Electronegativity and entropy design of layered oxides for sodium-ion batteries

Domain: physics
Published: 2026-01-08
Editorial outcome: minor_revision

Abstract
Exploringsodium-ionlayeredoxideswithbroadcompositionaldiversityisan
importantapproachforthedevelopmentofhigh-performancepositiveelec-trodes.Structuralchemistrydeterminedbycompositionplaysadecisiverole
inperformanceimprovement,buttherelationshipbetweencompositionand
structurebecomesmoreelusiveincomplexmulti-componentsystems.Here
weproposeanelectronegativityentropyweightconcepttounderstand
entropy-dominatedphasesformation.Electronegativityandconfigurational
entropyareusedtoquantifykeyinteractionsinlayeredmaterials.Guidedby
thisunderstanding,wedesignasodium-deficientlayeredoxidewithanO3
stackingsequence.Thismaterialdemonstratesgoodstructuralandthermal
stability,alongwithairstability(negligibleperformancedegradationafterair
exposure),cyclingstability(93.02%capacityretentionafter200cycles),and
ratecapability(retaining69.1%capacityretentionfrom86.5mAg⁻¹to
1.73Ag⁻¹).Eveninpotassium-ionbatterieswithlargerinsertedions,the
materialstillexhibitscyclingstability.Thisstrategyprovidesvaluablecom-positionalguidancefortherationaldesignofhigh-performancelayeredoxide
materials.

Introduction
Sodium-ion batteries (SIBs) have shown significant potential as an promisingcandidatesowingtotheirhightheoreticalcapacities,tun-alternativetolithium-ionbatteries,especiallyforapplicationsinthe ableoperatingvoltage,andeaseofsynthesis6.MostNa TMO canbe
x 2
field of large-scale energy storage due to the abundance and cost classified into P2- and O3-type structures according to the local Na
advantage of sodium resources1,2. Many efforts have been made to coordinationenvironmentandtheoxygenstackingsequence,andthe
develophigh-performancepositiveelectrodematerialstowardrealiz- correspondingstructurediagramisdisplayedinSupplementaryFig.17.
inghigh-performanceSIBs3–5.Amongvariouspositiveelectrodes,the Generally,Na TMO withahighNacontent(x>0.80)tendstoforman
x 2
layered transition metal oxides Na TMO (TM refers to transition O3-typestructurewithnarrowoctahedralNa+sites,originatingfrom
x 2
metals, such as Ni, Co, Fe, Mn, etc.) are considered as one of the thestrongshieldingeffectofpositivelychargedNa+intheadjacent
TMO slabs8.Similarly,theP2structurewithopenprismaticpathsis entropyoxidematerialsisstillintheearlyexploratorystage.Adeeper
2
commonlyfoundinlowNacompoundsduetothedominantroleof understandingofthekeycompositionalfactorsinstructuralchemistry
electrostatic repulsive forces in low sodium systems9. Although the willhelpusmorerationallydesignhigh-performancematerials.

Results
The definition of electronegativity originates from the ability of an
atom to attract electrons, and the IEN concept is further proposed
based on the actual coordination environment of atoms. The IEN
valuesbasedonoxidationstates,spinstates,andcoordinatingcations
canbeusedtoqualitativelyassessthenatureandstrengthofchemical
bonds30.Paulingproposedthattheionicandcovalentcharacterofa
bondcanbeexpressedbythepercentageofioniccharacterinasingle
bond,whichisdeterminedbytheelectronegativitydifference(Δχ)of
the bonding atoms31. The greater the electronegativity difference
betweenthebondinganionandcation,thehigherthepercentageof
ionic bonding and the smallerthecovalentbondingpercentage32.The
typicalNa TMO layeredstructureconsistsofalternatelystackingof
x 2
edge-sharingTMO octahedralandNaionslayers(Fig.1a).IntheO−TM
2
−O−A−Oconfigurationofthelayeredoxide,oxygenatomsaresimul-
taneouslysubjectedtoCoulombicattractionfromthetransitionmetal
andalkalimetalinoppositedirections33.IntheTM−O−Astructure,a
higherIENvalueofTMleadstoreducedelectronegativitydifference
ΔχbetweenTMandO,whichenhancestheirorbitaloverlapandpro-
motes more covalent TM−O bonding with stronger binding and
shorterd distances.ThisstrengthenedTM−Ointeractioncon-
(O-TM-O)
currentlyweakenstheNa−ObondinginthesameTM−O−Aconfig-
uration, yielding more open AO structural arrangements with
expandedd spacing(Fig.1b).Differentialchargedensityanalysis
(O-A-O)
on multicomponent TM systems was performed to provide further
evidenceforthesignificantinfluenceofelectronegativityonelectronic
structure.AsshowninFig.1c(detailsinSupplementaryData1),TMs
withhigherelectronegativity(e.g.,Ni,Cu,Co,χ>1:8)exhibitgreater
chargeaccumulationalongTM−Obonds,indicatingstrongercovalent
character.Incontrast,TMswithlowerelectronegativity(e.g.,Mn,Ti,
χ<1:6)showmorechargetransfertooxygen,reflectingstrongerionic
characteristics.

