Extreme Materials

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Recent advances in high-entropy ceramics: Design principles, structural characteristics, and emerging properties

Yiran Li, Donghui Pan, Jiehui Cao, Wenhui Fang, Yiwang Bao, Bin Liu

Extreme Materials, 2025, 1(2): 42-72. DOI: 10.1016/j.exm.2025.05.002

Categories	Materials	Key Findings	Ref
Mechanical	(Al_1/6Cr_1/6Nb_1/6TaTi_1/3)O₂	elastic modulus ( $275.24\pm 32.26\mathrm{G}\mathrm{P}\mathrm{a}$ ) $H=13.58\pm 2.05\mathrm{G}\mathrm{P}\mathrm{a}$	[197]
	HE TM _0.8Sc_0.2 B₂	B=254GPa	[198]
	HE TM _0.75Sc_0.25 B₂	G=237GPa
	HE TM _0.75Lu_0.25 B₂	E=539GPa
	(HfMoNbTaTi)C	$\mu =0.1$ low friction and wear ( 0.1 and 107 mm³/Nm )	[199]
		H=18.7GPa
	(WTaNbZrTi)C	H=21.0GPa	[14]
	( CeZrLaSmNdY $){\mathrm{O}}_{2-\delta }$	K_IC=8.07MPa⋅m^1/2	[96]
	(TiTaNbZr)C	${K}_{IC}=6.93\pm 0.27\mathrm{M}\mathrm{P}\mathrm{a}\cdot {\mathrm{m}}^{1/2}$	[13]
Thermal	$\left((\mathrm{Z}\mathrm{r}\mathrm{H}\mathrm{f}\mathrm{C}\mathrm{e}\mathrm{Y}\mathrm{E}\mathrm{r}{)}_{(1-x)/5}\mathrm{T}\mathrm{i}\mathrm{x}\right){\mathrm{O}}_{2-\delta }$	$\kappa =1.34\text{ }\mathrm{W}/(\mathrm{m}\cdot \mathrm{K})$ (at ${1100}^{\circ }\mathrm{C}$ )	[200]
	${\mathrm{C}\mathrm{e}}_{1-2x}\left(\mathrm{N}\mathrm{d}\mathrm{S}\mathrm{m}{)}_{x}\right(\mathrm{V}\mathrm{N}\mathrm{b}\mathrm{T}\mathrm{a}{)}_{1/3}{\mathrm{O}}_{4+\delta }$	$\mathrm{\Delta }R/{R}_{O}=0.23\mathrm{\%}$ at 873 K for 1000 h	[201]
		lattice thermal conductivity of 2.54 W/(m⋅K) at 1073 K
	⟨001⟩-textured (LaSrBaCa) _0.85TiO₃	ZT=0.13	[203]
	Zr_0.279(Y_0.0708Yb_0.0302Ta_0.0329Nb_0.0402)O_0.5469	$\kappa =1.55\text{ }\mathrm{W}/(\mathrm{m}\cdot \mathrm{K})$ at 1200 K CTE=10.6∼10.9×10^-6 K^-1 (at ${1400}^{\circ }\mathrm{C}$ )	[204]
	(LaNdSmEuGd)CrO₃	$\mathrm{\Delta }R/{R}_{0}=4.5\mathrm{\%}$ following 1000 h of aging	[205]
Electircal	${\mathrm{P}\mathrm{r}}_{0.2}{\mathrm{S}\mathrm{m}}_{0.2}{\mathrm{N}\mathrm{d}}_{0.2}{\mathrm{G}\mathrm{d}}_{0.2}{\mathrm{L}\mathrm{a}}_{0.2}{\mathrm{B}\mathrm{a}\mathrm{C}\mathrm{o}}_{2}{\mathrm{O}}_{5+\delta }$	maximum power density of 2.03 W/cm²	[206]
	${\mathrm{B}\mathrm{a}}_{0.95}{\text{ }\mathrm{K}}_{0.05}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{Z}\mathrm{n}}_{0.2}{\mathrm{G}\mathrm{a}}_{0.2}{\mathrm{Z}\mathrm{r}}_{0.2}{\mathrm{Y}}_{0.2}{\mathrm{O}}_{3-\delta }$	PPD=1.33 W/cm²	[207]
