理论计算在高熵陶瓷领域的研究进展

doi:10.15541/jim20250342

摘要/Abstract

摘要： 高熵陶瓷(High-entropy ceramics,HEC)凭借其高熵效应、晶格畸变效应、迟滞扩散效应、鸡尾酒效应,展现出优异的热学性能、力学性能和化学稳定性,在航空航天、能源、核工业等领域具有巨大的应用潜力。然而,由于HEC巨大的成分与结构空间,传统试错法存在周期长、成本高等问题,难以有效开展针对复杂体系的研究。因此,理论计算成为破解这一难题的核心工具。为梳理近年来理论计算在HEC领域的研究进展,本文聚焦当前主流的理论计算方法,包括第一性原理计算、分子动力学模拟、机器学习以及相图计算技术等,并结合高通量计算与性能描述符等研究范式,全面论述这些方法在HEC研究中的关键作用与具体应用。本文首先简要概述HEC的基本特性和核心效应,接着重点剖析上述计算方法的理论基础,并详细阐述其在HEC组分设计、性能预测、微观结构解析与相稳定性评估等方面的应用实例。最后,总结理论计算在研究多组元体系时面临的主要挑战,如高质量数据集稀缺、构效关系模糊等,并对该领域在数据驱动设计、跨尺度关联、极端环境模拟等方向进行了前瞻性展望。

关键词: 高熵陶瓷, 理论计算, 第一性原理, 多尺度模拟, 机器学习, 综述

Abstract: High-entropy ceramics (HECs) demonstrate exceptional thermal and mechanical properties, along with outstanding chemical stability, which can be attributed to their high entropy, lattice distortion, sluggish diffusion, and cocktail effects. However, the expansive compositional and structural space associated with HEC renders traditional trial-and-error methods time-consuming, costly, and inadequate for the investigation of complex systems. Thus, theoretical calculation has become an indispensable tool for addressing these challenges. To outline recent advances in theoretical calculation for HEC, this article focuses on prevalent calculation methods, including first-principles calculations, molecular dynamics, machine learning, and calculation of phase diagrams. Additionally, it discusses research paradigms such as high-throughput computing and performance descriptors, providing a comprehensive overview of their key roles and specific applications in HEC. The article first outlines the fundamental characteristics and core effects of HEC, then turns to critically examine the theoretical basis of these calculation methods, elaborating on their applications through specific examples in composition design, property prediction, microstructural parsing, and phase stability assessment. Finally, this paper summarizes the major challenges encountered in theoretical calculations in the study of multi-component systems, such as the scarcity of high-quality datasets and the ambiguity of structure-property relationships. It concludes with a forward-looking outlook on the directions in this field, including data-driven design, cross-scale correlation, and extreme environment simulation.

Key words: high-entropy ceramic, theoretical calculation, first principles, multiscale simulation, machine learning, review

中图分类号:

TB321

解陈一, 缪花明, 张蔚然, 刘荣军, 王衍飞, 李端. 理论计算在高熵陶瓷领域的研究进展[J]. 无机材料学报, DOI: 10.15541/jim20250342.

XIE Chenyi, MIAO Huaming, ZHANG Weiran, LIU Rongjun, WANG Yanfei, LI Duan. Research Progress of Theoretical Calculation in the Field of High-entropy Ceramics[J]. Journal of Inorganic Materials, DOI: 10.15541/jim20250342.

