Phase formation capability and compositional design of β-phase multiple rare-earth principal component disilicates

A key strategy to design environmental barrier coatings focuses on doping multiple rare-earth principal components into β-type rare-earth disilicates (RE₂Si₂O₇) to achieve versatile property optimization. However, controlling the phase formation capability of (nRE_xi)₂Si₂O₇ remains a crucial challenge, due to the complex polymorphic phase competitions and evolutions led by different RE³⁺ combination. Herein, by fabricating twenty-one model (RE^I_0.25RE^II_0.25RE^III_0.25RE^IV_0.25)₂Si₂O₇ compounds, we find that their formation capability can be evaluated by the ability to accommodate configurational randomness of multiple RE³⁺ cations in β-type lattice while preventing the β-to-γ polymorphic transformation. The phase formation and stabilization are controlled by the average RE³⁺ radius and the deviations of different RE³⁺ combinations. Subsequently, based on high-throughput density-functional-theory calculations, we propose that the configurational entropy of mixing is a reliable descriptor to predict the phase formation of β-type (nRE_xi)₂Si₂O₇. The results may accelerate the design of (nRE_xi)₂Si₂O₇ materials with tailored compositions and controlled polymorphic phases.