:High entropy oxide

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.{{Cite journal |last1=Yeh |first1=J.-W. |last2=Chen |first2=S.-K. |last3=Lin |first3=S.-J. |last4=Gan |first4=J.-Y. |last5=Chin |first5=T.-S. |last6=Shun |first6=T.-T. |last7=Tsau |first7=C.-H. |last8=Chang |first8=S.-Y. |title=Nanostructured High-Entropy Alloys with Multiple Principal Elements: Novel Alloy Design Concepts and Outcomes |url=https://doi.org/10.1002/adem.200300567 |journal=Advanced Engineering Materials |year=2004 |volume=6 |issue=5|pages=299–303 |doi=10.1002/adem.200300567 |s2cid=137380231 |url-access=subscription }} 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.{{Cite journal |last1=Hsu |first1=Chin-You |last2=Juan |first2=Chien-Chang |last3=Wang |first3=Woei-Ren |last4=Sheu |first4=Tsing-Shien |last5=Yeh |first5=Jien-Wei |last6=Chen |first6=Swe-Kai |date=2011-04-25 |title=On the superior hot hardness and softening resistance of AlCoCrxFeMo0.5Ni high-entropy alloys |url=https://www.sciencedirect.com/science/article/pii/S0921509311000943 |journal=Materials Science and Engineering: A |language=en |volume=528 |issue=10 |pages=3581–3588 |doi=10.1016/j.msea.2011.01.072 |issn=0921-5093|url-access=subscription }} HEA research substantially accelerated in the 2010s.{{Cite journal |last1=Tsai |first1=Ming-Hung |last2=Yeh |first2=Jien-Wei |date=2014-07-03 |title=High-Entropy Alloys: A Critical Review |journal=Materials Research Letters |language=en |volume=2 |issue=3 |pages=107–123 |doi=10.1080/21663831.2014.912690 |s2cid=56099930 |issn=2166-3831|doi-access=free }}

The first HEO, (MgNiCuCoZn)_0.2O in a rock salt structure, was reported in 2015 by Rost et al. 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.

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.

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:

$\backslash Delta\; G=\backslash Delta\; H\; -\; T\backslash Delta\; S$

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 ($\backslash Delta\; S\_\{mix\}$). For an ideal mixture, $\backslash Delta\; S\_\{mix\}$ takes the form:

$\backslash Delta\; S\_\{mix\}\; =\; -R\backslash sum\_\{i=1\}^n\; c\_i\backslash ln\; c\_i$

where R is the ideal gas constant, n is the number of components, and c_i is the atomic fraction of component i. The value of $\backslash Delta\; S\_\{mix\}$ increases as the number of components increases. For a given number of components, $\backslash Delta\; S\_\{mix\}$ 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. 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, suggesting that configurational entropy stabilizes the material.

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.