参考文献

[1] HUANG P K, YEH J W, SHUN T T,et al. Multi‐principal‐element alloys with improved oxidation and wear resistance for thermal spray coating. Advanced Engineering Materials, 2004, 6(1): 74.
[2] CANTOR B, CHANG I T H, KNIGHT P,et al. Microstructural development in equiatomic multicomponent alloys. Materials Science and Engineering: A, 2004, 375: 213.
[3] ROST C M, SACHET E, BORMAN T,et al. Entropy-stabilized oxides. Nature Communications, 2015, 6: 8485.
[4] XIE C Y, MIAO H M, WANG Y F,et al. Preparation of (Zr_0.25Hf_0.25Ta_0.25Nb_0.25)C high-entropy ceramic nanopowders via liquid-phase precursor route at a low temperature of 1500 ℃. Ceramics International, 2024, 50(23): 51243.
[5] XIE C Y, MIAO H M, WAN F,et al. Preparation of (Ti_0.2Zr_0.2Hf_0.2Nb_0.2Ta_0.2)C high-entropy ceramic nanopowders via liquid-phase precursor. Journal of the American Ceramic Society, 2024, 107(7): 5105.
[6] CUI N, ZHANG Y X, WANG L J,et al. Single-phase formation process and carbon vacancy regulation of (TiVNbMoW)C_x high-entropy ceramics. Journal of Inorganic Materials, 2025, 40(5): 511.
[7] BAI Y H, LI J R, LU H,et al. Ultrafast high-temperature sintering of high-entropy oxides with refined microstructure and superior lithium-ion storage performance. Journal of Advanced Ceramics, 2023, 12(10): 1857.
[8] CHEN G J, LI C W, JIA H M,et al. A novel approach for the composition design of high-entropy fluorite oxides with low thermal conductivity. Journal of Advanced Ceramics, 2024, 13(9): 1369.
[9] LI W G, LIU D G, WANG K W,et al. High entropy oxide ceramics (MgCoNiCuZn)O: flash sintering synthesis and properties. Journal of Inorganic Materials, 2022, 37(12): 1289.
[10] LIU D, WEN T Q, YE B L,et al. Synthesis of superfine high-entropy metal diboride powders. Scripta Materialia, 2019, 167: 110.
[11] GILD J, ZHANG Y Y, HARRINGTON T,et al. High-entropy metal diborides: a new class of high-entropy materials and a new type of ultrahigh temperature ceramics. Scientific Reports, 2016, 6: 37946.
[12] YU L Y Y, ZHAO F X, ZHANG S X,et al. Preparation of high-entropy boride powders for plasma spraying by inductive plasma spheroidization. Journal of Inorganic Materials, 2025, 40(7): 808.
[13] LIU X, LU Y J, XU Q,et al. Synthesis of (HfZrTiNbTa)N powders via nitride thermal reduction with soft mechano-chemical assistance. Journal of Advanced Ceramics, 2023, 12(3): 565.
[14] WANG P X, YU Z L, MO P C,et al. The effect of N vacancy on the synthesis and properties of high-entropy nitride ceramics (Ti_0.25V_0.25Cr_0.25Nb_0.25)N_0.825. Journal of Solid State Chemistry, 2025, 344: 125202.
[15] KUANG J, ZHANG P, WANG Q Q,et al. Formation and oxidation behavior of refractory high-entropy silicide (NbMoTaW)Si₂ coating. Corrosion Science, 2022, 198: 110134.
[16] SHIVAKUMAR S, QIN M D, ZHANG D W,et al. A new type of compositionally complex M₅Si₃ silicides: cation ordering and unexpected phase stability. Scripta Materialia, 2022, 212: 114557.
[17] NI B, LIU H W, ZOU S,et al. Enhancing electrical resistivity of titanium-substituted rare-earth orthoferrite high-entropy ceramics by engineering grain and grain boundary. Ceramics International, 2024, 50(9): 15750.
[18] NI B, ZOU S, GU Y H,et al. Entropy regulated ferroelectric properties of rare-earth and transition metal perovskite type ceramics. Journal of Alloys and Compounds, 2024, 984: 173820.
[19] ZHU J T, LOU Z H, ZHANG P,et al. Preparation and thermal properties of rare earth tantalates (RETaO₄) high-entropy ceramics. Journal of Inorganic Materials, 2021, 36(4): 411.
[20] FENG L, FAHRENHOLTZ W G, HILMAS G E.Low-temperature sintering of single-phase, high-entropy carbide ceramics.Journal of the American Ceramic Society, 2019, 102(12): 7217.
