room temperature? $(1$p$)$

b$)$ If the nominal composition of the SnIn alloy is $xS{n}^2=0\mathrm{.}6$ and $T=50C,$ what

phases are in equilibrium, what are their compositions and what are their relative

amounts $($fractions$)?(3$p$)$

c$)$ Please explain, how the above mentioned equilibrium and $\{$:$T=50C)$ can

be determined from the Gibbs energy $-$ composition diagram $($Figure $1b)$ and show

graphically, what is the chemical potential of $Sn$ in $-$ and $-$ phases and ${}_{Sn}^{})$

in that equilibrium. $(2p$

d$)$ Explain the equilibrium $(D_{\text{L}\text{i}\text{q}}=D_{\text{s}\text{o}\text{l}\text{i}\text{d}}=)$ solidification $($i$.$e$.$ the compositions and

amounts$/$fractions of phases as a function of temperature$)$ from $250C$ to $25C$

when the nominal composition of the alloy is $x_{Sn}=0\mathrm{.}75.(2$p$)$

e$)$ Please discuss, how the solidification of the same alloy $(\{$:$x_{Sn}=0\mathrm{.}75)$ could differ,

if microsegregation and $\{$:$D_{\text{s}\text{o}\text{l}\text{i}\text{d}}=0)$ would occur? $(1$p$)$