Entry by Emily Redston
A eutectic diagram can be thought of as the intersection of two solid solution diagrams. At the intersection of the two liquidus lines, the melt is in equilibrium with the two solid phases. According to Gibbs Phase Rule, we know that the number of degrees of freedom is <math>F=\left( C+2-P \right)=2+2-2=0 </math>. Zero degrees of freedom means that we cannot have a solidification range, and thus the melt must solitify at exactly one point --- the eutectic point!