[21] YANG H T, KLEMM S, MÜLLER J,et al. Synthesis of high-entropy carbides from multi-metal polymer precursors. Journal of the European Ceramic Society, 2023, 43(10): 4233.
[22] YE F X, MENG F W, LUO T Y,et al. Ultrafast high-temperature sintering of high-entropy (La_0.2Nd_0.2Sm_0.2Eu_0.2Gd_0.2)₂Hf₂O₇ ceramics with fluorite structure. Ceramics International, 2022, 48(23): 35649.
[23] ZENG J J, ZHANG K B, CHEN D M,et al. Preparation of (La_0.2Nd_0.2Sm_0.2Gd_0.2Er_0.2)₂Zr₂O₇ high-entropy transparent ceramics by vacuum sintering. Journal of Inorganic Materials, 2021, 36(4): 418.
[24] ZHANG X Y, LIU X Y, YAN J H,et al. Preparation and property of high-entropy(La_0.2Li_0.2Ba_0.2Sr_0.2Ca_0.2)TiO₃ perovskite ceramics. Journal of Inorganic Materials, 2021, 36(4): 379.
[25] CHEN Y Q, LI R, ZHANG Y,et al. Preparation and dielectric properties of lead-free perovskite-structured high-entropy ceramics of (La_0.25Sr_0.25Ba_0.25Na_0.25)(Ti_0.5Me0.5)O₃-_δ, 2023, 49(1): 1038.
[26] ZHANG R Z, REECE M J.Review of high entropy ceramics: design, synthesis, structure and properties.Journal of Materials Chemistry A, 2019, 7(39): 22148.
[27] WANG J S, JIANG J Z, LIAW P K,et al. Data science in order and disorder of high-entropy materials. Metals, 2025, 15(6): 632.
[28] LIU H Y, CHEN B, CHEN R,et al. Computational simulation of short-range order structures in high-entropy alloys: a review on formation patterns, multiscale characterization, and performance modulation mechanisms. Advances in Physics: X, 2025, 10(1): 2527417.
[29] OSES C, TOHER C, CURTAROLO S.High-entropy ceramics.Nature Reviews Materials, 2020, 5(4): 295.
[30] WRIGHT A J, LUO J.A step forward from high-entropy ceramics to compositionally complex ceramics: a new perspective.Journal of Materials Science, 2020, 55(23): 9812.
[31] MOSKOVSKIKH D O, VOROTILO S, SEDEGOV A S,et al. High-entropy (HfTaTiNbZr)C and (HfTaTiNbMo)C carbides fabricated through reactive high-energy ball milling and spark plasma sintering. Ceramics International, 2020, 46(11): 19008.
[32] FENG L, FAHRENHOLTZ W G, HILMAS G E,et al. Synthesis of single-phase high-entropy carbide powders. Scripta Materialia, 2019, 162: 90.
[33] SUN Y N, CHEN F H, QIU W F,et al. Synthesis of rare earth containing single-phase multicomponent metal carbides via liquid polymer precursor route. Journal of the American Ceramic Society, 2020, 103(11): 6081.
[34] DU B, LIU H H, CHU Y H.Fabrication and characterization of polymer-derived high-entropy carbide ceramic powders.Journal of the American Ceramic Society, 2020, 103(8): 4063.
[35] YAN X L, CONSTANTIN L, LU Y F,et al.(Hf_0.2Zr_0.2Ta_0.2Nb_0.2Ti_0.2)C high-entropy ceramics with low thermal conductivity. Journal of the American Ceramic Society, 2018, 101(10): 4486.
[36] WANG K, CHEN L, XU C G,et al. Microstructure and mechanical properties of (TiZrNbTaMo)C high-entropy ceramic. Journal of Materials Science & Technology, 2020, 39: 99.
[37] 林奕希, 蒋雨桥, 冯相民, 等. 机器学习原子间势分子动力学模拟在电化学储能材料研究中的应用进展. 中国材料进展, 2025, 44(4): 330.
[38] 张聪, 刘杰, 解树一, 等. 高通量计算与机器学习驱动高熵合金的研究进展. 材料工程, 2023, 51(3): 1.
[39] 张勇, 朱祥涵. 高熵陶瓷的功能性应用和数据驱动设计. 四川师范大学学报(自然科学版), 2025, 48(3): 285.
[40] 郑博远, 吴一栋, 惠希东. 高熵碳化物陶瓷第一性原理计算研究进展与展望. 智能安全, 2024, 3(2): 87.
[41] 鲁楠, 何鹏飞, 种晓宇, 等. 多尺度模拟计算方法在超高温高熵陶瓷材料中的应用进展. 宇航材料工艺, 2023, 53(1): 1.
[42] 林洋, 卜文刚, 何鹏飞, 等. 材料智能计算在多主元超高温金属陶瓷设计中的应用进展. 智能安全, 2024, 3(3): 100.
[43] LIU B, ZHAO J L, LIU Y C,et al. Application of high-throughput first-principles calculations in ceramic innovation. Journal of Materials Science & Technology, 2021, 88: 143.
[44] LI J, FANG Q H, LIAW P K.Microstructures and properties of high-entropy materials: modeling, simulation, and experiments.Advanced Engineering Materials, 2021, 23(1): 2001044.
