Reasons for existence of eutectic point for alloy systems

Why does a eutectic point exist for a system of alloy ? Why is it that there is such a definite ratio of composition at which this occurs ? 




First, there are several other answers that you might be interested in looking at first (full disclosure - they include some by me). 


[A question on Physics SE on eutectics](https://physics.stackexchange.com/questions/196686/what-causes-a-eutectic-point)


[Ideal vs regular solutions and eutectics on Chemistry SE](https://chemistry.stackexchange.com/questions/37635/plot-binary-eutectic-from-temperature-of-melting-and-enthalpy)


These together go in to some detail on why the eutectic forms (when the liquid free energy drops down and touches the tie-line between the two solid phases - the Physics one), and the interactions one needs to get the liquid phase to drop below the tie line between the solids (the Chemistry one). To get a eutectic you need an interaction term in the liquid Gibbs free energy.


As for why it happens at such a definite composition, the glib answer is the Gibbs phase rule. In a system at fixed pressure, three phases can coexist at only one point.


Given that this question is, in general, a duplicate of the ones listed above, particularly of the Chemistry SE one, I have no particular need of the bounty. Go read those and see if they help.


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