Modelling evaporation in electron‑beam physical vapour deposition of thermal barrier coatings

This work presents computational models of ingot evaporation for electron-beam physical vapour deposition (EB-PVD) that can be applied to the deposition and development of thermal barrier coatings (TBCs). TBCs are insulating coatings that protect aero-engine components from high temperatures, which can be above the component’s melting point. The development of advanced TBCs is fuelled by the need to improve engine efficiency by increasing the engine operating temperature. Rare-earth zirconates (REZ) have been proposed as the next-generation TBCs due to their low coefficient of thermal conductivity and resistance to molten calcium-magnesium alumina-silicates (CMAS). However, the evaporation of REZ has proven to be challenging, with some coatings displaying compositional segregation across their thickness. The computational models form part of a larger analytical model that spans the whole EB-PVD process. The computational models focus on ingot evaporation, have been implemented in MATLAB and include data from 6 oxides: ZrO2, Y2O3, Gd2O3, Er2O3, La2O3 and Yb2O3. Two models (2D and 3D) successfully evaluate the evaporation rates of constituent oxides from multiple-REZ ingots, which can be used to highlight incompatibilities and preferential evaporation of some of these oxides. A third model (local composition activated, LCA) successfully predicts the evaporation rate of the whole ingot and replicates the cyclic change in composition of the evaporated plume, which is manifested as changes in compositional segregation across the coating’s thickness. The models have been validated with experimental data from Cranfield University’s EB-PVD coaters, published vapour pressure calculations and evaporation rate formulas described in the literature.