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 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.{{Cite journal |last1=Asim |first1=Muhammad |last2=Hussain |first2=Akbar |last3=Khan |first3=Safia |last4=Arshad |first4=Javeria |last5=Butt |first5=Tehmeena Maryum |last6=Hana |first6=Amina |last7=Munawar |first7=Mehwish |last8=Saira |first8=Farhat |last9=Rani |first9=Malika |last10=Mahmood |first10=Arshad |last11=Janjua |first11=Naveed Kausar |date=January 2022 |title=Sol-Gel Synthesized High Entropy Metal Oxides as High-Performance Catalysts for Electrochemical Water Oxidation |journal=Molecules |language=en |volume=27 |issue=18 |pages=5951 |doi=10.3390/molecules27185951 |issn=1420-3049 |pmc=9504205 |pmid=36144684|doi-access=free }}{{Cite journal |last1=Petrovičovà |first1=Beatrix |last2=Xu |first2=Wenlei |last3=Musolino |first3=Maria Grazia |last4=Pantò |first4=Fabiola |last5=Patanè |first5=Salvatore |last6=Pinna |first6=Nicola |last7=Santangelo |first7=Saveria |last8=Triolo |first8=Claudia |date=January 2022 |title=High-Entropy Spinel Oxides Produced via Sol-Gel and Electrospinning and Their Evaluation as Anodes in Li-Ion Batteries |journal=Applied Sciences |language=en |volume=12 |issue=12 |pages=5965 |doi=10.3390/app12125965 |issn=2076-3417|doi-access=free }} 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.{{Cite journal |last1=Musicó |first1=Brianna L. |last2=Wright |first2=Quinton |last3=Delzer |first3=Cordell |last4=Ward |first4=T. Zac |last5=Rawn |first5=Claudia J. |last6=Mandrus |first6=David G. |last7=Keppens |first7=Veerle |date=July 2021 |title=Synthesis method comparison of compositionally complex rare earth-based Ruddlesden–Popper n = 1 T′-type cuprates |url=https://onlinelibrary.wiley.com/doi/10.1111/jace.17750 |journal=Journal of the American Ceramic Society |language=en |volume=104 |issue=7 |pages=3750–3759 |doi=10.1111/jace.17750 |osti=1777687 |s2cid=233945514 |issn=0002-7820}} 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,{{Cite journal |last1=Nguyen |first1=My H. |last2=Lee |first2=Sang-Jin |last3=Kriven |first3=Waltraud M. |date=October 1999 |title=Synthesis of oxide powders by way of a polymeric steric entrapment precursor route |url=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 |journal=Journal of Materials Research |language=en |volume=14 |issue=8 |pages=3417–3426 |doi=10.1557/JMR.1999.0462 |bibcode=1999JMatR..14.3417N |s2cid=94373425 |issn=2044-5326|url-access=subscription }} which may be pressed into a green body and sintered. This method was first reported by Nguyen et al. in 2011. In 2017, Kriven and Tseng reported the first polymeric steric entrapment HEO synthesis.{{Cite journal |last1=Kriven |first1=Waltraud |last2=Tseng |first2=Kuo-Pin |date=2017-11-14 |title=High-temperature behavior in entropy-stabilized oxide (Mg0.2Co0.2Ni0.2Cu0.2Zn0.2)O |url=https://dc.engconfintl.org/composites_all_2017/13 |journal=Composites at Lake Louise 2017}}

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. 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 that have been used to synthesize HEOs include:

