$($a$)$ If a composition of $10$ mole $\%$ KF$,10$ mole $\%$ NaF, $80$ mole $\%$ MgF$,$ is heated, at what temperature does it form a single$-$phase liquid?

$($b$)$ If a powder mixture of the three pure end members is prepared, what is the minimum temperature at which a liquid will form? Assume that a very sensitive calorimeter is used, which can detect the exotherm for forming very small amounts of liquid.

$($c$)$ Explain the crystallization path for a single$-$phase liquid of the composition marked A$.$ How does it differ from that marked B$?$ Is there an opportunity for nonequilibrium cooling in either case? Explain.

$($d$)$ For the composition A$.$ determine the phases present and the fractions of each phase at a temperatures of: $800\backslash$deg C$,725\backslash$deg C$,$ and room temperature