Smart design A₂Zr₂O₇-type high-entropy oxides through lattice-engineering toughening strategy

The fracture toughness (K_IC) of high-entropy oxides (HEOs) is critically important for several applications, but identification and quantification of the toughening mechanisms resulting from lattice-engineering/distortion in HEOs is challenging. Here, based on the classic Griffith criteria, a physics-driven theoretical equation combined with a knowledge-enabled data-driven machine-learning algorithm is proposed to predict the K_IC and elucidate the toughening mechanisms of A₂Zr₂O₇-type HEOs. Together with experimental verification, our proposed model is applied to a dataset comprising 41208 (nRE_1/n)₂Zr₂O₇ (n = 2~7) HEOs, considering the contributions of the intrinsic brittleness and increased toughness due to the local lattice distortion (LLD), thereby addressing the challenge of accurate estimating K_IC in complex HEOs using the rule of mixtures. During crack tip propagation, the interaction mechanism of cations induces stress fields and charge variations of LLD and dissipates crack energy, thus, to yield the crack tip softening and the elastic shielding and to enhance the toughness of HEOs.