• Nebulized spray pyrolysis{{Cite journal |last1=Sarkar |first1=Abhishek |last2=Djenadic |first2=Ruzica |last3=Wang |first3=Di |last4=Hein |first4=Christina |last5=Kautenburger |first5=Ralf |last6=Clemens |first6=Oliver |last7=Hahn |first7=Horst |date=2018-05-01 |title=Rare earth and transition metal based entropy stabilised perovskite type oxides |url=https://www.sciencedirect.com/science/article/pii/S0955221917308671 |journal=Journal of the European Ceramic Society |language=en |volume=38 |issue=5 |pages=2318–2327 |doi=10.1016/j.jeurceramsoc.2017.12.058 |issn=0955-2219}}{{Cite journal |last1=Wang |first1=Qingsong |last2=Sarkar |first2=Abhishek |last3=Li |first3=Zhenyou |last4=Lu |first4=Yang |last5=Velasco |first5=Leonardo |last6=Bhattacharya |first6=Subramshu S. |last7=Brezesinski |first7=Torsten |last8=Hahn |first8=Horst |last9=Breitung |first9=Ben |date=2019-03-01 |title=High entropy oxides as anode material for Li-ion battery applications: A practical approach |journal=Electrochemistry Communications |language=en |volume=100 |pages=121–125 |doi=10.1016/j.elecom.2019.02.001 |s2cid=104458246 |issn=1388-2481|doi-access=free }}
• Pulsed laser deposition{{Cite journal |last1=Braun |first1=Jeffrey L. |last2=Rost |first2=Christina M. |last3=Lim |first3=Mina |last4=Giri |first4=Ashutosh |last5=Olson |first5=David H. |last6=Kotsonis |first6=George N. |last7=Stan |first7=Gheorghe |last8=Brenner |first8=Donald W. |last9=Maria |first9=Jon-Paul |last10=Hopkins |first10=Patrick E. |date=December 2018 |title=Charge-Induced Disorder Controls the Thermal Conductivity of Entropy-Stabilized Oxides |journal=Advanced Materials |language=en |volume=30 |issue=51 |pages=1805004 |doi=10.1002/adma.201805004 |issn=0935-9648 |pmc=9486463 |pmid=30368943|bibcode=2018AdM....3005004B }}{{Cite journal |last1=Meisenheimer |first1=P. B. |last2=Kratofil |first2=T. J. |last3=Heron |first3=J. T. |date=2017-10-17 |title=Giant Enhancement of Exchange Coupling in Entropy-Stabilized Oxide Heterostructures |journal=Scientific Reports |language=en |volume=7 |issue=1 |pages=13344 |doi=10.1038/s41598-017-13810-5 |pmid=29042610 |pmc=5645335 |s2cid=205613906 |issn=2045-2322|doi-access=free |bibcode=2017NatSR...713344M }}
• Magnetron sputtering{{Cite journal |last1=Yang |first1=Zhao-Ming |last2=Zhang |first2=Kun |last3=Qiu |first3=Nan |last4=Zhang |first4=Hai-Bin |last5=Wang |first5=Yuan |last6=Chen |first6=Jian |date=April 2019 |title=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 |url=https://iopscience.iop.org/article/10.1088/1674-1056/28/4/046201 |journal=Chinese Physics B |volume=28 |issue=4 |pages=046201 |doi=10.1088/1674-1056/28/4/046201 |s2cid=250758900 |issn=1674-1056|url-access=subscription }}{{Cite journal |last1=Kirnbauer |first1=Alexander |last2=Spadt |first2=Christoph |last3=Koller |first3=Christian M. |last4=Kolozsvári |first4=Szilard |last5=Mayrhofer |first5=Paul H. |date=2019-10-01 |title=High-entropy oxide thin films based on Al–Cr–Nb–Ta–Ti |url=https://www.sciencedirect.com/science/article/pii/S0042207X19312588 |journal=Vacuum |language=en |volume=168 |pages=108850 |doi=10.1016/j.vacuum.2019.108850 |bibcode=2019Vacuu.16808850K |s2cid=201214183 |issn=0042-207X|url-access=subscription }}
• Sol-gel method
• Anodizing HEA precursors{{Cite journal |last1=Lei |first1=Zhifeng |last2=Liu |first2=Xiongjun |last3=Li |first3=Rui |last4=Wang |first4=Hui |last5=Wu |first5=Yuan |last6=Lu |first6=Zhaoping |date=2018-03-15 |title=Ultrastable metal oxide nanotube arrays achieved by entropy-stabilization engineering |url=https://www.sciencedirect.com/science/article/pii/S135964621730725X |journal=Scripta Materialia |language=en |volume=146 |pages=340–343 |doi=10.1016/j.scriptamat.2017.12.025 |issn=1359-6462|url-access=subscription }}
• Hot pressing{{Cite journal |last1=Ren |first1=Xiaomin |last2=Tian |first2=Zhilin |last3=Zhang |first3=Jie |last4=Wang |first4=Jingyang |date=2019-07-15 |title=Equiatomic quaternary (Y1/4Ho1/4Er1/4Yb1/4)2SiO5 silicate: A perspective multifunctional thermal and environmental barrier coating material |url=https://www.sciencedirect.com/science/article/pii/S1359646219302180 |journal=Scripta Materialia |language=en |volume=168 |pages=47–50 |doi=10.1016/j.scriptamat.2019.04.018 |s2cid=150218458 |issn=1359-6462|url-access=subscription }}
• Thermolysis of mixed precursors