This shift in electron density on TM−O and O−Na bonds is
essentiallyadelocalization/localizationphenomenonofelectronson
chemical bonds34. Moreover, the degree of disorder introduced by
high-entropy components also exerts a significant influence on the
stackingstructure.Thehighentropystrategyisusuallyintroducedto
construct highly disordered ion arrangements and consequently
delocalizedelectronicstructure.Thedisorderedionarrangementscan
promote delocalized electronic structures, which results in a wea-
kenedinteractionbetweenTMandO,andthusastrongerNa−Obonds
andacontractiveNalayerofO3structure.

In order to identify a quantitative indicator for the interlayer
interactionsinlayeredoxides,wedefinetheelectronegativityentropy
weighttoexpresstheweightsofelectronegativityandconfigurational
entropyinstructureformation:

Wχ= χ \times S config \times r TM
Cation R

Where χ QCation represents the cationic electronegativity index,
definedas χ = nA \times χ \times Δχ ; nA isthemolarratioofalkali
Cation nCation A TM nCation
tototalcations,whichservesasaquantitativedescriptorforattraction
O of alkali metal ions; χ represents the average electronegativity
A
difference between O and alkali metal in the AO layer. Since the
2
layeredoxidescrystallizewiththecoordinationnumberCN=6,theχ
i
value of IEN is chosen as the reference (Supplementary Fig. 2)35;
Δχ =χ -χ isthedifferenceinelectronegativitybetweenOand
TM O TM
theaverageχ ofTMions.Δχ isusedtoquantifytheionicdegreeof
i TM
bondformationbetweentr-ansitio-nmetalionsandoxygen,definedas
the bond polarity index. S config represents the absolute value of
configurationalentropy(SupplementaryEquation(2))36.r r T - A Mistheratio
oftheaverageradiusoftransitionmetaltoalkalimetalions.

By calculating the Wχ values of a series of reported low/high/
medium-entropyP2-/O3-typelayeredoxides(detailedinformationin
Supplementary Tables 2–4), we identified a clearlinearrelationship
between Wχ and Δχ values (Fig. 1d). Further data examination
TM
revealedthatthereisacleardistinctioninWχvaluesamongdifferent
stackingstructures.Spearman’srankcorrelation coefficient(Fig.1e)
revealsastrongpositivecorrelationbetweenWχandtheO3structure.
ComponentswithhigherWχvaluesaremoreinclinedtoformtheO3
phase,whereasthosewithlowerWχvaluesfavortheformationofthe
P2 phase. We further performed a comprehensive analysis of basic
operationsinvolvingthefeaturevariablesintheformulabyintegrating
machine learning techniques. Among the 5488 combinations
obtained,thecurrentformulademonstratesaprominentcorrelation
of 0.8182 (Fig. 1f). Notably, the analyzed data also include P2-type
layeredoxideswithananomaloushighsodiumcontent,indicatingthat
thesodiumconcentrationisnotthesoledeterminantofthestacking
structure. These findings reveal the critical role of the Wχ value in
describingtheinterlayerinteractionsandtheNa+coordinationenvir-
onment of multicomponent materials. The high Wχ values are gen-
erallyassociatedwithhighprobabilitiesofO-typestructureformation,
andviceversa.TheclosecorrelationbetweenWχandstructurepro-
vides a theoretical direction for designing advanced materials. To
furtherelucidatetheroleofconfigurationalentropy,machinelearning
approacheswereemployedforanalysis.Theinfluenceofentropyon
structural properties was found to be negligible in systems where
jS config j<1. However, as jS config j≥1, its effect becomes increasingly
apparent,exertinganotableimpactontheresultingstructure(Sup-
plementaryFig.3).WefurtherinvestigatedtheinfluencesofΔχ and
TM
jS config jonWχtogainadeeperunderstandingoftheirimpactsonthe
evolutionofstackingstructures.

