Chemistry:High entropy oxide

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Short description: Complex oxide molecules that contain five or more metal ions
Structure of high-entropy oxide (MgNiCoCuZn)0.2O with site occupancies shown. Oxygen atoms are shown in red.

High-entropy oxides (HEOs) are complex oxides that contain five or more principal metal cations and have a single-phase crystal structure. The first HEO, (MgNiCuCoZn)0.2O in a rock salt structure, was reported in 2015 by Rost et al.[1] HEOs have been successfully synthesized in many structures, including fluorites,[2] perovskites, and spinels.[3] HEOs are currently being investigated for applications as functional materials.[3][4][5]

History

In the realm of high-entropy materials, HEOs are preceded by high-entropy alloys (HEAs), which were first reported by Yeh et al. in 2004.[6] HEAs are alloys of five or more principal metallic elements. Some HEAs have been shown to possess desirable mechanical properties, such as retaining strength/hardness at high temperatures.[7] HEA research substantially accelerated in the 2010s.[8]

The first HEO, (MgNiCuCoZn)0.2O in a rock salt structure, was reported in 2015 by Rost et al.[1] Similar to HEAs, (MgNiCuCoZn)0.2O is a multicomponent single-phase material. The cation site in (MgNiCuCoZn)0.2O material is compositionally disordered, similar to HEAs. However, unlike HEAs, (MgNiCuCoZn)0.2O contains an ordered anion sublattice. Following the discovery of HEOs in 2015, the field rapidly expanded.[3][4]

Since the discovery of HEOs, the field of high-entropy materials has expanded to include high-entropy metal diborides, high-entropy carbides, high-entropy sulfides, and high-entropy alumino-silicides.[4]

Predicting HEO Formation

Principle of Entropy Stabilization

The formation of HEOs is based on the principle of entropy stabilization. Thermodynamics predicts that the structure which minimizes Gibbs free energy for a given temperature and pressure will form. The formula for Gibbs free energy is given by:

[math]\displaystyle{ \Delta G=\Delta H - T\Delta S }[/math]

where G is Gibbs free energy, H is enthalpy, T is absolute temperature, and S is entropy. It can clearly be seen from this formula that a large entropy reduces Gibbs free energy and thus favors phase stability. It can also be seen that entropy becomes increasingly important in determining phase stability at higher temperatures. In a multi-component system, one component of entropy is the entropy of mixing ([math]\displaystyle{ \Delta S_{mix} }[/math]). For an ideal mixture, [math]\displaystyle{ \Delta S_{mix} }[/math] takes the form:

[math]\displaystyle{ \Delta S_{mix} = -R\sum_{i=1}^n c_i\ln c_i }[/math]

where R is the ideal gas constant, n is the number of components, and ci is the atomic fraction of component i. The value of [math]\displaystyle{ \Delta S_{mix} }[/math] increases as the number of components increases. For a given number of components, [math]\displaystyle{ \Delta S_{mix} }[/math] is maximized when the atomic fractions of the components approach equimolar amounts.

Evidence for entropy stabilization is given by the original rock salt HEO (MgNiCuCoZn)0.2O. Single-phase (MgNiCuCoZn)0.2O may be prepared by solid-state reaction of CuO, CoO, NiO, MgO, and ZnO.[1] Rost et al. reported that under solid state reaction conditions that produce single-phase (MgNiCuCoZn)0.2O, the absence of any one of the five oxide precursors will result in a multi-phase sample,[1] suggesting that configurational entropy stabilizes the material.

Other Considerations

It can clearly be seen from the formula for Gibbs free energy that enthalpy reduction is another important indicator of phase stability. For an HEO to form, the enthalpy of formation must be sufficiently small to be overcome by configurational entropy. Furthermore, the discussion above assumes that the reaction kinetics allow for the thermodynamically favored phase to form.

Synthesis Methods

Solid-State Reaction

Bulk samples of HEOs may be prepared by the solid-state reaction method. In this technique, oxide precursors are ball milled and pressed into a green body, which is sintered at a high temperature. The thermal energy provided accelerates diffusion within the green body, allowing new phases to form within the sample. Solid-state reactions are often carried out in the presence of air to allow oxygen-rich and oxygen-deficient mixtures to release and absorb oxygen from the atmosphere, respectively. Oxide precursors are not required to have the same crystal structure as the desired HEO for the solid-state reaction method to be effective. For example, CuO and ZnO may be used as precursors to synthesize (MgNiCuCoZn)0.2O. At room temperature, CuO has the tenorite structure and ZnO has the wurtzite structure.

