  Rare-earth silicates are the current standard material for use as
environmental barrier coatings for SiC-based ceramic matrix composites as
hot-section components in gas-turbine engines. Expanding the design space to
all available rare-earth elements to facilitate optimizing functionality
requires an understanding of systematic trends in $RE_2$Si$_2$O$_7$ properties.
In this work, we combine first-principles calculations with experimental
measurements of Young's modulus, coefficient of thermal expansion, and thermal
conductivity for a range of different $RE_2$Si$_2$O$_7$ compositions and
phases. Clear trends are observed in these properties as a function of the
radius of the rare-earth cation. In the case of Young's modulus and thermal
expansion, these trends also hold for multi-component systems; while the
thermal conductivity of multi-component systems is noticeably lower, indicating
the potential of such materials to also act as thermal barriers. These results
provide design rules for developing new thermal and environmental barrier
coatings with stiffness and thermal expansion engineered to match that of the
substrate, while simultaneously having reduced thermal conductivity.