Basedontheaboveunderstanding,wedesignaspecificmaterial
withO3stackingstructurebutwithtraditionalP-typesodiumcontent
byadjustingS config andΔχ TM (Fig.2a).Firstly,theimpactofconfig-
urationalentropyisquantitativelyanalyzed.Wechosesixelements(Ni,
Mn,Cu,Co,Fe,andTi)toformtheTMcomponentsaccordingtothe
followingcriteria(SupplementaryTable5):a)theselectedTMoxide
precursors have different crystal structure and space group, which
preventstheobtainedsystemfromformingtheprecursorconfigura-
tionbutinsteadformingalayeredstructuredifferentfromtheoxide
precursor37.b)Theelementspresentdistinguishedvalancestatesand
electronic structures in the multicomponentsystem,thuspromoting
therealizationofhighentropyproperties.c)Thesimilarionicradius
facilitates an easier complete miscibility in a single phase. A high
temperature up to 950°Cis set in order to highlight the impactof
S config . Based on the common oxide with Ni and Mn component
Na 0.67 Ni 0.33 Mn 0.67 O 2 (abbreviated as N=2), we gradually added Cu,
Co,Fe,andTiintothetransitionmetallayer(abbreviatedasN=3,4,5,
6)andcharacterizedtheevolutionofcrystalstructures.Asshownin
Fig. 2b, the (002) diffraction peak of P2 phase generallyshifts to a
higherangleastheincreaseoftransitionmetalspecies,reflectingthe
contractionoftheunitcellalongthec-axis.ThepeaksfromtheO3
phaseappearwhentheTMspeciesisincreasedto5(Supplementary
Fig.4),andthematerialwith6TMspeciesshowsapureO3structure.
ThejS joftheactualsynthesizedsystems(N=2,3,4,5,6inFig.2c)
config
are1.05R,1.21R,1.42R,1.60R,and1.74R,respectively.Accordingto
the refined crystallographic data summarized in Supplementary
Tables 6–10, the components of the P2 phase gradually decrease,
accompaniedbytheincreaseoftheO3phasewiththeS config increase,
andfinallythepureO3phaseisobtained.AcomparisonofthePDOSof
the O 2p orbitals in the multi-component and mono-TM systems
(Fig.2dandSupplementaryFig.5)furthershowsbroaderbandwidths
in multi-component TM systems, signifying greater global electron
delocalization. These results establish that the high-entropy multi-
componentsystemmakesthestructuremoredelocalizedinthestate
of disordered ion arrangement. Modulating configuration entropy
enablestheregulationofelectrondelocalization/localization,thereby
directingthestructuralevolutionoflayeredoxides.Wefurtherstudy
the effect of entropy in structural configuration by regulating the
synthesis temperature. The powder sample N=6 with a pure
O3structurewasreheatedat750°C,andtheimpurityphaseappeared
(SupplementaryFig.6).Theenthalpy(ΔH=TΔS)drivenphasesegre-
gationoccurs at a lower temperature, which proves that configura-
tionalentropyplaysadecisiveroleinthesolidsolutionphasestructure
at high-temperature synthesis conditions. We further confirm the
effectofahighentropystrategytodesignananomalousconfiguration
byincreasingtheTMspeciesNfrom6to8(SupplementaryFig.7).

Wefurtherdemonstratetheinfluenceoftransitionmetalcations
onphasestructureformation.IntheN=6systemwithoneoftheTM
components removed (abbreviated as No TM in Fig. 2e, f and Sup-
plementaryTables11–15),nosolidsolutionO3phasecanbesynthe-
sized for jS j below 1.74R. It is noteworthy that materials with
config
similarvaluesofjS j(1.60Rand1.61R)canexhibitdifferentP/O
config
compositephasestructures,indicatinganotherkeyfactor,inaddition
toconfigurationalentropy,affectsthestackingstructure.

