Show the evolution of eutectic phase diagram by deriving one to one correspondence of

compositions from free energy competition curves.

Deduce the relation for the driving force for solidification with the appropriate G vi$.$ T Diagram

V$.$ Show the effect of $\backslash$Delta H$\_\{$ma$\}$ and $-$T$\backslash$Delta S$\_\{$min$\}$ on $\backslash$Delta G$\_\{$mis$\}$ for all the four conditions $(<0,$ high T$.$ O$,$ low T$,2>0,$ high T and $\backslash$Omega$>0.$ low T$).$ Also prove why the free energy of a system always decreases first and then increases..

Constract the hypothetical phase diagram for metals A and B between room temperature and

$700\backslash$deg C given the following information: The melting temperature of metal A is $480\backslash$deg C and metal B is $600\backslash$deg C

The maximum solubility of B in A is $4$wt$\%$ which occurs at $420\backslash$deg C

The solubility of B in A is $0$ wt$\%$ at room temperature.

One eutectic occurs at $420\backslash$deg C and $18$ wt$\%$ B$-82$ wt$\%$ A$.$

A second eutectic occurs at $475\backslash$deg C and $42$ wt$\%$ B$-58$ wt$\%$ A$.$

The intermetallic compound AB exists at $30$ wt$\%$ B$-70$ wt$\%$ A and melts congruently at $525\backslash$deg C The maximum solubility of A in B is $13$ wt$\%$ which occurs at $475\backslash$deg C$.$

The solubility of A in B is $3$ wt$\%$ at room temperature.