Polymeric Steric Entrapment

Polymeric steric entrapment is a wet chemistry technique for synthesizing oxides. It is based on similar principles as the sol–gel process, which has also been used to synthesize HEOs.[9][10] Polymeric steric entrapment requires water-soluble compounds containing the desired metal cation (e.g., metal acetates, metal chlorides) to be placed in a solution with water and a water-soluble polymer (e.g., PVA, PEG). In solution, the cations are thoroughly mixed and held close together by the polymer chains.[11] The water is driven off to produce a foam whose organic components are burned off with a calcining step, producing a fine and pure mixed oxide powder,[12] which may be pressed into a green body and sintered. This method was first reported by Nguyen et al. in 2011.[12] In 2017, Kriven and Tseng reported the first polymeric steric entrapment HEO synthesis.[13]

Polymeric steric entrapment can be used to synthesize bulk HEO samples that are difficult to successfully synthesize the solid-state method. For example, Musico et al. synthesized the high entropy cuprate (LaNdGdTbDy)0.4CuO4 using solid-state reaction and polymeric steric entrapment.[11] X-ray diffraction of the sample prepared with solid-state reaction showed small inclusions of a second phase, and energy-dispersive X-ray spectroscopy showed inhomogeneous distributions of some cations. Neither impurity peaks nor evidence of inhomogeneous cation distribution was found in the sample of this material prepared with polymeric steric entrapment.

Other Techniques

Other techniques that have been used to synthesize HEOs include:

HEO Materials

The first HEOs synthesized had the rock-salt structure. Since then, the family of HEOs has expanded to include perovskite, spinel, fluorite, and other structures.[22][11][23][24][25][26] Some of these structures, such as the perovskite structure, are notable in that they have two cation sites, each of which may independently possess compositional disorder. For example, high entropy perovskites (GdLaNdSmY)0.2MnO3 (A-site configurational entropy), Gd(CoCrFeMnNi)0.2O3 (B-site configurational entropy), and (GdLaNdSmY)0.2(CoCrFeMnNi)0.2O3 (A-site and B-site configurational entropy) have been synthesized.[27][28]

Examples of HEO materials and their crystal structures
Structure Example Reference
Rock Salt (MgNiCuCoZn)0.2O Rost et al[1]
Fluorite (CeGdHfLaZr)O0.2 and (GdHfLaYZr)O0.2(CeZrHfSnTi)0.2O2 Anandkumar et al[29]

Chen et al[26]

Spinel (CoCrFeMnNi)0.6O4 Dabrowa et al[23]
Perovskite Sr(ZrSnTiHfMn)0.2O3 Jiang et al[24]
Pyrochlore (GdEuSmNdLa)0.4Zr2O7 Teng et al[25]
Cuprate Perovskite (LaNdGdTbDy)0.4CuO4 Musico et al[11]

Properties and Applications

In contrast to HEAs, which are typically investigated for their mechanical properties, HEOs are often studied as functional materials. The original HEO, (MgNiCuCoZn)0.2O, has been investigated as a promising material for applications in energy production and storage, e.g. as anode material in Li-ion batteries,[30] or as large k dielectric material,[31] or in catalysis.[32][33]

Low Thermal Conductivity

It has been shown that increasing the configurational entropy of a material reduces its lattice thermal conductivity.[34] Correspondingly, HEOs typically have lower thermal conductivities than materials with the same crystal structure and only one cation per lattice site.[35][36] The thermal conductivity of HEOs is usually greater than or comparable to the thermal conductivity of amorphous materials containing the same components.[3] However, crystalline materials typically have higher elastic moduli than amorphous materials of the same components. The combination of these factors leads to HEOs occupying a unique region of the property space by having the highest elastic modulus to thermal conductivity ratios of all materials.[35]