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.{{Cite journal |last1=Anandkumar |first1=Mariappan |last2=Bhattacharya |first2=Saswata |last3=Deshpande |first3=Atul Suresh |date=2019-08-23 |title=Low temperature synthesis and characterization of single phase multi-component fluorite oxide nanoparticle sols |journal=RSC Advances |language=en |volume=9 |issue=46 |pages=26825–26830 |doi=10.1039/C9RA04636D |issn=2046-2069 |pmc=9070433 |pmid=35528557|bibcode=2019RSCAd...926825A }}{{Cite journal |last1=Dąbrowa |first1=Juliusz |last2=Stygar |first2=Mirosław |last3=Mikuła |first3=Andrzej |last4=Knapik |first4=Arkadiusz |last5=Mroczka |first5=Krzysztof |last6=Tejchman |first6=Waldemar |last7=Danielewski |first7=Marek |last8=Martin |first8=Manfred |date=2018-04-01 |title=Synthesis and microstructure of the (Co,Cr,Fe,Mn,Ni)3O4 high entropy oxide characterized by spinel structure |url=https://www.sciencedirect.com/science/article/pii/S0167577X17319134 |journal=Materials Letters |language=en |volume=216 |pages=32–36 |doi=10.1016/j.matlet.2017.12.148 |issn=0167-577X|url-access=subscription }}{{Cite journal |last1=Jiang |first1=Sicong |last2=Hu |first2=Tao |last3=Gild |first3=Joshua |last4=Zhou |first4=Naixie |last5=Nie |first5=Jiuyuan |last6=Qin |first6=Mingde |last7=Harrington |first7=Tyler |last8=Vecchio |first8=Kenneth |last9=Luo |first9=Jian |date=2018-01-01 |title=A new class of high-entropy perovskite oxides |url=https://www.sciencedirect.com/science/article/pii/S1359646217305043 |journal=Scripta Materialia |language=en |volume=142 |pages=116–120 |doi=10.1016/j.scriptamat.2017.08.040 |issn=1359-6462|url-access=subscription }}{{Cite journal |last1=Teng |first1=Zhen |last2=Zhu |first2=Lini |last3=Tan |first3=Yongqiang |last4=Zeng |first4=Sifan |last5=Xia |first5=Yuanhua |last6=Wang |first6=Yiguang |last7=Zhang |first7=Haibin |date=2020-04-01 |title=Synthesis and structures of high-entropy pyrochlore oxides |url=https://www.sciencedirect.com/science/article/pii/S0955221919308520 |journal=Journal of the European Ceramic Society |language=en |volume=40 |issue=4 |pages=1639–1643 |doi=10.1016/j.jeurceramsoc.2019.12.008 |s2cid=214404247 |issn=0955-2219|url-access=subscription }}{{Cite journal |last1=Chen |first1=Kepi |last2=Pei |first2=Xintong |last3=Tang |first3=Lei |last4=Cheng |first4=Haoran |last5=Li |first5=Zemin |last6=Li |first6=Cuiwei |last7=Zhang |first7=Xiaowen |last8=An |first8=Linan |date=2018-09-01 |title=A five-component entropy-stabilized fluorite oxide |journal=Journal of the European Ceramic Society |language=en |volume=38 |issue=11 |pages=4161–4164 |doi=10.1016/j.jeurceramsoc.2018.04.063 |s2cid=102857005 |issn=0955-2219|doi-access=free }} 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.{{Cite journal |last1=Sarkar |first1=Abhishek |last2=Djenadic |first2=Ruzica |last3=Wang |first3=Di |last4=Hein |first4=Christina |last5=Kautenburger |first5=Ralf |last6=Clemens |first6=Oliver |last7=Hahn |first7=Horst |date=2018-05-01 |title=Rare earth and transition metal based entropy stabilised perovskite type oxides |url=https://www.sciencedirect.com/science/article/pii/S0955221917308671 |journal=Journal of the European Ceramic Society |language=en |volume=38 |issue=5 |pages=2318–2327 |doi=10.1016/j.jeurceramsoc.2017.12.058 |issn=0955-2219}}{{Cite journal |last1=Witte |first1=Ralf |last2=Sarkar |first2=Abhishek |last3=Kruk |first3=Robert |last4=Eggert |first4=Benedikt |last5=Brand |first5=Richard A. |last6=Wende |first6=Heiko |last7=Hahn |first7=Horst |date=2019-03-13 |title=High-entropy oxides: An emerging prospect for magnetic rare-earth transition metal perovskites |url=https://link.aps.org/doi/10.1103/PhysRevMaterials.3.034406 |journal=Physical Review Materials |volume=3 |issue=3 |pages=034406 |doi=10.1103/PhysRevMaterials.3.034406|arxiv=1901.02395 |bibcode=2019PhRvM...3c4406W |s2cid=118925048 }}

Note: (MgNiCuCoZn)_0.2O refers to the lower entropy rock structure MO where the 0.2 value refers to the ideal (equimolar) contribution of an individual cation

