REFERENCES
1. Clarke, D. R. Materials selection guidelines for low thermal conductivity thermal barrier coatings. Surf. Coat. Technol. 2003, 163-4, 67-74.
2. Padture, N. P.; Gell, M.; Jordan, E. H. Thermal barrier coatings for gas-turbine engine applications. Science 2002, 296, 280-4.
3. Ashofteh, A.; Rajabzadeh, M. Advances in thermal barrier coatings modeling, simulation, and analysis: a review. J. Eur. Ceram. Soc. 2024, 44, 116693.
4. Kumar, V.; Balasubramanian, K. Progress update on failure mechanisms of advanced thermal barrier coatings: a review. Prog. Org. Coat. 2016, 90, 54-82.
6. Song, D.; Ryu, M.; Kwon, J.; et al. Blocking of radiative thermal conduction in Zn2+-incorporated high-entropy A2B2O7 fluorite oxides. Ceram. Int. 2021, 47, 33544-53.
7. Schelling, P. K.; Phillpot, S. R.; Wolf, D. Mechanism of the cubic‐to‐tetragonal phase transition in zirconia and yttria‐stabilized zirconia by molecular‐dynamics simulation. J. Am. Ceram. Soc. 2001, 84, 1609-19.
8. Xiang, H.; Xing, Y.; Dai, F.; et al. High-entropy ceramics: present status, challenges, and a look forward. J. Adv. Ceram. 2021, 10, 385-441.
9. Wu, S.; Zhao, Y.; Li, W.; Liu, W.; Wu, Y.; Liu, F. Research progresses on ceramic materials of thermal barrier coatings on gas turbine. Coatings 2021, 11, 79.
10. Chen, L.; Hu, M.; Wang, J.; Li, B.; Feng, J. Dominant mechanisms of thermo-mechanical properties of weberite-type RE3TaO7 (RE = La, Pr, Nd, Eu, Gd, Dy) tantalates toward multifunctional thermal/environmental barrier coating applications. Acta. Mater. 2024, 270, 119857.
11. Chen, L.; Li, B.; Feng, J. Rare-earth tantalates for next-generation thermal barrier coatings. Prog. Mater. Sci. 2024, 144, 101265.
12. Haoming, Z.; Hongsong, Z.; Xiaoqin, G.; et al. Phase compositions and thermophysical performances for (Sm1-xYbx)3TaO7 compounds. Cerams. Int. 2024, 50, 18576-83.
13. Riffe, W. T.; Zare, S.; Ardrey, K. D.; et al. Broadband optical phonon scattering reduces the thermal conductivity of multi-cation oxides. Nat. Commun. 2025, 16, 3333.
14. Jia, H.; Li, C.; Chen, G.; Gong, B.; An, L.; Chen, K. Thermodynamic calculation, preparation and properties of Y2(Zr1/6Ti1/3Ge1/6Hf1/12Sn1/4)2O7 high-entropy pyrochlore ceramics. Ceram. Int. 2024, 50, 22671-8.
15. Wei, M.; Xu, J.; Zhu, J.; et al. Influence of size disorder parameter on the thermophysical properties of rare‐earth‐zirconate medium‐entropy ceramics. J. Am. Ceram. Soc. 2023, 106, 2037-48.
16. Wan, C.; Qu, Z.; Du, A.; Pan, W. Order–disorder transition and unconventional thermal conductivities of the (Sm1-xYbx)2Zr2O7 series. J. Am. Ceram. Soc. 2011, 94, 592-6.
17. Ren, S.; Zong, H. X.; Tao, X. F.; et al. Boson-peak-like anomaly caused by transverse phonon softening in strain glass. Nat. Commun. 2021, 12, 5755.
18. Wright, A. J.; Wang, Q.; Hu, C.; Yeh, Y.; Chen, R.; Luo, J. Single-phase duodenary high-entropy fluorite/pyrochlore oxides with an order-disorder transition. Acta. Mater. 2021, 211, 116858.
19. Teng, Z.; Tan, Y.; Zeng, S.; et al. Preparation and phase evolution of high-entropy oxides A2B2O7 with multiple elements at A and B sites. J. Eur. Ceram. Soc. 2021, 41, 3614-20.
20. Ren, G.; Zhang, H.; Che, J.; et al. Oxygen ion diffusion in RE3TaO7: why long-range migration of O2- is prohibited in the defective-fluorite structure? Acta. Mater. 2024, 281, 120362.
