Al$-$Si alloys are commonly used in foundries as casting alloys. The Al$-$Si binary phase diagram

a$)$ A foundry producing Al$-$Si castings found that the alloys have to contain between $80$

and $85\%$ eutectic component after solidification to ensure good fluidity in the mould.

For the sake of mechanical properties, the alloys have to be hypo$-$eutectic. Determine

the alloy composition limits required to ensure the presence of $80$ to $85\%$ eutectic

component after solidification.

b$)$ An alloy consisting of $90\%Al$ is cooled under equilibrium conditions.

i$.$ Is this alloy hypo$-$ or hypereutectic?

$[1$ mark$]$

ii$.$ What is the liquidus temperatures of this alloy?

iii. Determine which phase$($s$)$ are present in the structure at a temperature of $700$

$C.$ Also determine the chemical composition of each phase, and the amount

of each phase present in the alloy at this temperature.

$[3$ marks$]$

iv$.$ At a temperature just below $577C(577C-T),$ calculate the amount $-Al$

and $Si$ in the eutectic component.

$[4$ marks$]$

c$)$ Draw the heating curve of temperature versus time for the alloy $(95\%Al$ and $5\%Si)$

from $350C$ to $700C$ indicating the phases and phase transformation $($if any$)$ in each

segment.

$[2$ marks$]$

d$)$ Sketch the schematic free energy diagrams for the equilibrium phases at $580C,577$

$C$ and $500C.$

e$)$ Calculate the $\%$ eutectic component in $Al-1\%Si$ alloy, if the alloy solidified under

following conditions:

i$.$ Equilibrium solidification, and

ii$.$ No diffusion in the solid, complete mixing in the liquid and local equilib

the solid$-$liquid interface during solidification.

iii. Plot the schematic solute concentration profile assuming

solidification under non$-$equilibrium solidification

$[4$ m

$[6$ marks$]$

f$)$ Determine the chemical compositions $($silicon contents$)$ containing the following

microstructural components after cooling at a temperature just slightly below $577C$

$(577C-T)$ :

i$.10\%$ eutectic $Si($hypereutectic composition$).$

$[6$ marks$]$

ii$.70\%$ lamellar structure which is total amounts of eutectic $-$Al and eutectic $Si$

$($hypoeutectic composition$).$

$[2$ marks$]$

iii. equal amounts of pro$-$eutectic alpha$-$Al and eutectic alpha

OUESTION $2$

$[12$ marks$]$

a$.$ For the solidification of pure gold. calculate the critical radius $r^{**}$ and the activation