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,{{cite journal |last1=Sarkar |first1=Abhishek |last2=Velasco |first2=Leonardo |last3=Wang |first3=Di |last4=Wang |first4=Quingsong |last5=Talasila |first5=Gopichand |last6=de Biasi |first6=Lea |last7=Kübel |first7=Christian |last8=Brezeniski |first8=Torsten |last9=Battacharya |first9=Subramshu S. |last10=Hanh |first10=Horst |last11=Breitung |first11=Ben |date=2018 |title=High entropy oxides for reversible energy storage |journal=Nature Communications |volume=9 |issue=1 |page=3400 |bibcode=2018NatCo...9.3400S |doi=10.1038/s41467-018-05774-5 |pmc=6109100 |pmid=30143625}} or as large k dielectric material,{{cite journal |last1=Béradan |first1=David |last2=Franger |first2=Sylvain |last3=Dragoe |first3=Diana |last4=Meena |first4=Arun Kuman |last5=Dragoe |first5=Nita |date=2016 |title=Colossal dielectric constant in high entropy oxides |journal=Physica Status Solidi RRL |volume=10 |issue=4 |pages=328–333 |arxiv=1602.07842 |bibcode=2016PSSRR..10..328B |doi=10.1002/pssr.201600043 |s2cid=101808600}} or in catalysis.{{cite journal |last1=Chen |first1=Hao |last2=Zhang |first2=Pengfei |last3=Peng |first3=Honggeng |last4=Abney |first4=Carter W. |last5=Jie |first5=Kecheng |last6=Liu |first6=Xiaoming |last7=Chi |first7=Miaofang |author-link7=Miaofang Chi |last8=Dai |first8=Sheng |date=2018 |title=Entropy-stabilized metal oxide solid solutions as CO oxidation catalysts with high-temperature stability |journal=Journal of Materials Chemistry A |volume=6 |issue=24 |page=11129 |doi=10.1039/c8ta01772g}}{{cite journal |last1=Fracchia |first1=Martina |last2=Ghigna |first2=Paolo |last3=Pozzi |first3=Tommaso |last4=Anselmi Tamburini |first4=Umberto |last5=Colombo |first5=Valentina |last6=Braglia |first6=Luca |last7=Torelli |first7=Piero |date=2020 |title=Stabilization by Configurational Entropy of the Cu(II) Active Site during CO Oxidation on Mg0.2Co0.2Ni0.2Cu0.2Zn0.2O |journal=Journal of Physical Chemistry Letters |volume=11 |issue=9 |pages=3589–3593 |doi=10.1021/acs.jpclett.0c00602 |pmc=8007101 |pmid=32309955 |doi-access=free}}

It has been shown that increasing the configurational entropy of a material reduces its lattice thermal conductivity.{{Cite journal |last1=Liu |first1=Ruiheng |last2=Chen |first2=Hongyi |last3=Zhao |first3=Kunpeng |last4=Qin |first4=Yuting |last5=Jiang |first5=Binbin |last6=Zhang |first6=Tiansong |last7=Sha |first7=Gang |last8=Shi |first8=Xun |last9=Uher |first9=Ctirad |last10=Zhang |first10=Wenqing |last11=Chen |first11=Lidong |date=October 2017 |title=Entropy as a Gene-Like Performance Indicator Promoting Thermoelectric Materials |url=https://onlinelibrary.wiley.com/doi/10.1002/adma.201702712 |journal=Advanced Materials |language=en |volume=29 |issue=38 |pages=1702712 |doi=10.1002/adma.201702712|pmid=28833741 |bibcode=2017AdM....2902712L |hdl=2027.42/138909 |s2cid=20987488 |hdl-access=free }} Correspondingly, HEOs typically have lower thermal conductivities than materials with the same crystal structure and only one cation per lattice site.{{Cite journal |last1=Braun |first1=Jeffrey L. |last2=Rost |first2=Christina M. |last3=Lim |first3=Mina |last4=Giri |first4=Ashutosh |last5=Olson |first5=David H. |last6=Kotsonis |first6=George N. |last7=Stan |first7=Gheorghe |last8=Brenner |first8=Donald W. |last9=Maria |first9=Jon-Paul |last10=Hopkins |first10=Patrick E. |date=December 2018 |title=Charge-Induced Disorder Controls the Thermal Conductivity of Entropy-Stabilized Oxides |journal=Advanced Materials |language=en |volume=30 |issue=51 |pages=1805004 |doi=10.1002/adma.201805004 |issn=0935-9648 |pmc=9486463 |pmid=30368943|bibcode=2018AdM....3005004B }}{{Cite journal |last1=Gild |first1=Joshua |last2=Samiee |first2=Mojtaba |last3=Braun |first3=Jeffrey L. |last4=Harrington |first4=Tyler |last5=Vega |first5=Heidy |last6=Hopkins |first6=Patrick E. |last7=Vecchio |first7=Kenneth |last8=Luo |first8=Jian |date=2018-08-01 |title=High-entropy fluorite oxides |journal=Journal of the European Ceramic Society |language=en |volume=38 |issue=10 |pages=3578–3584 |doi=10.1016/j.jeurceramsoc.2018.04.010 |s2cid=103888713 |issn=0955-2219|doi-access=free }} The thermal conductivity of HEOs is usually greater than or comparable to the thermal conductivity of amorphous materials containing the same components. 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.