	LiNi_0.8Co_0.15Al_0.05O₂	Coulombic efficiencies of Li-ion batteries over 99.9 %	[208]
	(MgTiZnCuF)₃O₄	Reversible capacity of 504 mA h/g	[209]
	${\mathrm{L}\mathrm{a}}_{0.2}{\mathrm{P}\mathrm{r}}_{0.2}{\mathrm{N}\mathrm{d}}_{0.2}{\mathrm{S}\mathrm{m}}_{0.2}{\mathrm{B}\mathrm{a}}_{0.1}{\mathrm{S}\mathrm{r}}_{0.1}{\mathrm{C}\mathrm{o}}_{0.2}{\mathrm{F}\mathrm{e}}_{0.6}{\mathrm{N}\mathrm{i}}_{0.1}{\mathrm{C}\mathrm{u}}_{0.1}{\mathrm{O}}_{3-\delta }$	Electrical conductivity 635.15 S/cm at ${800}^{\circ }\mathrm{C}$	[210]
	$\left[\right(\mathrm{B}\mathrm{i},\mathrm{N}\mathrm{a}\left)\right(\mathrm{L}\mathrm{a},\mathrm{L}\mathrm{i}\left)\right(\mathrm{C}\mathrm{e},\mathrm{K}\left)\mathrm{C}\mathrm{a}\mathrm{S}\mathrm{r}\right]{\mathrm{T}\mathrm{i}\mathrm{O}}_{3}$	Initial discharge capacity of 125.9 mA h/g	[211]
Catalytic	(FeMnCoNiCr)₃O₄	PPD=1.33 W/cm² at solid oxide fuel cells	[33]
	(TiVCrMo)B₂	FE=97.9% (at hydrogenation process of NO₃ ^-RR )	[212]
	${\mathrm{L}\mathrm{a}}_{2}\left(\right.$ CoNiMgZnNaLiRuO ₆	overpotential of 40.7 mV at 10 mA/cm²	[21]
	(FeCoNiCuZn)₃O₄	HER ( $\eta =207\mathrm{m}\mathrm{V}$ at 10 mA/cm² )	[20]
	Ru_0.13/Ba_0.3Sr_0.3Bi_0.4(ZrHfTiFe)O₃	51%CO conversion at ${90}^{\circ }\mathrm{C}$ within time of less than 1 s	[49]
Magnetic	(CrMnFeCoNi)₃O₄	ferrimagnetic behavior with a saturation magnetization of 22emu/g at 2 K and 7.2emu/g at 300 K	[35]
	LaCr_0.2Mn_0.2Fe_0.2Al_0.2Ga_0.2O₃	Magnetic behavior driven by competing interactions among Cr,Mn, and Fe sublattices	[34]
	(LaNdSmGd)_1-xYb_xMnO₃	$Mr/Ms\approx 0.42$ at 5 K	[56]
Dielectric	SrLa(Al_0.50-xGaxZn_0.125Mg_0.125Ti_0.25)O₄	Q_f=98,000GHz	[214]
	(MgCoNiCuZn)O,	PD=332.88MW/cm³	[215]
	0.8Na_0.5Bi_0.5TiO₃-0.2Sr(ZrSnHfTiNb)O₃	high ${\epsilon }_{\mathrm{r}}>2000$ at ${150}^{\circ }\mathrm{C}$ and low tand $\delta \left(<\mathrm{0.01,90}-{341}^{\circ }\mathrm{C}\right)$	[217]
	$0.91\left(0.9\mathrm{B}\mathrm{a}\left({\mathrm{T}\mathrm{i}}_{0.97}{\mathrm{C}\mathrm{a}}_{0.03}\right){\mathrm{O}}_{3}-0.1{\mathrm{B}\mathrm{i}}_{0.55}{\mathrm{N}\mathrm{a}}_{0.45}\right.\left.{\mathrm{T}\mathrm{i}\mathrm{O}}_{3}\right)-0.09\mathrm{B}\mathrm{i}\left(\mathrm{L}\mathrm{i}\mathrm{Y}\mathrm{M}\mathrm{g}\mathrm{T}\mathrm{i}\mathrm{T}\mathrm{a}\right){\mathrm{O}}_{3}$	W_rec=4.89 J/cm3,g=91.2%	[218]

Table 5 Summary of properties of high-entropy ceramics.

