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Page 12 of 17 Zhang et al. J. Mater. Inf. 2026, 6, 11

Figure 7. Correlation analysis across RE 3 TaO 7 and RE 2 Zr 2 O 7 between target properties and fundamental descriptors, including are-earth
ionic radius (r RE3+ ), equilibrium volume (V0), total energy (E0), formation energy (E form ), bond energy (E b ) for RE–O, Ta–O, and Zr–O bonds,
bond-length disorder (D b ) and Bader charge disorder (D e ). Pearson correlation heatmap for (A) RE 3 TaO 7 and (B) RE 2 Zr 2 O 7 . Colored
sidebars indicate feature clusters derived from hierarchical clustering; (C) SHAP analysis showing the top five most influential features
(ranked by mean SHAP value) for predicting K IC and κ L in each system. RE: Rare-earth; SHAP: SHapley Additive exPlanations.

In RE TaO oxides, as shown in Figure 7A, strong positive correlations are observed between r RE3+ , E 0 and
3
7
E b RE–O with both K and κ . This indicates that larger RE ions and stronger RE–O bonding contribute to
IC
L
enhanced structural rigidity and thermal transport capacity. Conversely, descriptors capturing local lattice
disorder, such as bond-length heterogeneity (D b REO7/8 ) and RE-site Bader charge disorder (D ), also show
RE
e
positive correlation with K , suggesting that structural distortion aids crack resistance by disrupting crack
IC
propagation pathways. Interestingly, Ta–O E (E b Ta–O ) and its associated disorder (D b TaO6 ) display inverse
b
correlations with κ , indicating that stronger, more heterogeneous Ta–O interactions exacerbate phonon
L
scattering, thereby suppressing thermal conductivity. These findings reinforce the dual role of bonding
strength and disorder in tailoring functional performance. As shown in Figure 7B, the RE Zr O pyrochlore
2
7
2
oxides exhibit similar, though somewhat attenuated, correlation patterns. This attenuation is attributed to
their higher symmetry and reduced chemical complexity. Nevertheless, key descriptors such as Zr–O E b
(E b Zr–O ), RE Bader charge disorder (D ) and RE–O bond-length disorder (D b REO8 ) remain strongly correlated
RE
e
with both K and κ , confirming their general importance across systems.
IC
L