I am studying the concept of incongruent melting and invariant reactions. I was wondering, would all the invariant reactions that I show below be incongruent? As I understand it, we can only have congruent melting when the liquid to which our solid melts to has the exact same composition, and by the definition of these invariant reactions, this seems not to be the case in any of them.

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You are correct, none of the reactions are congruent reactions.

Per IUPAC GoldBook:

Congruent Transition: A transition in which the two-phase equilibrium of melting, vaporization or allotropism of a compound involves phases of the same composition.

The key term here is "phases of the same composition." Since all of the reactions have two phases transforming into one phase (or vise-versa) the reaction is not congruent.

See the phase diagram for silicon and titanium. Congruent melting occurs for $\ce{Ti5Si3}$ and $\ce{TiSi2}$ where you observe a $\ce{\color{red}{comp A (s)} -> \color{red}{comp A (l)}}$ transition, whereas at the eutectics you have $\ce{\color{blue}{comp B (s)} + \color{green}{comp C (s)} -> \color{red}{comp A (l)}} $ transition where $\mathrm{B \ne C \ne A \ne B}$. Thus the eutectics are not congruent transitions.

Si-Ti Phase diagram


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