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Fig. 1. (a) All the constituent elements reported in HECs to date. (b) Total number of publications on major HECs over the last decade. Data was retrieved from Web of Science on February 28, 2025, using keywords: "high-entropy", "oxide", "boride", "carbide", "nitride", "silicide", "fluoride", "hydride", "phosphide", "sulfide", and "ceramics".
Table 1 Parameters and Descriptors Related to Theoretical Design.
Fig. 2. (a) Pairwise correlations of computational parameters: atomic radius deviations, lattice parameters, stabilization factors for miscible binary carbides, and electrochemical factors on different scales (top); correlations between different electronegativity scales (bottom). Reproduced from Ref [64]. Copyright Elsevier 2024. (b) Atomic size difference and atomic mass difference vs. thermal conductivity (left) and thermal expansion coefficient (right) at $1100{ }^{\circ }\mathrm{C}$. Reproduced from Ref [67]. Copyright Elsevier 2024. (c) DFT (Density Functional Theory)-computed formation energies of the six model cation arrangements relative to the DFT-derived ground-state cation arrangement (left); oxide compositions are sorted in descending order of the highest DFT-computed formation energy relative to the ground state (right). Reproduced from Ref [60]. Copyright Elsevier 2024. (d) Workflow of machine learning for HECs. Reproduced from Ref [68]. Copyright Elsevier 2024.
Fig. 3. (a) The 3D plots of the NET (neural network) training set were generated based on three parameters (bulk modulus, Young's modulus, and cohesive energy). Reproduced from Ref [79]. Copyright Elsevier 2024. (b) A plot of (iDOS( E_pg,E_F )) vs. VEC composed of nine solid solution high-entropy carbides shows that iDOS increases linearly along with VEC, and Pearson's correlation coefficient was 0.99. Reproduced from Ref [82]. Copyright Elsevier 2024. (c) The stress-strain curves from the AIMD (Ab Initio Molecular Dynamics) tensile simulations of MEC and HEC. Reproduced from Ref [77]. Copyright Elsevier 2024. (d) SHAP (Shapley Additive exPlanations) visualization features importance ranking. Reproduced from Ref [84]. Copyright Elsevier 2024.
Fig. 4. (a) The fitting formation energy curve of (TiVNbTa)C_x with variation of anionic vacancy concentration; Curves of anionic carbon and vacancy fraction under changing carbon content. Reproduced from Ref [86]. Copyright Elsevier 2024. (b) Average YSSs and ROM (rule of mixture) predictions for (HfTiZr) ${ }_{1-x}\left(\mathrm{N}\mathrm{b}\mathrm{T}\mathrm{a}{)}_{x}\mathrm{C}\right(\mathrm{l}\mathrm{e}\mathrm{f}\mathrm{t})$; for each x/ VEC (valence electron concentration) value, whether partial slip occurs when shearing along the 10 direction in five supercells with different atomic distributions (right). Reproduced from Ref [89]. Copyright American Physical Society 2024. (c) Diffusion energy barriers for oxygen ions on the RE-RE edge (left) and on the RE-Ta and Ta-Ta edges (right), respectively, in RE₃TaO₇. Reproduced from Ref [91]. Copyright Elsevier 2024.
Fig. 5. Typical crystal structures of high-entropy ceramics. Here, two color schemes are used to clarify the difference between simple and complex oxides, and 2×2×2 supercells for the three crystal structures at left side for better comparison.
Table 2 Synthesis methods for high-entropy simple oxides corresponding product features.
