Consider the eutectic reaction in the $Si{O}_{2^{-}}A{l}_2{O}_3$ system.

$($a$)$ Write down the equation for the eutectic reaction on cooling.

$($b$)$ Write down the compositions of all of the phases in the eutectic reaction.

$7)$What overall material composition would be required to give a material made up of $0\mathrm{.}4$ weight fraction mullite and $0\mathrm{.}6$ weight fraction alumina at $1400C?$