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 RETaO ₄ (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 RETaO ₄ 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 RETaO ₄ as ceramic coatings is estimated. It indicates that the maximum tensile stress exists at the ceramic and thermal-grown oxide coating interface. Notably, TBCs_NdTaO ₄ exhibits the highest tensile stress, reaching up to 2093 MPa, while TBCs_GdTaO ₄ 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 RETaO ₄ with small Poisson`s ratio, strong electronegativity, small heat capacity, and thermal expansion coefficients is helpful to achieving low σ in TBCs. GdTaO ₄, YTaO ₄ and (Ho _0.5Er _0.5)TaO ₄ 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.