[45] SHAO H, SANDVIK A W.Progress on stochastic analytic continuation of quantum Monte Carlo data.Physics Reports, 2023, 1003: 1.
[46] VYATSKIKH A L, MACDONALD B E, DUPUY A D,et al. High entropy silicides: CALPHAD-guided prediction and thin film fabrication. Scripta Materialia, 2021, 201: 113914.
[47] ZHANG J, XIANG X P, XU B,et al. Rational design of high-entropy ceramics based on machine learning-a critical review. Current Opinion in Solid State and Materials Science, 2023, 27(2): 101057.
[48] NISAR A, ZHANG C, BOESL B,et al. A perspective on challenges and opportunities in developing high entropy-ultra high temperature ceramics. Ceramics International, 2020, 46(16): 25845.
[49] WANG Z S, LIU G T, GAO W H,et al. Mechanical behavior of high entropy ceramic (TiZrHfVNb)C₅ under extreme conditions: a first-principles density functional theory study. Ceramics International, 2024, 50(6): 9820.
[50] LIU S Y, CUI J, ZHANG C,et al. First-principles study on the thermodynamic miscibility and mechanical properties of high-entropy quaternary metal nitrides. Materials Today Communications, 2025, 45: 112157.
[51] FENG X K, WANG X C, WU L F,et al. The effects of refractory elements on the properties of quaternary high entropy carbides—a first-principles and experiment study. Computational Materials Science, 2024, 245: 113324.
[52] YU H Y, LIANG W P, MIAO Q,et al. Study on the wear resistance and thermodynamic stability of (MNbTaZrTi)N (M = Cr, Hf) high-entropy nitride coatings at elevated temperatures. Surface and Coatings Technology, 2025, 497: 131792.
[53] XU L, GAO H F, HE X,et al. Understanding the CMAS corrosion behavior of high-entropy (La_0.2Sm_0.2Er_0.2Y0.2Yb_0.2)₂Ce₂O₇. Journal of the American Ceramic Society, 2025, 108(5): e20355.
[54] YAN R X, LIANG W P, MIAO Q,et al. Corrosion mechanisms of high-entropy rare earth zirconate (Gd_0.2Y_0.2Er_0.2Tm_0.2Yb_0.2)₂Zr₂O₇ exposed to CMAS and multi-medium (NaVO₃+CMAS). Journal of the European Ceramic Society, 2024, 44(5): 3277.
[55] ZHOU X T, XU Y J, CHEN Y,et al. Mechanism on lattice thermal conductivity of carbon-vacancy and porous medium entropy ceramics. Scripta Materialia, 2025, 259: 116568.
[56] BAI Y, LIANG Y X, BI J,et al. Sintering, high-temperature stability, and thermal conductivity of (Zr, Nb, Hf, Ta)(C, N) high-entropy carbonitrides. Ceramics International, 2025, 51(18): 24731.
[57] MENG H, LIU Y W, YU H L,et al. Machine-learning-potential-driven prediction of high-entropy ceramics with ultra-high melting points. Cell Reports Physical Science, 2025, 6(2): 102449.
[58] NITOL M S, ECHEVERRIA M J, DANG K,et al. New modified embedded-atom method interatomic potential to understand deformation behavior in VNbTaTiZr refractory high entropy alloy. Computational Materials Science, 2024, 237: 112886.
[59] LU W Y, XU J R, HUANG S S,et al. The coupling of carbon non-stoichiometry and short-range order in governing mechanical properties of high-entropy ceramics. npj Computational Materials, 2025, 11: 64.
[60] WANG X Y, ZHAN Z J, CAO H Y,et al. CALPHAD, preparation, and mechanical properties of quaternary solid solution nitrides with various nitrogen stoichiometry. Ceramics International, 2024, 50(19): 34914.
[61] KIM M, KIM J, KIM H,et al. High-throughput data-driven machine learning prediction of thermal expansion coefficients of high-entropy solid solution carbides. International Journal of Refractory Metals and Hard Materials, 2024, 122: 106738.
[62] DAI F Z, SUN Y J, WEN B,et al. Temperature dependent thermal and elastic properties of high entropy (Ti_0.2Zr_0.2Hf_0.2Nb_0.2Ta_0.2)B₂: molecular dynamics simulation by deep learning potential. Journal of Materials Science & Technology, 2021, 72: 8.