HEOs enhance functional property tunability through cation selection. Magnetic,{{Cite journal |last1=Johnstone |first1=Graham H. J. |last2=González-Rivas |first2=Mario U. |last3=Taddei |first3=Keith M. |last4=Sutarto |first4=Ronny |last5=Sawatzky |first5=George A. |last6=Green |first6=Robert J. |last7=Oudah |first7=Mohamed |last8=Hallas |first8=Alannah M. |date=2022-11-16 |title=Entropy Engineering and Tunable Magnetic Order in the Spinel High-Entropy Oxide |url=https://pubs.acs.org/doi/abs/10.1021/jacs.2c06768 |journal=Journal of the American Chemical Society |language=en |volume=144 |issue=45 |pages=20590–20600 |doi=10.1021/jacs.2c06768 |pmid=36321637 |arxiv=2211.15798 |bibcode=2022JAChS.14420590J |osti=1923148 |s2cid=253258048 |issn=0002-7863}}{{Cite journal |last1=Musicó |first1=Brianna |last2=Wright |first2=Quinton |last3=Ward |first3=T. Zac |last4=Grutter |first4=Alexander |last5=Arenholz |first5=Elke |last6=Gilbert |first6=Dustin |last7=Mandrus |first7=David |last8=Keppens |first8=Veerle |date=2019-10-21 |title=Tunable magnetic ordering through cation selection in entropic spinel oxides |url=http://dx.doi.org/10.1103/physrevmaterials.3.104416 |journal=Physical Review Materials |volume=3 |issue=10 |page=104416 |doi=10.1103/physrevmaterials.3.104416 |bibcode=2019PhRvM...3j4416M |osti=1606826 |s2cid=210803956 |issn=2475-9953}} catalytic,{{Cite journal |last1=Pan |first1=Yingtong |last2=Liu |first2=Ji-Xuan |last3=Tu |first3=Tian-Zhe |last4=Wang |first4=Wenzhong |last5=Zhang |first5=Guo-Jun |date=2023-01-01 |title=High-entropy oxides for catalysis: A diamond in the rough |url=https://www.sciencedirect.com/science/article/pii/S1385894722041407 |journal=Chemical Engineering Journal |language=en |volume=451 |pages=138659 |doi=10.1016/j.cej.2022.138659 |bibcode=2023ChEnJ.45138659P |s2cid=251658133 |issn=1385-8947|url-access=subscription }} and thermophysical{{Cite journal |last1=Luo |first1=Xuewei |last2=Huang |first2=Ruiqi |last3=Xu |first3=Chunhui |last4=Huang |first4=Shuo |last5=Hou |first5=Shuen |last6=Jin |first6=Hongyun |date=2022-12-10 |title=Designing high-entropy rare-earth zirconates with tunable thermophysical properties for thermal barrier coatings |url=https://www.sciencedirect.com/science/article/pii/S092583882203105X |journal=Journal of Alloys and Compounds |language=en |volume=926 |pages=166714 |doi=10.1016/j.jallcom.2022.166714 |s2cid=251455931 |issn=0925-8388|url-access=subscription }} 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.{{Cite journal |last1=Cao |first1=X. Q. |last2=Vassen |first2=R. |last3=Stoever |first3=D. |date=2004-01-01 |title=Ceramic materials for thermal barrier coatings |url=https://www.sciencedirect.com/science/article/pii/S0955221903001298 |journal=Journal of the European Ceramic Society |language=en |volume=24 |issue=1 |pages=1–10 |doi=10.1016/S0955-2219(03)00129-8 |issn=0955-2219|url-access=subscription }} Due to their innate tunability, HEOs have been proposed as candidates for advanced material applications such as thermal barrier coatings.