Property Tunability Through Cation Selection

HEOs enhance functional property tunability through cation selection. Magnetic,[37][38] catalytic,[39] and thermophysical[40] properties may be tuned by modifying the cation composition of a given HEO. Many material applications demand a highly specific set of properties. For example, thermal barrier coatings require thermal expansion coefficient matching with a metal surface, high-temperature phase stability, low thermal conductivity, and chemical inertness, among other properties.[41] Due to their innate tunability, HEOs have been proposed as candidates for advanced material applications such as thermal barrier coatings.[40]

Terminology

The definition of high-entropy oxide is debated. In oxide literature, the term is commonly used to refer to any oxide with at least five principal cations.[42] However, it has been suggested that this is a misnomer, as most reports neglect to calculate configurational entropy.[42] Additionally, a survey of 10 HEOs found that only 3 were entropy-stabilized.[43] It has been suggested that the term HEO be replaced with three terms: compositionally complex oxide, high-entropy oxide, and entropy-stabilized oxide.[42] In this scheme, compositionally complex refers to materials with multiple elements occupying the same sublattice, high-entropy refers to materials where configurational entropy plays a role in stabilization, and entropy-stabilized refers to materials where entropy dominates the enthalpy term and is necessary for the formation of a crystalline phase.

See also

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 Rost, Christina M.; Sachet, Edward; Borman, Trent; Moballegh, Ali; Dickey, Elizabeth C.; Huo, Dong; Jones, Jacob L.; Curtarolo, Stefano et al. (2015). "Entropy-stabilized oxides". Nature Communications 6: 8485. doi:10.1038/ncomms9485. PMID 26415623. Bibcode: 2015NatCo...6.8485R. 
  2. ↑ Anandkumar, Mariappan; Bhattacharya, Saswata; Deshpande, Atul Suresh (2019-08-23). "Low temperature synthesis and characterization of single phase multi-component fluorite oxide nanoparticle sols" (in en). RSC Advances 9 (46): 26825–26830. doi:10.1039/C9RA04636D. ISSN 2046-2069. PMID 35528557. 
  3. ↑ 3.0 3.1 3.2 3.3 Zhang, Rui-Zhi; Reece, Michael J. (2019-10-08). "Review of high entropy ceramics: design, synthesis, structure and properties" (in en). Journal of Materials Chemistry A 7 (39): 22148–22162. doi:10.1039/C9TA05698J. ISSN 2050-7496. 
  4. ↑ 4.0 4.1 4.2 Musicó, Brianna L.; Gilbert, Dustin; Ward, Thomas Zac; Page, Katharine; George, Easo; Yan, Jiaqiang; Mandrus, David; Keppens, Veerle (2020-04-01). "The emergent field of high entropy oxides: Design, prospects, challenges, and opportunities for tailoring material properties". APL Materials 8 (4): 040912. doi:10.1063/5.0003149. 
  5. ↑ Kotsonis, George N.; Almishal, Saeed S. I.; Marques dos Santos Vieira, Francisco; Crespi, Vincent H.; Dabo, Ismaila; Rost, Christina M.; Maria, Jon‐Paul (2023-06-24). "High‐entropy oxides: Harnessing crystalline disorder for emergent functionality" (in en). Journal of the American Ceramic Society 106 (10): 5587–5611. doi:10.1111/jace.19252. ISSN 0002-7820. 
  6. ↑ Yeh, J.-W.; Chen, S.-K.; Lin, S.-J.; Gan, J.-Y.; Chin, T.-S.; Shun, T.-T.; Tsau, C.-H.; Chang, S.-Y. (2004). "Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes". Advanced Engineering Materials 6 (5): 299–303. doi:10.1002/adem.200300567. https://doi.org/10.1002/adem.200300567. 