[63] DAI F Z, WEN B, SUN Y J,et al. Theoretical prediction on thermal and mechanical properties of high entropy (Zr_0.2Hf_0.2Ti_0.2Nb_0.2Ta_0.2)C by deep learning potential. Journal of Materials Science & Technology, 2020, 43: 168.
[64] 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. Journal of Materials Science & Technology, 2024, 168: 131.
[65] LIU S Y, QIN L, ZHANG H L,et al. Design of superhard high-entropy diborides via high-throughput DFT and thermodynamics calculations. Ceramics International, 2024, 50(10): 17977.
[66] SARKER P, HARRINGTON T, TOHER C,et al. High-entropy high-hardness metal carbides discovered by entropy descriptors. Nature Communications, 2018, 9: 4980.
[67] NING S S, WEN T Q, YE B L,et al. Low-temperature molten salt synthesis of high-entropy carbide nanopowders. Journal of the American Ceramic Society, 2020, 103(3): 2244.
[68] HOSSAIN M D, BORMAN T, OSES C,et al. Entropy landscaping of high-entropy carbides. Advanced Materials, 2021, 33(42): 2102904.
[69] DIVILOV S, ECKERT H, HICKS D,et al. Disordered enthalpy-entropy descriptor for high-entropy ceramics discovery. Nature, 2024, 625(7993): 66.
[70] MENG H, YU H L, ZHUANG L,et al. Data-driven acceleration of high-entropy ceramic discovery. Matter, 2024, 7(8): 2646.
[71] DEY D, LIANG L B, YU L P.Mixed enthalpy-entropy descriptor for the rational design of synthesizable high-entropy materials over vast chemical spaces.Journal of the American Chemical Society, 2024, 146(8): 5142.
[72] JIANG S C, HU T, GILD J,et al. A new class of high-entropy perovskite oxides. Scripta Materialia, 2018, 142: 116.
[73] SUN Q D, YIN W J.Thermodynamic stability trend of cubic perovskites.Journal of the American Chemical Society, 2017, 139(42): 14905.
[74] WRIGHT A J, WANG Q Y, KO S T,et al. Size disorder as a descriptor for predicting reduced thermal conductivity in medium- and high-entropy pyrochlore oxides. Scripta Materialia, 2020, 181: 76.
[75] MENG H, YU R W, TANG Z Y,et al. Formation ability descriptors for high-entropy carbides established through high-throughput methods and machine learning. Cell Reports Physical Science, 2023, 4(8): 101512.
[76] MENG H, YU R W, TANG Z Y,et al. Formation ability descriptors for high-entropy diborides established through high-throughput experiments and machine learning. Acta Materialia, 2023, 256: 119132.
[77] MENG H, WEI P, TANG Z Y,et al. Data-driven discovery of formation ability descriptors for high-entropy rare-earth monosilicates. Journal of Materiomics, 2024, 10(3): 738.
[78] MITRA R, BAJPAI A, BISWAS K.ADASYN-assisted machine learning for phase prediction of high entropy carbides.Computational Materials Science, 2023, 223: 112142.
[79] ZHANG H Z, LIN W W, REN L, et al. Phase structure prediction of high-entropy carbide ceramics based on two-stage data enhancement. Journal of the Australian Ceramic Society, DOI: 10.1007/s41779-025-01204-0.
[80] PAK A Y, SOTSKOV V, GUMOVSKAYA A A,et al. Machine learning-driven synthesis of TiZrNbHfTaC₅ high-entropy carbide. npj Computational Materials, 2023, 9: 7.
[81] LIU D Q, HOU Y Q, ZHANG A J,et al. Experimental studies on critical compositions for fabricating single-phase high entropy carbides based on the calculated phase diagram of (VNbTaMoW)_0.5C_x(0 < x < 0.6). Journal of the European Ceramic Society, 2021, 41(15): 7488.
[82] ARAI Y, SAITO M, SAMIZO A,et al. Material design using calculation phase diagram for refractory high-entropy ceramic matrix composites. International Journal of Applied Ceramic Technology, 2024, 21(4): 2702.
[83] LU W Y, CHEN L, ZHANG W,et al. Single-phase formation and mechanical properties of (TiZrNbTaMo)C high-entropy ceramics: first-principles prediction and experimental study. Journal of the European Ceramic Society, 2022, 42(5): 2021.