Based on the understanding, we design an anomalous
O3 structure with at a low Na content of 0.538 (designated as
Na 0.538 Ni 0.18 Cu 0.18 Fe 0.15 Co 0.15 Mn 0.17 Ti 0.17 O 2 (O3-Na0.538) in Supple-
mentaryFig.8)bymaintainingWχ valueabovethiscriticalthreshold.
Inductivelycoupledplasma-opticalemissionspectroscopy(ICP-OES)
analysis of O3-Na0.538 confirmed the Na content (Supplementary
Table16),arelativelylowvalueforO3-typematerials.Inaddition,we
synthesizedmoremedium-andhigh-entropymaterialstoexplorethe
factorsinfluencingthestructure(SupplementaryFig.9).Wecalculated
theWχvaluesforaseriesofmaterialsbasedonEq.(1)andcompared
them with Δχ as presented in Fig. 2g and Supplemen-
TM
taryTables17–18.ThereisapositivecorrelationobservedbetweenWχ
andΔχ TM .ItisworthnotingthatthecomponentwithaWχintherange
of0.58–0.71oftenexhibitsamixedP/Ophase,andslightvariationsin
synthesis conditions can significantly affect phase stability. These
findingsunderscorethattheS config andΔχ TM playingacriticaland
synergisticroleindeterminingthestackingstructureoftheentropy-
drivenmaterials.

High entropy O3-Na0.67 is synthesized by a simple solid-state
reactionasastudiedobjectandcomparedwithcommonP2materials
withanormalNacontentof0.67.SupplementaryTable19displaysthe
ICP-OESresultofO3-Na0.67,consistentwithourinitialdesigncom-
positions. The X-ray powder diffractometer (XRD) pattern of O3-
Na0.67isfullyindexedtotheO3-typelayerstructurewithaR3m space
group(Fig.3a)38.TheRietveldrefinementresultsfurtherindicateits
common O3-structure lattice parameters of a=b=2.955Å,
c=16.335Å,and1.555ofd /d value.Alldiffractionpeaks
(O-Na-O) (O-TM-O)
are well-fitted with a structural model in which six transition metal
components are randomly distributed in the TMO slabs. No sig-
2
nificantcharacteristicsuperstructurepeakcanbeobserved,originat-
ing from the high entropy component breaking the ordering
distribution in the AB-plane. The transmission electron microscope
(TEM)image(Fig.3b)alsodemonstratesthelayeredstructurewitha
latticeplanedistanceof0.546nm,correspondingtothe(003)planeof
theO3phase.Thescanningelectronmicroscope(SEM)imageinFig.3c
showsthebulksampleswithaparticlesizerangefrom3to5μm.The
uniformdistributionofvariouselementsisdemonstratedbyenergy
dispersivespectroscopy(EDS)mapping(Fig.3d).TheextendedX-ray
absorption fine structure spectra (EXAFS) in Fig. 3e provide more
informationonthelocalcoordinationstructure,andthecorrespond-
ing refined bond lengths of TM–O and TM–TM are summarized in
SupplementaryTable20.ThefirstshellofMn–Obondlengthisabout
1.91Å,whiletheotherbondlengthsarehigherthan1.95Å.Thebond
length between the transition metal and oxygen is susceptible to
valencestatethehigherthevalencestatetheshorterthebondlength.
The second shell TM–TM bond lengths are almost the same for all
elements, which means thatthe transition metal ions are randomly
distributed in TMO with a disordered arrangement39,40. The homo-
2
geneous distribution of metal ions results in a more homogeneous
redox reaction and reduces the heterogeneity of the composition,
resultinginlowerstressesandbetterinterparticlestability.