21. Wright, A. J.; Wang, Q.; Ko, S.; Chung, K. M.; Chen, R.; Luo, J. Size disorder as a descriptor for predicting reduced thermal conductivity in medium- and high-entropy pyrochlore oxides. Scr. Mater. 2020, 181, 76-81.
22. Toher, C.; Oses, C.; Esters, M.; et al. High-entropy ceramics: propelling applications through disorder. MRS. Bull. 2022, 47, 194-202.
23. Han, Y.; Liu, X.; Zhang, Q.; et al. Ultra-dense dislocations stabilized in high entropy oxide ceramics. Nat. Commun. 2022, 13, 2871.
24. Yang, Y.; Song, Z.; Lu, G.; et al. Intrinsic toughening and stable crack propagation in hexagonal boron nitride. Nature 2021, 594, 57-61.
25. Lee, S.; Esfarjani, K.; Luo, T.; Zhou, J.; Tian, Z.; Chen, G. Resonant bonding leads to low lattice thermal conductivity. Nat. Commun. 2014, 5, 3525.
26. Singh, P.; Vela, B.; Ouyang, G.; et al. A ductility metric for refractory-based multi-principal-element alloys. Acta. Mater. 2023, 257, 119104.
27. Zhang, Y.; Ren, K.; Wang, W. Y.; et al. Discovering the ultralow thermal conductive A2B2O7-type high-entropy oxides through the hybrid knowledge-assisted data-driven machine learning. J. Mater. Sci. Technol. 2024, 168, 131-42.
28. Gu, H.; Rohmer, J.; Jetter, J.; et al. Exploding and weeping ceramics. Nature 2021, 599, 416-20.
29. Braun, J. L.; Rost, C. M.; Lim, M.; et al. Charge-induced disorder controls the thermal conductivity of entropy-stabilized oxides. Adv. Mater. 2018, 30, e1805004.
30. Sarkar, A.; Wang, Q.; Schiele, A.; et al. High-entropy oxides: fundamental aspects and electrochemical properties. Adv. Mater. 2019, 31, e1806236.
31. He, J.; Xia, Y.; Lin, W.; et al. Accelerated discovery and design of ultralow lattice thermal conductivity materials using chemical bonding principles. Adv. Funct. Mater. 2022, 32, 2108532.
33. Sun, C.; Huang, Y.; Shen, Q.; et al. Embedding two-dimensional graphene array in ceramic matrix. Sci. Adv. 2020, 6, eabb1338.
34. Ritchie, R. O. Toughening materials: enhancing resistance to fracture. Philos. Trans. A. Math. Phys. Eng. Sci. 2021, 379, 20200437.
35. Porz, L.; Klomp, A. J.; Fang, X.; et al. Dislocation-toughened ceramics. Mater. Horiz. 2021, 8, 1528-37.
36. Han, J.; Kim, I.; Cho, N.; et al. Toward accurate machine learning-driven prediction of polymeric composites properties based on experimental data. MGE. Adv. 2025, 3, e70027.
37. Wang, W. Y.; Zhang, S.; Li, G.; et al. Artificial intelligence enabled smart design and manufacturing of advanced materials: the endless frontier in AI+ era. MGE. Adv. 2024, 2, e56.
38. Shang, Y.; Xiong, Z.; An, K.; Hauch, J. A.; Brabec, C. J.; Li, N. Materials genome engineering accelerates the research and development of organic and perovskite photovoltaics. MGE. Adv. 2024, 2, e28.
39. Wang, W. Y.; Yin, J.; Chai, Z.; et al. Big data-assisted digital twins for the smart design and manufacturing of advanced materials: from atoms to products. J. Mater. Inf. 2022, 2, 1.
40. Gao, X.; Wang, W. Y.; Chen, X.; et al. ProME: an integrated computational platform for material properties at extremes and its application in multicomponent alloy design. MGE. Adv. 2025, 3, e70029.
41. Divilov, S.; Eckert, H.; Hicks, D.; et al. Disordered enthalpy-entropy descriptor for high-entropy ceramics discovery. Nature 2024, 625, 66-73.
42. Xu, D.; Zhang, Q.; Huo, X.; Wang, Y.; Yang, M. Advances in data-assisted high-throughput computations for material design. MGE. Adv. 2023, 1, e11.
43. Zhang, S.; Wang, W. Y.; Wang, X.; et al. Large language models enabled intelligent microstructure optimization and defects classification of welded titanium alloys. J. Mater. Inf. 2024, 4, 34.