Fig. 6. (a) X-ray diffractograms of four-component derivatives of (MgCoNiCuZn)O as a substrate; (b) DFT analysis of four diffractive phase compositions by mixing enthalpy. Reproduced from Ref [94]. Copyright Elsevier 2024. (c) Side diagram of thin film battery with 50 nmLi(CrMnFeCoNiCu)₂ (001) as positive electrode, and cyclic voltammogram. Reproduced from Ref [95]. Copyright American Chemical Society 2022. (d) CTE and Fracture toughness of HEO-La, Nd, Gd, Dy. Reproduced from Ref [97]. Copyright Elsevier 2024. (e) the XRD patterns of the samples. It can be seen that RE₂Zr₂O₇ and RE₂Hf₂O₇ failed to form single-phase high-entropy pyrochlore phase; RE₂Ce₂O₇ and RE₂Pr₂O₇HEOs, exhibited a single phase structure with a fluorite-type structure. Reproduced from Ref [99]. Copyright Elsevier 2025. (f) Calculation of thermal conductivity of (EuErLuYYb)₂O₃,(SmErLuYYb)₂O₃ and Y₂O₃. Reproduced from Ref [105]. Copyright Tsinghua University Press 2021. (g) Thermal conductivity $\kappa $ curve of HEO4, 5, 7-10 and Eu₂O₃. Reproduced from Ref [104]. Copyright Elsevier 2023.
Table 3 Synthesis methods for high-entropy complex oxides corresponding product features.
Fig. 7. (a) Schematic diagram representation of the conversion of Li₂O,LiF, and Li₂CO₃ during the cycling process of the preconditioned HEOs. Reproduced from Ref [112]. Copyright Elsevier 2024. (b) Comparison of thermal properties at X=Ta,Nb. Reproduced from Ref [117]. Copyright The Royal Society of Chemistry 2024. (c) Effect of different configurational entropy (different x ) on energy storage performance. Reproduced from Ref [120]. (d) Effect of the introduction of Zr⁴⁺ on the content of the pyrochlore phase (PY) and monoclinic phase (MPr). Reproduced from Ref [137]. Copyright Elsevier 2023. (e) Corrosion depths of different component HEREDs at 1673 K,60 h; time-dependent curves of corrosion depths of 5HERED vs. 7HERED at 1673 K. Reproduced from Ref [121]. Copyright Elsevier 2024. (f) Thermal conductivity, CTE, and Grüneisen parameters as a function of temperature. Reproduced from Ref [140]. Copyright The Royal Society of Chemistry 2024.
Table 4 Synthesis methods for high-entropy non-oxides corresponding product features.
Fig. 8. (a) Schematic diagram of ultra-fast pressure sintering apparatus. Reproduced from Ref [149]. Copyright Elsevier 2025. (b) TEM cross-sections of the two samples sintered by SPS and SLS respectively, the sample with SPS has a uniform morphology and the sample sintered by SLS has a three-layer structure. Reproduced from Ref [148]. Copyright American Ceramic Society 2024. (c) XRD patterns of the samples oxidized for different durations, and Ti₂(Nb,Ta)₁₀O₂₉ appeared at 4 h ; The schematic diagram of the oxidation mechanism of (TiZrNbTaCr)C in steam at ${120}^{\circ }\mathrm{C}$. Reproduced from Ref [147]. Copyright Elsevier 2024. (d) The function of H_v of sample sintered with applied loads. Reproduced from Ref [159]. Copyright Elsevier 2024. (e) Comparison of various properties mechanical properties of HEC-SiCw with different C content. Reproduced from Ref [162]. Copyright Elsevier 2024.
Fig. 9. (a) Crystal structures of different HEBs. Reproduced from Ref [167,170-172]. Copyright Elsevier 2021. (b) Prediction of multiple HEB₂ syntheses by DEED: Compared with the results of EFA and VEC, the prediction of DEED was significantly better than the other two. Reproduced from Ref [10]. Copyright The Nature Publishing Group 2024. (c) Correlation between hardness, lattice distortion, and Atomic-size difference $\delta $ of HEB ceramics. Reproduced from Ref [164]. Copyright Elsevier 2023. (d) Oxidation depth of twelve samples oxidized at 1673 K for 2 h. Reproduced from Ref [145]. Copyright American Ceramic Society 2025. (e) HEB ₂-Nd sample's oxide layer consists of a porous-dense-porous-dense four-layer structure; the oxide layer of the HEB₂-Cr sample exhibits a distinct layer structure. Reproduced from Ref [166]. Copyright Elsevier 2025.