Theeffectoftherandomdistributionoftransitionmetalionson
theelectrochemicalperformancewasalsoexaminedbygalvanostatic
charge/discharge (GCD) tests in Na half-cells. The unmodified P2-
Na 0.67 Ni 0.33 Mn 0.67 O 2 (P2-Na0.67) with low entropy component and
traditionalP2structureisselectedtobethecontrolgroup.Fromthe
XRDpatternsinSupplementaryFig.10,P2-Na0.67containsobvious
Na+/vacancyorderinginalkalimetallayers,indicatedfromthesuper-
latticepeaksat27.2°and28.4°41.Thesuperlatticecharacteristicisin
stark contrast to the highly disordering of high-entropy system
discussed above. O3-Na0.67 also shows unusual electrochemical
behaviorsbenefited from the different structurefeatures. Figure 4a
displaystheGCDcurveofthefirstcycletestedatacurrentdensityof
86.5mAg−1(1C=173mAhg−1)inthevoltagerangeof2.0–4.0V.
Four improvements of O3-Na0.67 are observed, firstly, 107.7% of initial
Coulombicefficiencyisachievedinsteadofthecommon~80%inlow
O3
Nacontentsystems,whichisanimportantindicatorforthematerial
practicality42–45.Secondly,O3-Na0.67displaysasmoothercharge/dis-

chargecurveabove3.3V,indicatingasolid-solutionbehaviorwithout
Na+/vacancysuperlatticerearrangement,whichisdifferentfromthe
multipleplateausoftraditionalO3orP2materials.Thirdly,O3-Na0.67
affords a better rate performance originating from the highly dis-
orderingstructure.AsshowninFig.4b,O3-Na0.67candeliverahigh-
capacityretentionof84.2%and69.1%evencycledat865mAg−1and
1.73Ag−1. Lastly, a good cycling stability is obtained with 93.02%
capacityretentionafter200cyclesat86.5mAg−1,whichiscompetitive
intheconventionalO3materialswithmultiphasetransition(Supple-
mentaryTable21).Moreover,theO3-Na0.67cancyclefor837times
with70%capacityretention(Fig.4c),andO3-Na0.538demonstrated
goodrateandcycleperformance(SupplementaryFig.11).

TheinsituXRDmeasurementsduringthefirstelectrochemical
cyclewereexecutedat17.3mAg−1withinavoltagerangeof2.0−4.0V
toexplorethestructureevolutionuponde-/sodiation(Supplementary
Fig.12).Figure4disthecontourmapsofthemaindiffractionpeaks
evolution and corresponding electrochemical curves. When Na+ is
beingextractedfromthecrystalstructure,the(003)peakoftheO3
phasegraduallymovestoaloweranglewithouttheappearanceofany
newpeaks,indicatingasolidsolutionreactionwiththec-axisexpan-
sion. Upon further charging, the electrochemical curve exhibits a
plateauatapproximately3.0V,correspondingtotheformationofthe
O'3phaseandanO–Ptwo-phaseregion.Thisphasetransitionisevi-
dencedbyareductionintheintensityandsplittingofthe(104) peak
andaccompaniedbytheemergenceofP3phasediffractionpeaks46.
AfterthecompletedisappearanceoftheOphase,materialcontinues
tobedesodiatedwithP3structureuntilchargedto4.0V,consistent
withasolidsolutionreactionoftheslopingregionabove3.0V.Upon
thedischargingprocess,theXRDpatternsundergoanoppositeevo-
lution,indicatingthehighreversibilityoftheO−Pphasetransition.We
furtheranalyzedthevariationoflatticeparametersandvolumeofO3-
Na0.67alongwithNaextraction/insertion.AsFig.4eshown,thelattice
parametersa,candvolumeVchangeby2.47%,3.44%and1.74%upon
chargedto4.0V,respectively.Whendischargedto2.0V,thea,candV
valuesonlyvariedby0.088%,0.154%and0.021%relativetotheori-
ginalstructure.Thematerialundergoesonlyonerapidphasetransi-
tionofO−Pthroughoutthechargingprocess,andtheP3phasewitha
largediffusionchannelexistsinahigh-capacityrangeofupto86.35%
(Fig.4f),whichresultsinsmallvolumechangesandgoodstructure
stabilityandrateperformance.Thegalvanostaticintermittenttitration
technique (GITT) measurements were performed to obtain more
insightintoNa+transportduringcharge/discharge.O3-Na0.67main-
tainsaNa+diffusioncoefficient(D )of8.2×10−12to1×10−11cm2s−1
Na+
throughout the plateau, and sloping regions of the charging curve
(SupplementaryFig.13).ThegentlefluctuationofD impliesthatthe
Na+
O-P phase transition is mild, which is different from traditional O3
materials.Besides,cyclicvoltammetry(CV)testswerecarriedoutata
scanningrateof0.1mVs−1inthevoltagerangeof2.0–4.0V(Fig.4g).It
canbeseenthatthefirstcycleofO3-Na0.67onlyshowsapairofmain
redox peaks assigned to O3–P3 phase transition at 2.6/3.1V. Com-
paratively,thetraditionalP2-Na0.67electrodewith0.67Nacontent
displaysthreepairsofadditionalpeaksat3.35/3.25,3.65/3.55and3.70/
3.63V(SupplementaryFig.14),whichrepresentNa+/vacancyrearran-
gement in the Na layer upon de/sodiation. The disruption of Na+/
vacancyorderoriginatesfromtheionicdisorderdistributionofthe
transitionmetallayerinthehighentropysystem,andthusfacilitates
efficientandreversibleNa+de/intercalation(SupplementaryFig.15).
Theseriesofcharacterizationconfirmstheanomalousstructurecan
effectivelysuppresstheNa+/vacancyrearrangement,exhibitsastable
electrochemicalbehaviorandgoodelectrochemicalproperties.

