Unveiling thermal stresses in RETaO4 (RE = Nd, Sm, Eu, Gd, Tb, Dy, Ho and Er) by first-principles calculations and finite element simulations

Thermal stress (σ) plays a critical role in regulating the stability and durability of thermal barrier coatings (TBCs) during service. However, its measurements are limited due to technical challenges. Here, thermal stresses in RETaO4 (RE = Nd, Sm, Eu, Gd, Tb, Dy, Ho, and Er) TBCs have been evaluated by a cross-scale model, integrating first-principles calculations and finite element simulations (FEM). The isobaric heat capacity, thermal expansion coefficients, density, Young's modulus, and Poisson's ratio of RETaO4 as a function of temperature have been determined by the quasi-harmonic approach (QHA) and the quasi-static approach (QSA). Taking these properties as the input data of FEM, the σ of TBCs with RETaO4 as ceramic coatings is estimated. It indicates that the maximum tensile stress exists at the ceramic and thermal-grown oxide coating interface. Notably, TBCs_NdTaO4 exhibits the highest tensile stress, reaching up to 2093 MPa, while TBCs_GdTaO4 has the lowest value at 1880 MPa. Furthermore, the key factors affecting σ are estimated using interpretable machine learning based on the decision tree algorithm. The RETaO4 with small Poisson's ratio, strong electronegativity, small heat capacity, and thermal expansion coefficients is helpful to achieving low σ in TBCs. GdTaO4, YTaO4 and (Ho0.5Er0.5)TaO4 emerge as more favorable options as ceramic layer due to their lower σ in TBCs. This present cross-scale model provides a successful tool for predicting σ and the reverse design of TBCs materials based on low σ in TBCs.