HEOs have shown significant potential as electrocatalysts for key energy conversion reactions, including the oxygen evolution reaction (OER) and the oxygen reduction reaction (ORR). HEOs have also shown promise as more abundant heterogenous catalysts for gaseous reactions such as carbon monoxide (CO) oxidation which is important in vehicle catalytic combustion. {{Cite journal |last=Riley |first=Christopher |last2=De La Riva |first2=Andrew |last3=Park |first3=James Eujin |last4=Percival |first4=Stephen J. |last5=Benavidez |first5=Angelica |last6=Coker |first6=Eric N. |last7=Aidun |first7=Ruby E. |last8=Paisley |first8=Elizabeth A. |last9=Datye |first9=Abhaya |last10=Chou |first10=Stanley S. |date=2021-02-24 |title=A High Entropy Oxide Designed to Catalyze CO Oxidation Without Precious Metals |url=https://pubs.acs.org/doi/10.1021/acsami.0c17446 |journal=ACS Applied Materials & Interfaces |volume=13 |issue=7 |pages=8120–8128 |doi=10.1021/acsami.0c17446 |issn=1944-8244|url-access=subscription }} The multiple cationic species in HEOs create a diverse range of active sites, improving catalytic efficiency and durability. Additionally, the high configurational entropy enhances phase stability, preventing material degradation under electrochemical conditions. These properties make HEOs attractive candidates for use in fuel cells and metal-air batteries.{{Cite journal |last1=Zi-Yu |first1=Liu |last2=Yu |first2=Liu |last3=Yujie |first3=Xu |last4=Hualiang |first4=Zhang |last5=Zongping |first5=Shao |last6=Zhenbin |first6=Wang |last7=Haisheng |first7=Chen |date=2023-05-06 |title=Novel high-entropy oxides for energy storage and conversion: From fundamentals to practical applications |url=https://www.sciencedirect.com/science/article/pii/S2468025723000614 |journal=Green Energy & Environment |language=en |volume=8 |issue=5 |pages=1341–1357 |doi=10.1016/j.gee.2023.04.007 |bibcode=2023GrEE....8.1341L |issn=2468-0257|doi-access=free }}

Due to their ability to accommodate multiple redox reactions, HEOs have been explored as electrode materials for supercapacitors. Their high surface area and tunable oxidation states contribute to improved capacitance and charge storage capabilities. Studies have demonstrated that HEO-based supercapacitors exhibit enhanced cycling stability compared to conventional transition metal oxides, making them suitable for high-power energy storage applications. For example, perovskite-type La(CoCrFeMnNiAl_x)_1/(5+x)O₃ {{Cite journal |last1=Meng |first1=Guo |last2=Yufeng |first2=Liu |last3=Fengnian |first3=Zhang |last4=Fuhao |first4=Cheng |last5=Chufei |first5=Cheng |last6=Yang |first6=Miao |last7=Feng |first7=Gao |last8=Jun |first8=Yu |date=2022-04-20 |title=Inactive Al3+ -doped La(CoCrFeMnNiAlx)1/(5+x)O3 high-entropy perovskite oxides as high performance supercapacitor electrodes |url=https://link.springer.com/article/10.1007/s40145-022-0568-4 |journal=Journal of Advanced Ceramics |language=en |volume=11 |issue=5 |pages=742–753 |doi=10.1007/s40145-022-0568-4 |issn=2226-4108|doi-access=free }} and La_0.7Bi_0.3Mn_0.4Fe_0.3Cu_0.3O₃ {{Cite journal |last1=Haoshan |first1=Nan |last2=Shuhui |first2=Lv |last3=Zijin |first3=Xu |last4=Yu |first4=Feng |last5=Yuxin |first5=Zhou |last6=Miao |first6=Liu |last7=Tianle |first7=Wang |last8=Xiaojuan |first8=Liu |date=2023-01-15 |title=Inducing the cocktail effect in yolk-shell high-entropy perovskite oxides using an electronic structural design for improved electrochemical applications |url=https://www.sciencedirect.com/science/article/pii/S1385894722049804 |journal=Chemical Engineering Journal |language=en |volume=452 |pages=139501 |doi=10.1016/j.cej.2022.139501 |bibcode=2023ChEnJ.45239501N |issn=1385-8947|url-access=subscription }} have been produced.