Theredoxmechanismoftransitionmetalsisfurthercorroborated
by ex situ XAS and XPS results over the electrochemical process.
Supplementary Fig. 16 presents the X-ray absorption near-edge
structure(XANES)spectraatNi,Fe,Co,andMnK-edges.Thespectra
oftheseelementsallexhibitanobviousshifttowardsthehigherenergy
regionatchargingandsubsequentlymovebackwardupondischarging
to2.0V,highlightingitsmulti-redoxcenterscharacteristic47,48.
Analysis of XPS spectroscopy evolution in Supplementary
Figs.17–18furtherconfirmstheactiveredoxcentersintheformsof
Ni2+/3+,Co2+/3+,Fe3+/4+,andMn3+/4+.Comparatively,nosignificantspectra
shift is observed for Cu and Ti throughout the charging and
discharging cycle (Supplementary Figs. 19–20), suggesting electro-
chemicallyinactivityandthestructuralpillarroleofCu2+andTi4+49.The
bindingenergyofallelementsreturnstotheoriginalpositionsatthe
discharging state,indicating the high reversibilityof the redox pro-
cess.Thecombinationcharacteristicsofmultipleredoxcenters,high
redoxreversibility,anddualpillarionpromisegoodcyclicstability.

Further tests, including structural stability, air/water stability,
thermal stability, potassium-ion battery and full cell performance,
wereperformedtoevaluatethepracticalapplicationcapabilityofthe
O3-Na0.67 materials. After 100 cycles at86.5mAg−1, the O3-Na0.67
positive electrode was characterized by XRD, and the pattern was
comparedwithuncycledmaterialtoinvestigatethestructuralinteg-
rity.Althoughthediffractionpeaksofcycledpositiveelectrodeslightly
shifttothehigherangles,thestructurestillretainsaclearO3phase
withoutanyadditionalphase,indicatinggoodstructuralreversibility
duringrepeatedNa+de-intercalation(Fig.5a).Totesttheairstability,
theas-preparedsamplewasagedinaboxwithacontrolledrelative
humidityof60%for18hours(Exp18h)orsoakedindeionizedwater
for12h(Water12h).Figure5bdisplaysthecomparisonofXRDresults
ofas-preparedandagedmaterials.AllthreesamplesshowapureO3-
typephasewithoutanynewpeak.Furthermore,airexposurehasvir-
tually no effect on electrochemical performance (Supplementary
Fig.21).Waterimmersiondoesnotleadtosignificantlydecayedelec-
trochemicalproperty(SupplementaryTable22)andonlyreducesthe
capacity by 5mAhg−1, and the cycling stability of soaked sample is
evenimproved(Fig.5c).ToeliminatetheeffectofCuelementonthe
stability of air and water, the Cu-free low-sodium O3 material we
synthesizedalsodemonstratedanequallycomparablestability(Sup-
plementaryFig.22).Adifferentialscanningcalorimetry(DSC)testwas
conductedona4.0Vchargedsampletoevaluateitsthermalstability.
Thethermalbehaviorofthepositiveelectrodeshowsanonsettem-
perature consistentwith typicallayeredoxides,while the measured
heatgenerationof208.2Jg⁻¹isreduced(Fig.5d)50.Inaddition,the
strategyalsopresentsanopportunityforpotassium-ionbatteriesde/
inserting larger charge carrier ions (Fig. 5e). Figure 5f and Supple-
mentary Fig. 23 show the electrochemical performance of K||O3-
Na0.67cellsinavoltagerangeof1.5–3.9Vat86.5mAg−1.Duetothe
obviouselectrostaticrepulsionbetweenpotassiumions,K+generally
tendstooccupyalargerprismaticpositionratherthananoctahedral
space. Consequently, the synthesis of O-type K 1−x TMO 2 layered
structuresposessignificantchallenges.O3-KCrO istheonlyelectro-
2
chemically active O-type K-ion layered oxide and exhibits multi-
platformelectrochemicalcurvesandpoorcyclingstabilityduringde/
potassiation51,52.ThepositiveelectrodeshowcasessmoothGCDpro-
filesandagoodcyclingstabilityof70.24%capacityretentionafter100
cycles.Afull cell with O3-Na0.67 asthe positive electrode and hard
carbon (HC) as the negative electrode wasassembled to assessthe
practicalapplicationpotential.Thecellcanshowaninitialreversible
specificcapacityof115.22mAhg−1andaninitialcoulombicefficiency
of 83.5%cycled within 1.0–4.0V at17.3mAg−1 (Fig. 5g), this perfor-
manceiscompetitiveamongrecentlyreportedlayeredoxidecathodes
withNacontentof0.67(SupplementaryTable23).Under cycledat
86.5mAg−1,thebatterymaintainsagoodcapacityretentionof83.28%
after150cycles(Fig.5h,i),indicatingthepracticalityofthematerial.