44. Carrete, J.; Li, W.; Mingo, N.; Wang, S.; Curtarolo, S. Finding unprecedentedly low-thermal-conductivity half-heusler semiconductors via high-throughput materials modeling. Phys. Rev. X. 2014, 4, 011019.
45. Li, Y.; Kowalski, P. M.; Beridze, G.; Birnie, A. R.; Finkeldei, S.; Bosbach, D. Defect formation energies in A2B2O7 pyrochlores. Scr. Mater. 2015, 107, 18-21.
46. Wang, Y.; Perdew, J. P. Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling. Phys. Rev. B. Condens. Matter. 1991, 44, 13298-307.
47. Amari, S.; Daoud, S. Structural phase transition, elastic constants and thermodynamic properties of TmAs: a DFT study. Comput. Condens. Matter. 2022, 33, e00764.
48. Söderlind, P.; Turchi, P. E.; Landa, A.; Lordi, V. Ground-state properties of rare-earth metals: an evaluation of density-functional theory. J. Phys. Condens. Matter. 2014, 26, 416001.
49. Loschen, C.; Carrasco, J.; Neyman, K. M.; Illas, F. First-principles LDA+U and GGA+U study of cerium oxides: dependence on the effective U parameter. Phys. Rev. B. 2007, 75, 035115.
50. Singh, P.; Del Rose, T.; Vazquez, G.; Arroyave, R.; Mudryk, Y. Machine-learning enabled thermodynamic model for the design of new rare-earth compounds. Acta. Mater. 2022, 229, 117759.
52. Chung, D. H.; Buessem, W. R. The Voigt-Reuss-Hill approximation and elastic moduli of polycrystalline MgO, CaF2, β-ZnS, ZnSe, and CdTe. J. Appl. Phys. 1967, 38, 2535-40.
53. Hill, R. The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. A. 1952, 65, 349-54.
54. Wan, C.; Zhang, W.; Wang, Y.; et al. Glass-like thermal conductivity in ytterbium-doped lanthanum zirconate pyrochlore. Acta. Mater. 2010, 58, 6166-72.
55. To, T.; Sørensen, S. S.; Stepniewska, M.; et al. Fracture toughness of a metal-organic framework glass. Nat. Commun. 2020, 11, 2593.
56. Griffith, A. A. VI. The phenomena of rupture and flow in solids. Philos. Trans. A. Math. Phys. Eng. Sci. 1921, 221, 163-98.
57. Zhang, Y.; Wang, W. Y.; Li, P.; et al. Hook’s law scaled broken-bond model for surface energy: from metals to ceramics. Scr. Mater. 2024, 244, 116026.
58. Niu, H.; Niu, S.; Oganov, A. R. Simple and accurate model of fracture toughness of solids. J. Appl. Phys. 2019, 125, 065105.
59. Mazhnik, E.; Oganov, A. R. A model of hardness and fracture toughness of solids. J. Appl. Phys. 2019, 126, 125109.
60. Wang, J.; Zhang, F.; Lian, J.; Ewing, R. C.; Becker, U. Energetics and concentration of defects in Gd2Ti2O7 and Gd2Zr2O7 pyrochlore at high pressure. Acta. Mater. 2011, 59, 1607-18.
61. Shamblin, J.; Tracy, C. L.; Palomares, R. I.; et al. Similar local order in disordered fluorite and aperiodic pyrochlore structures. Acta. Mater. 2018, 144, 60-7.
62. Zhang, Y.; Ren, K.; Wang, W. Y.; et al. Smart design A2Zr2O7-type high-entropy oxides through lattice-engineering toughening strategy. npj. Comput. Mater. 2024, 10, 1462.
63. Yokogawa, Y.; Yoshimura, M. Formation and stability regions of the high‐temperature fluorite‐related phase in the R2O3‐Ta2O5 system (R = La, Nd, Sm, Ho, Er, and Yb). J. Am. Ceram. Soc. 1997, 80, 1965-74.
64. Labrincha, J. A.; Frade, J. R.; Marques, F. M. B. La2Zr2O7 formed at ceramic electrode/YSZ contacts. J. Mater. Sci. 1993, 28, 3809-15.
65. Su, L.; Huyan, H.; Sarkar, A.; et al. Direct observation of elemental fluctuation and oxygen octahedral distortion-dependent charge distribution in high entropy oxides. Nat. Commun. 2022, 13, 2358.