  7. ↑ Hsu, Chin-You; Juan, Chien-Chang; Wang, Woei-Ren; Sheu, Tsing-Shien; Yeh, Jien-Wei; Chen, Swe-Kai (2011-04-25). "On the superior hot hardness and softening resistance of AlCoCrxFeMo0.5Ni high-entropy alloys" (in en). Materials Science and Engineering: A 528 (10): 3581–3588. doi:10.1016/j.msea.2011.01.072. ISSN 0921-5093. https://www.sciencedirect.com/science/article/pii/S0921509311000943. 
  8. ↑ Tsai, Ming-Hung; Yeh, Jien-Wei (2014-07-03). "High-Entropy Alloys: A Critical Review" (in en). Materials Research Letters 2 (3): 107–123. doi:10.1080/21663831.2014.912690. ISSN 2166-3831. 
  9. ↑ 9.0 9.1 Asim, Muhammad; Hussain, Akbar; Khan, Safia; Arshad, Javeria; Butt, Tehmeena Maryum; Hana, Amina; Munawar, Mehwish; Saira, Farhat et al. (January 2022). "Sol-Gel Synthesized High Entropy Metal Oxides as High-Performance Catalysts for Electrochemical Water Oxidation" (in en). Molecules 27 (18): 5951. doi:10.3390/molecules27185951. ISSN 1420-3049. PMID 36144684. 
  10. ↑ 10.0 10.1 Petrovičovà, Beatrix; Xu, Wenlei; Musolino, Maria Grazia; Pantò, Fabiola; Patanè, Salvatore; Pinna, Nicola; Santangelo, Saveria; Triolo, Claudia (January 2022). "High-Entropy Spinel Oxides Produced via Sol-Gel and Electrospinning and Their Evaluation as Anodes in Li-Ion Batteries" (in en). Applied Sciences 12 (12): 5965. doi:10.3390/app12125965. ISSN 2076-3417. 
  11. ↑ 11.0 11.1 11.2 11.3 Musicó, Brianna L.; Wright, Quinton; Delzer, Cordell; Ward, T. Zac; Rawn, Claudia J.; Mandrus, David G.; Keppens, Veerle (July 2021). "Synthesis method comparison of compositionally complex rare earth‐based Ruddlesden–Popper n = 1 T′‐type cuprates" (in en). Journal of the American Ceramic Society 104 (7): 3750–3759. doi:10.1111/jace.17750. ISSN 0002-7820. https://onlinelibrary.wiley.com/doi/10.1111/jace.17750. 
  12. ↑ 12.0 12.1 Nguyen, My H.; Lee, Sang-Jin; Kriven, Waltraud M. (October 1999). "Synthesis of oxide powders by way of a polymeric steric entrapment precursor route" (in en). Journal of Materials Research 14 (8): 3417–3426. doi:10.1557/JMR.1999.0462. ISSN 2044-5326. https://www.cambridge.org/core/journals/journal-of-materials-research/article/abs/synthesis-of-oxide-powders-by-way-of-a-polymeric-steric-entrapment-precursor-route/8851439A9271998219E502F2C352EB68. 
  13. ↑ Kriven, Waltraud; Tseng, Kuo-Pin (2017-11-14). "High-temperature behavior in entropy-stabilized oxide (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)O". Composites at Lake Louise 2017. https://dc.engconfintl.org/composites_all_2017/13. 
  14. ↑ Sarkar, Abhishek; Djenadic, Ruzica; Wang, Di; Hein, Christina; Kautenburger, Ralf; Clemens, Oliver; Hahn, Horst (2018-05-01). "Rare earth and transition metal based entropy stabilised perovskite type oxides" (in en). Journal of the European Ceramic Society 38 (5): 2318–2327. doi:10.1016/j.jeurceramsoc.2017.12.058. ISSN 0955-2219. https://www.sciencedirect.com/science/article/pii/S0955221917308671. 
  15. ↑ Wang, Qingsong; Sarkar, Abhishek; Li, Zhenyou; Lu, Yang; Velasco, Leonardo; Bhattacharya, Subramshu S.; Brezesinski, Torsten; Hahn, Horst et al. (2019-03-01). "High entropy oxides as anode material for Li-ion battery applications: A practical approach" (in en). Electrochemistry Communications 100: 121–125. doi:10.1016/j.elecom.2019.02.001. ISSN 1388-2481. 