[84] SONG J T, CHEN G Q, XIANG H M,et al. Regulating the formation ability and mechanical properties of high-entropy transition metal carbides by carbon stoichiometry. Journal of Materials Science & Technology, 2022, 121: 181.
[85] BAI Y, LIANG Y X, BI J,et al. Role of carbon vacancies in determining the structural, mechanical, and thermodynamic properties of (HfTaZrNb)C₁-_x high entropy carbides: a first-principles study. Journal of Materials Science, 2024, 59(40): 19112.
[86] LIU Y W, MENG H, ZHU Z J,et al. Predicting mechanical and thermal properties of high-entropy ceramics via transferable machine-learning-potential-based molecular dynamics. Advanced Functional Materials, 2025, 35(16): 2418802.
[87] LIU Y W, FU Y M, GU F C,et al. Lattice-distortion-driven reduced lattice thermal conductivity in high-entropy ceramics. Advanced Science, 2025, 12(19): 2501157.
[88] WEN W, YAN X X, PEI X H,et al. Multi-dimensional anisotropic feature interaction with machine learning to predict the thermal conductivity of A₂B₂O₇-type high-entropy ceramics. Ceramics International, 2025, 51(13): 17860.
[89] ZHENG X W, CUI J, GU C,et al. Superhard high-entropy dodecaboride with high electrical conductivity. Scripta Materialia, 2022, 220: 114938.
[90] CUI J, ZHENG X W, BAO W C,et al. Coexistence of superhardness and metal-like electrical conductivity in high-entropy dodecaboride composite with atomic-scale interlocks. Nano Letters, 2023, 23(20): 9319.
[91] ZHENG B Y, WU Y D, LIN D Y,et al. First-principles study on the structure, mechanical and thermodynamic properties of (Ti, Hf, Nb, Ta)C high-entropy carbide ceramics. Ceramics International, 2024, 50(13): 23097.
[92] ZENG L Y, HU X W, ZHOU Y Z,et al. Superconductivity in the high-entropy ceramics Ti_0.2Zr_0.2Nb_0.2Mo_0.2Ta_0.2C_x with possible nontrivial band topology. Advanced Science, 2024, 11(5): 2305054.
[93] LIU Y W, YU H L, MENG H,et al. Atomic-level insights into the initial oxidation mechanism of high-entropy diborides by first-principles calculations. Journal of Materiomics, 2024, 10(2): 423.
[94] FAN Y, CHEN Y Y, WANG J,et al. Insights into crystal growth and morphology evolution mechanism of multi-component carbide: experiments and first-principles calculations. Journal of Materials Science & Technology, 2026, 240: 27.
[95] LI Y L, HE L, PAN H,et al. Compositional optimization for enhanced oxidation resistance of high-entropy carbide ceramics. Acta Materialia, 2025, 282: 120463.
[96] YE S B, ZHU J P, WANG H L,et al. Phase evolution and thermal stability of novel high-entropy (Mo_0.2Nb_0.2Ta_0.2V_0.2W_0.2)Si₂ ceramics. Journal of the European Ceramic Society, 2022, 42(13): 5314.
[97] ZHOU J, WANG A Z, WANG H F,et al. Data-driven assisted design and quantitative prediction of hardness in high-entropy boride ceramics. Materials Today Communications, 2025, 46: 112800.
[98] ZHOU Q, XU F, GAO C Z,et al. Design of high-performance high-entropy nitride ceramics via machine learning-driven strategy. Ceramics International, 2023, 49(15): 25964.
[99] XU X Q, WANG X B, WU S Y,et al. Design of super-hard high-entropy ceramics coatings via machine learning. Ceramics International, 2022, 48(21): 32064.
[100] 刘娟, 田传进, 汪长安. 基于机器学习设计和制备高熵氮化物陶瓷. 硅酸盐学报, 2023, 51(12): 3095.
[101] WEI T X, ZOU J Z, ZHOU X F,et al. High-entropy assisted capacitive energy storage in relaxor ferroelectrics by chemical short-range order. Nature Communications, 2025, 16: 807.
[102] ZHANG Z X, HOU C Y, ZHANG Z Y,et al. Data-driven design of spinodal decomposition in (Ti, Zr, Hf)C composite carbides for optimizing the hardness-toughness trade-off. Advanced Functional Materials, 2025, 35(36): 2502555.