DFTcalculationswerecarriedouttogainadeeperunderstanding
ofthestructuralevolutionandhighstability(Theatomiccoordinates
oftheoptimizedstructuresareprovidedinSupplementaryData1).In
themono-TMsystems,thetransitionmetalexhibitsamixedvalence
stateof+3/+4.Giventhelackofreportedstableelectronicconfig-
urations for Cu and Ti within a layered oxide structure, mono-TM
configurations of other elements (Mn, Co, Fe, and Ni) are used for
calculation comparison. The formation energy calculations for
Na TMO configurationindicatethattypicalmono-TMcompounds
0.67 2
exhibittheP2phasewithpositiveE −E energy,whereasthehigh-
O3 P2
entropy material still maintains the thermodynamically stable O3
phaseat0.67ofNacontent(Fig.6a),consistentwiththeaforemen-
tioned XRD observations. The structural inversion is primarily
attributed to the configurational anisotropy of the transition metal
layers within the high-entropy system, as shown in the electronic
localizationfunction(ELF)calculationresultsinFig.6band Supple-
mentary Fig. 24. The disordered ion arrangement originates from
diverse transition metal ion components. By reducing the average
ionicelectronegativityoftransitionmetals,wecanenhancetheioni-
cityofTM−O,increasethebondlength,andalleviatethelatticedis-
tortioncausedbythelocaldistortionofionsduetotheJahn-Teller
effect.Thecalculatedpartialdensityofstates(PDOS)inFig.6cfurther
substantiates the multiple redox centers feature in high-entropy
material upon the desodiation process from Na TMO to
0.67 2
Na TMO .Thevastmajorityoftransitionmetalelements,namelyNi,
0.33 2
Co,Cu,Fe,andMn,areactivelyinvolvedinchargecompensation,as
evidencedbytheelectronicstatevariation.ThePDOSchangeforCuis
relativelyinsignificant,andthusitsredoxbehaviorcannotbeobserved
intheexperimentalspectrum.Incontrast,Tiservesasaninactivepillar
elementtoimprovestructuralstability,primarilybecausetheTi3dt
2g
level locatedatrelativelylowerenergyandfarfromtheFermilevelis
less likely to participate in redox reactions53. We also compare the
bond length variations of elements upon desodiation in multi-
component and corresponding mono-TM systems, as illustrated in
Fig.6d.Forsingle-componentmaterials,redoxcentersuniformlydis-
tribute throughout the crystal lattice and undergo more consistent
localstructuralvariationduringchargecompensation,whichreadily
leads to substantial structural alterations. Comparatively, the coex-
istence of 6 TMs in high-entropy materials forms multi-level redox
centers.Thesecenterspreventexcessiveaccumulationoflocalchar-
gesthroughstep-basedredoxreactions,avoidphasetransitionstress
causedbyintensevoltagejumpsofsingleelements,andenhancethe
stabilityofthestructureduringcharginganddischarging.Benefiting
from the combined effects of structural anisotropy, multiple redox
centers, and pillar elements, the local structural changes in high-
entropy systems are considerably minimized, contributing a good
long-termcyclingstability.