  16. ↑ Braun, Jeffrey L.; Rost, Christina M.; Lim, Mina; Giri, Ashutosh; Olson, David H.; Kotsonis, George N.; Stan, Gheorghe; Brenner, Donald W. et al. (December 2018). "Charge‐Induced Disorder Controls the Thermal Conductivity of Entropy‐Stabilized Oxides" (in en). Advanced Materials 30 (51): 1805004. doi:10.1002/adma.201805004. ISSN 0935-9648. PMID 30368943. 
  17. ↑ Meisenheimer, P. B.; Kratofil, T. J.; Heron, J. T. (2017-10-17). "Giant Enhancement of Exchange Coupling in Entropy-Stabilized Oxide Heterostructures" (in en). Scientific Reports 7 (1): 13344. doi:10.1038/s41598-017-13810-5. ISSN 2045-2322. PMID 29042610. 
  18. ↑ Yang, Zhao-Ming; Zhang, Kun; Qiu, Nan; Zhang, Hai-Bin; Wang, Yuan; Chen, Jian (April 2019). "Effects of helium implantation on mechanical properties of (Al 0.31 Cr 0.20 Fe 0.14 Ni 0.35 )O high entropy oxide films". Chinese Physics B 28 (4): 046201. doi:10.1088/1674-1056/28/4/046201. ISSN 1674-1056. https://iopscience.iop.org/article/10.1088/1674-1056/28/4/046201. 
  19. ↑ Kirnbauer, Alexander; Spadt, Christoph; Koller, Christian M.; Kolozsvári, Szilard; Mayrhofer, Paul H. (2019-10-01). "High-entropy oxide thin films based on Al–Cr–Nb–Ta–Ti" (in en). Vacuum 168: 108850. doi:10.1016/j.vacuum.2019.108850. ISSN 0042-207X. https://www.sciencedirect.com/science/article/pii/S0042207X19312588. 
  20. ↑ Lei, Zhifeng; Liu, Xiongjun; Li, Rui; Wang, Hui; Wu, Yuan; Lu, Zhaoping (2018-03-15). "Ultrastable metal oxide nanotube arrays achieved by entropy-stabilization engineering" (in en). Scripta Materialia 146: 340–343. doi:10.1016/j.scriptamat.2017.12.025. ISSN 1359-6462. https://www.sciencedirect.com/science/article/pii/S135964621730725X. 
  21. ↑ Ren, Xiaomin; Tian, Zhilin; Zhang, Jie; Wang, Jingyang (2019-07-15). "Equiatomic quaternary (Y1/4Ho1/4Er1/4Yb1/4)2SiO5 silicate: A perspective multifunctional thermal and environmental barrier coating material" (in en). Scripta Materialia 168: 47–50. doi:10.1016/j.scriptamat.2019.04.018. ISSN 1359-6462. https://www.sciencedirect.com/science/article/pii/S1359646219302180. 
  22. ↑ Anandkumar, Mariappan; Bhattacharya, Saswata; Deshpande, Atul Suresh (2019-08-23). "Low temperature synthesis and characterization of single phase multi-component fluorite oxide nanoparticle sols" (in en). RSC Advances 9 (46): 26825–26830. doi:10.1039/C9RA04636D. ISSN 2046-2069. PMID 35528557. 
  23. ↑ 23.0 23.1 Dąbrowa, Juliusz; Stygar, Mirosław; Mikuła, Andrzej; Knapik, Arkadiusz; Mroczka, Krzysztof; Tejchman, Waldemar; Danielewski, Marek; Martin, Manfred (2018-04-01). "Synthesis and microstructure of the (Co,Cr,Fe,Mn,Ni)3O4 high entropy oxide characterized by spinel structure" (in en). Materials Letters 216: 32–36. doi:10.1016/j.matlet.2017.12.148. ISSN 0167-577X. https://www.sciencedirect.com/science/article/pii/S0167577X17319134. 
  24. ↑ 24.0 24.1 Jiang, Sicong; Hu, Tao; Gild, Joshua; Zhou, Naixie; Nie, Jiuyuan; Qin, Mingde; Harrington, Tyler; Vecchio, Kenneth et al. (2018-01-01). "A new class of high-entropy perovskite oxides" (in en). Scripta Materialia 142: 116–120. doi:10.1016/j.scriptamat.2017.08.040. ISSN 1359-6462. https://www.sciencedirect.com/science/article/pii/S1359646217305043. 
