Computational design of high-entropy rare earth aluminum garnets for advanced thermal and environmental barrier coatings

To enhance the protection of Ni-based superalloys in gas turbine engines' high-temperature environments, it is crucial to develop advanced thermal/environmental barrier coating (T/EBC) materials with a balanced combination of thermal, environmental, and mechanical properties. This optimization is essential to safeguard against chemical and thermal challenges at high temperatures. In this study, we harness the power of density functional theory (DFT) in conjunction with combinatorial chemistry methodologies to engineer high-performance, high-entropy rare earth aluminum garnets of the $\mathit{R}{}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$ family (where $R$ denotes Y, Gd, Er, and Yb). These materials are meticulously designed to exhibit superior phase stability, a targeted coefficient of thermal expansion (CTE), low lattice thermal conductivity, and robust mechanical properties. The determination of CTE values is accomplished through phonon calculations at various volume settings within the quasiharmonic approximation, while lattice thermal conductivities are rigorously assessed employing the Debye-Callaway model, accounting for three distinct phonon processes. Our findings highlight the remarkable attributes of the solid solution ${({\mathrm{Y}}_{1/4}{\mathrm{Gd}}_{1/4}{\mathrm{Er}}_{1/4}{\mathrm{Yb}}_{1/4})}_{3}{\mathrm{Al}}_{5}{\mathrm{O}}_{12}$, which displays a noticeable reduction in lattice thermal conductivity compared to its individual constituents while maintaining a favorable range of CTE values. The T/EBC materials, distinguished by their multifaceted functionalities, are promising next-generation T/EBCs for protecting nickel-based superalloys in gas turbine engines. Furthermore, this work serves as a testament to the efficacy and reliability of our computational framework, which holds the potential to expedite the design of next-generation T/EBC materials.