The durability of gas-turbine engine components can be significantly affected by the ingestion of siliceous particles, which can melt at high temperature and corrode protective coatings that are essential for long life requirements. The silicate debris consists mainly of CaO-MgO-Al2O3-SiO2 (CMAS) and is usually ingested by aircraft engines during and after take-off, sticking to their hot surfaces and resulting in the formation of calcium rare-earth silicate oxyapatites. The thermochemistry of coatings and their reaction products with molten silicate debris are crucial to understand in order to improve the durability of gas-turbine engines. Here we discuss results of high temperature drop solution calorimetry, drop-and-catch calorimetry (DnC) and differential thermal analysis (DTA) techniques for the thermodynamic properties of both thermal barrier coatings (TBCs) and environmental barrier coatings (EBCs) and their reaction with CMAS compositions. The enthalpies of solution of Y2Si2O7, Yb2Si2O7, 31YSZ, and 16RESZ based coatings and the oxyapatite are moderately positive. However, oxyapatite formation is only favorable over coating dissolution in terms of enthalpy for 7YSZ. The enthalpies of mixing between the coatings and the molten silicate are less exothermic for Yb2Si2O7 and CaYb4Si3O13 than for 7YSZ, indicating lower energetic stability of the latter against molten silicate corrosion. We also report for the first time the calorimetric measurements of the enthalpies of formation of rare-earth silicate based EBC coatings and oxyapatites (rare-earth, RE = Y, Yb, Gd, Dy, Er, Nd and Sm).