  25. ↑ 25.0 25.1 Teng, Zhen; Zhu, Lini; Tan, Yongqiang; Zeng, Sifan; Xia, Yuanhua; Wang, Yiguang; Zhang, Haibin (2020-04-01). "Synthesis and structures of high-entropy pyrochlore oxides" (in en). Journal of the European Ceramic Society 40 (4): 1639–1643. doi:10.1016/j.jeurceramsoc.2019.12.008. ISSN 0955-2219. https://www.sciencedirect.com/science/article/pii/S0955221919308520. 
  26. ↑ 26.0 26.1 Chen, Kepi; Pei, Xintong; Tang, Lei; Cheng, Haoran; Li, Zemin; Li, Cuiwei; Zhang, Xiaowen; An, Linan (2018-09-01). "A five-component entropy-stabilized fluorite oxide" (in en). Journal of the European Ceramic Society 38 (11): 4161–4164. doi:10.1016/j.jeurceramsoc.2018.04.063. ISSN 0955-2219. 
  27. ↑ Sarkar, Abhishek; Djenadic, Ruzica; Wang, Di; Hein, Christina; Kautenburger, Ralf; Clemens, Oliver; Hahn, Horst (2018-05-01). "Rare earth and transition metal based entropy stabilised perovskite type oxides" (in en). Journal of the European Ceramic Society 38 (5): 2318–2327. doi:10.1016/j.jeurceramsoc.2017.12.058. ISSN 0955-2219. https://www.sciencedirect.com/science/article/pii/S0955221917308671. 
  28. ↑ Witte, Ralf; Sarkar, Abhishek; Kruk, Robert; Eggert, Benedikt; Brand, Richard A.; Wende, Heiko; Hahn, Horst (2019-03-13). "High-entropy oxides: An emerging prospect for magnetic rare-earth transition metal perovskites". Physical Review Materials 3 (3): 034406. doi:10.1103/PhysRevMaterials.3.034406. https://link.aps.org/doi/10.1103/PhysRevMaterials.3.034406. 
  29. ↑ Anandkumar, Mariappan; Bhattacharya, Saswata; Deshpande, Atul Suresh (2019-08-23). "Low temperature synthesis and characterization of single phase multi-component fluorite oxide nanoparticle sols" (in en). RSC Advances 9 (46): 26825–26830. doi:10.1039/C9RA04636D. ISSN 2046-2069. PMID 35528557. 
  30. ↑ Sarkar, Abhishek; Velasco, Leonardo; Wang, Di; Wang, Quingsong; Talasila, Gopichand; de Biasi, Lea; Kübel, Christian; Brezeniski, Torsten et al. (2018). "High entropy oxides for reversible energy storage". Nature Communications 9 (1): 3400. doi:10.1038/s41467-018-05774-5. PMID 30143625. Bibcode: 2018NatCo...9.3400S. 
  31. ↑ Béradan, David; Franger, Sylvain; Dragoe, Diana; Meena, Arun Kuman; Dragoe, Nita (2016). "Colossal dielectric constant in high entropy oxides". Physica Status Solidi RRL 10 (4): 328–333. doi:10.1002/pssr.201600043. Bibcode: 2016PSSRR..10..328B. 
  32. ↑ Chen, Hao; Zhang, Pengfei; Peng, Honggeng; Abney, Carter W.; Jie, Kecheng; Liu, Xiaoming; Chi, Miaofang; Dai, Sheng (2018). "Entropy-stabilized metal oxide solid solutions as CO oxidation catalysts with high-temperature stability". Journal of Materials Chemistry A 6 (24): 11129. doi:10.1039/c8ta01772g. 
  33. ↑ Fracchia, Martina; Ghigna, Paolo; Pozzi, Tommaso; Anselmi Tamburini, Umberto; Colombo, Valentina; Braglia, Luca; Torelli, Piero (2020). "Stabilization by Configurational Entropy of the Cu(II) Active Site during CO Oxidation on Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O". Journal of Physical Chemistry Letters 11 (9): 3589–3593. doi:10.1021/acs.jpclett.0c00602. PMID 32309955. 
  34. ↑ Liu, Ruiheng; Chen, Hongyi; Zhao, Kunpeng; Qin, Yuting; Jiang, Binbin; Zhang, Tiansong; Sha, Gang; Shi, Xun et al. (October 2017). "Entropy as a Gene-Like Performance Indicator Promoting Thermoelectric Materials" (in en). Advanced Materials 29 (38): 1702712. doi:10.1002/adma.201702712. PMID 28833741. https://onlinelibrary.wiley.com/doi/10.1002/adma.201702712. 