Fig. 10. (a) SEM images of surface and cross-sectional morphology of (MoNbTaTiZr) _1-x N_x coatings under different x; Deposition rates of (MoNbTaTiZr) _1-x N_x coatings with different RN. Reproduced from Ref [177]. Copyright Elsevier 2025. (b) Surface micro-hardness of W-Ta-Cr-V-N coatings. Reproduced from Ref [176]. Copyright Elsevier 2024. (c) Crystal Structures of HEC, HECN, and HEN. Reproduced from Ref [174]. Copyright Elsevier 2024. (d) Bond populations and density of states for HEN and HECN coatings; Crystal Structures of HEC, HECN, and HEN. Reproduced from Ref [179]. Copyright Elsevier 2024. (e) The increase in mass per unit area as a function of oxidation time reflects the variation of the surface mass of the sample with time at different oxidation durations.
Fig. 11. (a) Crystal structure of tetragonal transition metal disilicide (left), hexagonal transition metal disilicides (right). Reproduced from Ref [196]. Copyright Elsevier 2023. (b) Reversible phase transitions of HEA and HEH during hydrogen absorption. Reproduced from Ref [190]. Copyright Elsevier 2024. (c) Crystal structure of HEPO₄ monazites. Reproduced from Ref [191]. Copyright Elsevier 2019. (d) Electrical conductivity of the high-entropy sulfides. Reproduced from Ref [192]. Copyright American Chemical Society 2018. (e) A tomogram slices of the HE-MAX phase lattice structure as well as a picture of the crystal structure in the ideal case; Compressive stressstrain curves of the HE-MAX, Nb₂AlC, and Ti₂AlC at 1473 K, insets show the specimens after testing is completed. Reproduced from Ref [151]. Copyright Elsevier 2024.
Fig. 12. (a) Residual flexural strength after cyclic thermal shock at ${1500}^{\circ }\mathrm{C}$. Reproduced from Ref [200]. Copyright Elsevier 2024. (b) The cross-section morphology of the ((AlCrNbTa)₂Ti)O₂ coating. Reproduced from Ref [197]. Copyright Elsevier 2024. (c) (WTaNbZrTi)C before and after the application of pressure t-ZrO₂ and m-ZrO₂ content changes, and the martensitic phase transition of ZrO₂ under pressure schematic diagram, after the application of pressure the content of t-ZrO₂ is significantly reduced, and the content of m-ZrO₂ is increased accordingly. Reproduced from Ref [14]. Copyright The Nature Publishing Group 2023. (d) Comparison of the dependence of ideal tensile strength and nanoindentation hardness on VEC. The inset in A shows the geometric mean of the strain tensile strength recorded along [001] and. Reproduced from Ref [99] Copyright Elsevier 2025. as a function of VEC. Reproduced from Ref [220]. Copyright American Association for the Advancement of Science 2023. (e) Mapping of nanohardness and elastic modulus in HEA₅₀C. Reproduced from Ref [13]. Copyright Elsevier 2024.
Fig. 13. (a) Mechanical property comparisons between dual-phase zirconate/tantalate HECs, 8YSZ, YTaO₄, and others. Reproduced from Ref [204]. Copyright Elsevier 2024. (b) The fabrication process of (YErYbGdLa) ₂Zr₂O₇ ceramic aerogel and its thermal insulating properties. Reproduced from Ref [52]. Copyright Elsevier 2024. (c) Comparison of PF (power factor) and ZT of ceramics with reported high-entropy perovskites at x=0.10. Reproduced from Ref [202]. Copyright Elsevier 2023. (d) Comparison of the ZT in this study with those of previously reported high-entropy perovskites. Reproduced from Ref [203]. Copyright Elsevier 2024.