HEOs are being investigated as potential electrode materials for lithium-ion batteries (LIBs) and solid-state batteries due to their structural robustness and ability to facilitate ion transport. Their multi-element composition enables improved electronic conductivity and ionic diffusion, which are critical for high-performance battery electrodes. Additionally, HEOs exhibit enhanced resistance to phase transitions, addressing common issues such as capacity fading and poor cycle stability in conventional battery materials.

HEOs have been studied as potential electrode and electrolyte materials for solid oxide fuel cells (SOFCs). Their high entropy stabilizes oxygen vacancies, improving oxygen ion conductivity and electrochemical activity at lower operating temperatures. This could lead to more efficient and durable SOFCs, reducing the reliance on expensive rare-earth elements traditionally used in these systems.{{Cite journal |last1=Pikalova |first1=E. Y. |last2=Kalilina |first2=E. G. |last3=Pikalova |first3=N.S. |last4=Filonova |first4=E. A. |date=2022-12-08 |title=High-Entropy Materials in SOFC Technology: Theoretical Foundations for Their Creation, Features of Synthesis, and Recent Achievements. |journal=Materials |language=en |volume=15 |issue=24 |pages=8783 |doi=10.3390/ma15248783|doi-access=free |pmid=36556589 |pmc=9781791 |bibcode=2022Mate...15.8783P }}

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.{{Cite journal |last1=Brahlek |first1=Matthew |last2=Gazda |first2=Maria |last3=Keppens |first3=Veerle |last4=Mazza |first4=Alessandro R. |last5=McCormack |first5=Scott J. |last6=Mielewczyk-Gryń |first6=Aleksandra |last7=Musico |first7=Brianna |last8=Page |first8=Katharine |last9=Rost |first9=Christina M. |last10=Sinnott |first10=Susan B. |last11=Toher |first11=Cormac |last12=Ward |first12=Thomas Z. |last13=Yamamoto |first13=Ayako |date=2022-11-01 |title=What is in a name: Defining "high entropy" oxides |journal=APL Materials |volume=10 |issue=11 |pages=110902 |doi=10.1063/5.0122727|s2cid=251881696 |doi-access=free |arxiv=2208.12709 |bibcode=2022APLM...10k0902B }} However, it has been suggested that this is a misnomer, as most reports neglect to calculate configurational entropy. Additionally, a survey of 10 HEOs found that only 3 were entropy-stabilized.{{Cite journal |last1=Sarkar |first1=Abhishek |last2=Wang |first2=Qingsong |last3=Schiele |first3=Alexander |last4=Chellali |first4=Mohammed Reda |last5=Bhattacharya |first5=Subramshu S. |last6=Wang |first6=Di |last7=Brezesinski |first7=Torsten |last8=Hahn |first8=Horst |last9=Velasco |first9=Leonardo |last10=Breitung |first10=Ben |date=June 2019 |title=High-Entropy Oxides: Fundamental Aspects and Electrochemical Properties |journal=Advanced Materials |language=en |volume=31 |issue=26 |pages=1806236 |doi=10.1002/adma.201806236 |pmid=30838717 |s2cid=73472211 |issn=0935-9648|doi-access=free |bibcode=2019AdM....3106236S }} It has been suggested that the term HEO be replaced with three terms: compositionally complex oxide, high-entropy oxide, and entropy-stabilized oxide. 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.

• High-entropy alloy

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Category:Oxides