66. Cui, K.; Sun, T. L.; Liang, X.; et al. Multiscale energy dissipation mechanism in tough and self-healing hydrogels. Phys. Rev. Lett. 2018, 121, 185501.
67. Cui, K.; Ye, Y. N.; Sun, T. L.; et al. Effect of structure heterogeneity on mechanical performance of physical polyampholytes hydrogels. Macromolecules 2019, 52, 7369-78.
69. Zhao, X.; Guo, L.; Wang, C.; Zhang, Y.; Ye, F. Effect of phase structure evolution on thermal expansion and toughness of (Nd1-xScx)2Zr2O7 (x = 0, 0.025, 0.05, 0.075, 0.1) ceramics. J. Mater. Sci. Technol. 2017, 33, 192-7.
70. Hua, Y.; Jiang, B.; Chen, R.; Cao, J.; Shuai, W.; Li, R. Enhanced physical properties of TiSi2 doped Gd2Zr2O7 ceramic for thermal barrier coatings. Mater. Res. Express. 2019, 6, 056547.
71. Wang, C.; Guo, L.; Zhang, Y.; Zhao, X.; Ye, F. Enhanced thermal expansion and fracture toughness of Sc2O3-doped Gd2Zr2O7 ceramics. Ceram. Int. 2015, 41, 10730-5.
72. Tu, T.; Liu, J.; Zhou, L.; Liang, Y.; Zhang, G. Graceful behavior during CMAS corrosion of a high-entropy rare-earth zirconate for thermal barrier coating material. J. Eur. Ceram. Soc. 2022, 42, 649-57.
73. Liu, D.; Shi, B.; Geng, L.; Wang, Y.; Xu, B.; Chen, Y. High-entropy rare-earth zirconate ceramics with low thermal conductivity for advanced thermal-barrier coatings. J. Adv. Ceram. 2022, 11, 961-73.
74. Mao, W.; Wang, Y.; Huang, H.; et al. In situ characterizations of mechanical behaviors of freestanding (Gd0.9Yb0.1)2Zr2O7 coatings by bending tests under different temperatures based on digital image correlation. J. Eur. Ceram. Soc. 2020, 40, 491-502.
75. Wang, D.; Dong, S.; Zeng, J.; et al. Influence of doping Mg2+ or Ti4+ captions on the microstructures, thermal radiation and thermal cycling behavior of plasma-sprayed Gd2Zr2O7 coatings. Ceram. Int. 2020, 46, 13054-65.
76. Ren, X.; Wan, C.; Zhao, M.; Yang, J.; Pan, W. Mechanical and thermal properties of fine-grained quasi-eutectoid (La1-xYbx)2Zr2O7 ceramics. J. Eur. Ceram. Soc. 2015, 35, 3145-54.
77. Yan, R.; Liang, W.; Miao, Q.; et al. Mechanical, thermal and CMAS resistance properties of high-entropy (Gd0.2Y0.2Er0.2Tm0.2Yb0.2)2Zr2O7 ceramics. Ceram. Int. 2023, 49, 20729-41.
78. Ren, K.; Wang, Q.; Shao, G.; Zhao, X.; Wang, Y. Multicomponent high-entropy zirconates with comprehensive properties for advanced thermal barrier coating. Scr. Mater. 2020, 178, 382-6.
79. Guo, L.; Zhang, Y.; Zhao, X.; Wang, C.; Ye, F. Thermal expansion and fracture toughness of (RE0.9Sc0.1)2Zr2O7 (RE = La, Sm, Dy, Er) ceramics. Ceram. Int. 2016, 42, 583-8.
80. Zhang, Y.; Guo, L.; Zhao, X.; Wang, C.; Ye, F. Toughening effect of Yb2O3 stabilized ZrO2 doped in Gd2Zr2O7 ceramic for thermal barrier coatings. Mater. Sci. Eng. A. 2015, 648, 385-91.
81. Guo, L.; Guo, H.; Peng, H.; Gong, S. Thermophysical properties of Yb2O3 doped Gd2Zr2O7 and thermal cycling durability of (Gd0.9Yb0.1)2Zr2O7/YSZ thermal barrier coatings. J. Eur. Ceram. Soc. 2014, 34, 1255-63.
82. Wu, Y.; Zheng, L.; He, W.; He, J.; Guo, H. Effects of Yb3+ doping on phase structure, thermal conductivity and fracture toughness of (Nd1-xYbx)2Zr2O7. Ceram. Int. 2019, 45, 3133-9.