Fig. 14. (a) The rate discharge performance of HEO and HEO@PPy at various current densities; the rate performance of HEO@PPy significantly outperforms that of HEO. Reproduced from Ref [224]. Copyright Elsevier 2024. (b) Schematic and SEM cross-section of a single cell with (PrSmNdGdLa)BaCo ${ }_{2}{\mathrm{O}}_{5+\delta }$ cathode. Reproduced² from Ref [206]. Copyright American Chemical Society 2024. (c) Capacity retention of batteries utilizing commercial and decimal solvent-based electrolytes; comparison of capacity retention at $-{60}^{\circ }\mathrm{C}$ for batteries with electrolytes comprising different solvent combinations. Reproduced from Ref [225]. Copyright Chinese Chemical Society 2020. (d) In situ XRD measurements of (FeMnCoNiCr) ₃O₄ powder at ${600}^{\circ }\mathrm{C}$ under a CO₂-containing atmosphere as a function of time (e) The MLIP energy (left panel) and force (right panel) of minimizing the root mean squared errors (RMSE). The lower-left and upper-right triangles within each square correspond to the training and test errors, respectively. Reproduced from Ref [226]. Copyright American Chemical Society 2024. [33]. Copyright Tsinghua University Press 2022.
Fig. 15. (a) Temperature-dependent ( $\rho -T$ ) electrical resistivity test. Reproduced from Ref [20]. Copyright Royal Society of Chemistry 2022. (b) Overpotential and the stability durable time of La₂ (CNMZNL) RuO₆. Reproduced from Ref [21]. Copyright Wiley-VCH Verlag 2024 (c) CO production rate versus time. Reproduced from Ref [22]. Copyright Elsevier 2022. (d) Highly dispersed Pt particles (size range 2-3 nm ) on HEO particles (right), and CO₂ hydrogenation activity (left). Reproduced from Ref [230]. Copyright American Chemical Society 2019. (e) FE (Field Emission)-SEM images of HEO-CNT and rHEO-CNT surface morphologies. Reproduced from Ref [231]. Copyright American Chemical Society 2019.
Fig. 16. (a) Magnetic induction strength versus temperature for (a-b) LC, (c-d) LCM, (e-f) LCMF, (g-h) LCMFA, and (i-j) LCMFAG ceramics in ZFC (Zero Field Cooling) and FC (Field Cooling) modes at 100 Oe and 1000 Oe, inset show the ${\chi }^{-1}$ vs T and the straight line represents the C-W fitting. Reproduced from Ref [34]. Copyright Elsevier 2025. (b) Hysteresis loops of the prepared HEOs at 300 K. The inset shows the low-field region of the hysteresis loops. Reproduced from Ref [122]. Copyright Elsevier 2024. (c) Magnetization versus magnetic field curves for the samples at ${25}^{\circ }\mathrm{C}$. Reproduced from Ref [131]. Copyright Elsevier 2024.
Fig. 17. (a) W_rec and $\eta $ as a function of electric field and W_rec comparison of (SrBaPbLaNa) Nb₂O₆ with other entropic materials of different configurations. Reproduced from Ref [36]. Copyright The Nature Publishing Group 2024. (b) Crystal structures of the R (R3c) and T (P4bm) phases with octahedral tilt; The overall energy storage performance of the obtained dielectric ceramics is compared with other work reported. Reproduced from Ref [216]. Copyright John Wiley and Sons 2024. (c) Comparison of energy density and energy storage efficiency of generative learning screened compositions with pristine matrix Bi(Mg_0.5Ti_0.5)O₃ at different breakdown fields. Comparison of energy densities and breakdown fields between original experimental compositions, screened compositions, and the original matrix Bi(Mg_0.5Ti_0.5)O₃. Reproduced from Ref [234]. Copyright The Nature Publishing Group 2024.
Fig. 18. An overview diagram of HECs. The outer ring shows the percentage of studies on high-entropy oxides, carbides, nitrides, borides and others. The inner rings show the main applications of HECs, as well as the four core effects of high-entropy materials and a schematic of the disordered structure, respectively.

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