  35. ↑ 35.0 35.1 Braun, Jeffrey L.; Rost, Christina M.; Lim, Mina; Giri, Ashutosh; Olson, David H.; Kotsonis, George N.; Stan, Gheorghe; Brenner, Donald W. et al. (December 2018). "Charge‐Induced Disorder Controls the Thermal Conductivity of Entropy‐Stabilized Oxides" (in en). Advanced Materials 30 (51): 1805004. doi:10.1002/adma.201805004. ISSN 0935-9648. PMID 30368943. 
  36. ↑ Gild, Joshua; Samiee, Mojtaba; Braun, Jeffrey L.; Harrington, Tyler; Vega, Heidy; Hopkins, Patrick E.; Vecchio, Kenneth; Luo, Jian (2018-08-01). "High-entropy fluorite oxides" (in en). Journal of the European Ceramic Society 38 (10): 3578–3584. doi:10.1016/j.jeurceramsoc.2018.04.010. ISSN 0955-2219. 
  37. ↑ Johnstone, Graham H. J.; González-Rivas, Mario U.; Taddei, Keith M.; Sutarto, Ronny; Sawatzky, George A.; Green, Robert J.; Oudah, Mohamed; Hallas, Alannah M. (2022-11-16). "Entropy Engineering and Tunable Magnetic Order in the Spinel High-Entropy Oxide" (in en). Journal of the American Chemical Society 144 (45): 20590–20600. doi:10.1021/jacs.2c06768. ISSN 0002-7863. PMID 36321637. https://pubs.acs.org/doi/abs/10.1021/jacs.2c06768. 
  38. ↑ Musicó, Brianna; Wright, Quinton; Ward, T. Zac; Grutter, Alexander; Arenholz, Elke; Gilbert, Dustin; Mandrus, David; Keppens, Veerle (2019-10-21). "Tunable magnetic ordering through cation selection in entropic spinel oxides". Physical Review Materials 3 (10): 104416. doi:10.1103/physrevmaterials.3.104416. ISSN 2475-9953. http://dx.doi.org/10.1103/physrevmaterials.3.104416. 
  39. ↑ Pan, Yingtong; Liu, Ji-Xuan; Tu, Tian-Zhe; Wang, Wenzhong; Zhang, Guo-Jun (2023-01-01). "High-entropy oxides for catalysis: A diamond in the rough" (in en). Chemical Engineering Journal 451: 138659. doi:10.1016/j.cej.2022.138659. ISSN 1385-8947. https://www.sciencedirect.com/science/article/pii/S1385894722041407. 
  40. ↑ 40.0 40.1 Luo, Xuewei; Huang, Ruiqi; Xu, Chunhui; Huang, Shuo; Hou, Shuen; Jin, Hongyun (2022-12-10). "Designing high-entropy rare-earth zirconates with tunable thermophysical properties for thermal barrier coatings" (in en). Journal of Alloys and Compounds 926: 166714. doi:10.1016/j.jallcom.2022.166714. ISSN 0925-8388. https://www.sciencedirect.com/science/article/pii/S092583882203105X. 
  41. ↑ Cao, X. Q.; Vassen, R.; Stoever, D. (2004-01-01). "Ceramic materials for thermal barrier coatings" (in en). Journal of the European Ceramic Society 24 (1): 1–10. doi:10.1016/S0955-2219(03)00129-8. ISSN 0955-2219. https://www.sciencedirect.com/science/article/pii/S0955221903001298. 
  42. ↑ 42.0 42.1 42.2 Brahlek, Matthew; Gazda, Maria; Keppens, Veerle; Mazza, Alessandro R.; McCormack, Scott J.; Mielewczyk-Gryń, Aleksandra; Musico, Brianna; Page, Katharine et al. (2022-11-01). "What is in a name: Defining "high entropy" oxides". APL Materials 10 (11): 110902. doi:10.1063/5.0122727. 
  43. ↑ Sarkar, Abhishek; Wang, Qingsong; Schiele, Alexander; Chellali, Mohammed Reda; Bhattacharya, Subramshu S.; Wang, Di; Brezesinski, Torsten; Hahn, Horst et al. (June 2019). "High‐Entropy Oxides: Fundamental Aspects and Electrochemical Properties" (in en). Advanced Materials 31 (26): 1806236. doi:10.1002/adma.201806236. ISSN 0935-9648. PMID 30838717. 



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