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This lecture delves into the analysis of thermodynamic equilibria in binary systems, focusing on terminal solubility determination. It also explores ternary systems, discussing the equilibrium phases and compositions in a simple ternary eutectic. The dissolution of carbides in metallic melts is examined, showcasing the stability of Sic particles in liquid aluminum and the importance of Si content. The lecture concludes with a detailed study on the Gibbs free energy of formation and the chemical potential difference between liquid and solid silicon, providing insights into preventing the dissolution of Sic particles in composite processing.