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Zhang et al. J. Mater. Inf. 2026, 6, 11 Page 7 of 17

decomposition. For both RE TaO and RE Zr O systems, the first two principal components account for
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over 95% of the total variance, indicating that the dimensionality reduction retains the vast majority of
structural–thermodynamic information. The loading patterns suggest that E and V 0 contribute most
form
strongly to the first principal component (PC1), whereas r and E 0 dominate the second component (PC2).
RE3+
This orthogonal separation implies that atomic packing (reflected by V 0) and chemical stability (reflected by
E ) capture complementary axes of variability across the RE series.
form
Thermal conductivity and fracture toughness
The high-temperature performance of RE Zr O and RE TaO oxides as TBCs is strongly governed by their κ L
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and K . In this study, κ and K were systematically evaluated for the pyrochlore (Fd3m) RE Zr O and
¯
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L
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Weberite-type (C222 ) RE TaO phases using a combined model for κ and the Griffith-based energetic
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L
model for K . The adopted models for predicting κ and intrinsic K have been previously validated by prior
IC
L
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studies on HEOs [27,62] . Specifically, the Debye-Slack formalism and its extensions have shown predictive
accuracy within 15% when benchmarked against experimental κ for RE oxides, particularly those with
L
well-defined phonon spectra and moderate anharmonicity [27,44] . For K , the Griffith-based energetic models
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employed here, especially the variant incorporating surface energy and Young’s modulus, are recognized as
robust estimators for brittle systems, capturing relative trends and chemical effects despite neglecting
extrinsic toughening mechanisms . These models provide a reliable basis for high-throughput screening,
[62]
balancing physical realism with computational feasibility.
To ensure the validity of thermal conductivity predictions across the studied temperature range
(200-1,800 K), potential structural phase transitions were carefully considered. For RE Zr O , a
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well-established order–disorder transition from the pyrochlore to defect-fluorite phase occurs at elevated
temperatures, typically between 1,530 and 2,400 °C (1,803-2,673 K), depending on the r RE3+ [18] Similarly,
RE TaO oxides are known to undergo a transition from the orthorhombic weberite-type (C222 ) structure to
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a disordered fluorite phase at temperatures generally above 1,973 K [10,63] . These transition points lie beyond
the temperature range considered in this work. Accordingly, all κ calculations were conducted using the
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most stable DFT-predicted phase at 0 K for each composition. The quasi-harmonic Debye–Grüneisen model
employed here assumes a single, temperature-invariant phase and is therefore valid up to the onset of these
high-temperature transitions. As no phase changes are expected within the modeled range (200-1,800 K), the
resulting predictions reliably capture the intrinsic thermal transport behavior of the respective ground-state
structures.
The calculated temperature-dependent κ from 200 to 1,800 K, incorporating 5% porosity corrections for
L
representative oxides in both families is shown conceptually in Figure 3A and B. At lower temperatures, κ L
rapidly decreases following a typical inverse temperature dependence (1/T), governed by intrinsic
phonon–phonon Umklapp scattering. At higher temperatures, κ approaches a minimum limit (κ ) due to
L
min
phonon mean free paths converging toward interatomic distances, indicative of pronounced phonon
scattering. As shown in Figure 3C, RE TaO consistently exhibits lower κ (0.76-1.52 W·m ·K at 300 K)
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compared to RE Zr O (1.7-2.8 W·m ·K at 300 K), a trend maintained across the entire temperature range.
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The lower κ of RE TaO oxides primarily results from their inherently lower symmetry (C222 ), greater
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structural complexity and consequently increased phonon scattering. Additional factors, including larger
atomic mass differences and oxygen sublattice disorder, further reduce κ by intensifying phonon scattering
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channels.
For the identification of the optimal model for predicting K , Figure 3D-F compares the results obtained
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from various models (K 0 and K 0 for energetic, K 0 and K 0 for empirical) for oxides, alongside the
(2)
(1)
(4)
(3)
reported results. Among these models, K 0 = √ 2 [55] and K 0 = 2 [56] represent toughness estimates
(2)
√
(1)
1 − 2