Methods
Materialsynthesis
Na Ni Mn O (N=2, P2-Na0.67), Na Ni Cu Mn O (N=3),
0.67 0.33 0.67 2 0.67 0.18 0.18 0.64 2
Na Ni Cu Co Mn O (N=4), Na Ni Cu Co Fe Mn O (N=5),
0.67 0.18 0.18 0.15 0.49 2 0.67 0.18 0.18 0.15 0.15 0.34 2
Na Ni Cu Co Fe Mn Ti O (N=6,O3-Na0.67),Na Ni Cu Co Fe Mn Ti
0.67 0.18 0.18 0.15 0.15 0.17 0.17 2 0.538 0.18 0.18 0.15 0.15 0.17 0.17
O (O3-Na0.538), NaNi Cu Co Fe Mn Ti O (O3-Na1), Na Cu Co Fe Mn
2 0.18 0.18 0.15 0.15 0.17 0.17 2 0.67 0.18 0.15 0.15 0.35 0.17
Ti O (No Ni), Na Ni Co Fe Mn Ti O (NoCu),Na Ni Cu Fe Mn Ti O
2 0.67 0.18 0.15 0.15 0.35 0.17 2 0.67 0.18 0.18 0.15 0.32 0.17 2
(NoCo),Na Ni Cu Co Fe Mn Ti O (No Fe), Na Ni Cu Co Fe Mn O
0.67 0.18 0.18 0.15 0.32 0.17 2 0.67 0.18 0.18 0.15 0.15 0.34 2
(No Ti), Na Ni Cu Co Fe Ti O (No Mn), Na Ni Cu Mg Fe Mn Ti O
0.67 0.18 0.18 0.15 0.15 0.34 2 0.67 0.18 0.18 0.12 0.1 0.22 0.2 2
(N=6), Na Ni Cu Fe Co Mn Ti Sn O (N=7), Na Cu Mg Fe Co Mn Ti Sn
1 0.67 0.18 0.18 0.15 0.15 0.15 0.15 0.14 0.1 0.1 2 0.67 0.15 0.15 0.15 0.15 0.1 0.1 0.2
O (N=7), Na Ni Zn Mg Fe Co Al Mn Ti O (N=8)andmaterialsof
2 1 0.67 0.12 0.12 0.12 0.1 0.1 0.1 0.24 0.1 2
supplementaryinformationweresynthesizedthroughatypicalsolid-
state method from stoichiometric amounts of Na CO (5mol% excess,
2 3
99.5%, Aladdin), Li CO (99%, Aladdin), K CO (99%, Aladdin), NiO
2 3 2 3
(98%, Sinopharm Chemical ReagentCo.,Ltd),MnO (98%,Aladdin),
2
CuO(99.9%,Aladdin),Co O (99.9%,Aladdin),Fe O (99.9%,Aladdin),
3 4 2 3
SnO (99.5%,Aladdin),MgO (98.0%,Aladdin)andTiO (99.99%,
2 2
Aladdin).Thepowderwaspressedintopelletsunder16MPaand
heatedto950°Catarateof5°Cperminute,andcalcinedinairfor12h
(BTF-1200C-4D-4M,AnhuiBeyike EquipmentTechnologyCo,Ltd).
ThesamplestransfertothegloveboxfilledwithArimmediatelyafter
preparation(H OandO <0.1ppm).
2 2

Hydrationtests
Theexposed samples wereobtained byplacing fresh materials in a
constant temperature and constant humidity box with a controlled
relativehumidity(RH)valueof40%under25°Cintheair.Theaccurate
RHisdeterminedaccuracy±1%.Theexposedsampleswereobtained
bysoakingfreshsamplesindeionizedwaterfor12handthendriedina
vacuumdryingovenat80°Cfor12h.

Materialscharacterization
TheXRDdatawereacquiredbyaPerseeinstrumentwithCuKαradia-
tion (λ=1.5406Å) of Rigaku Ultima IV diffractometer. The residual
species in the samples was identified by TGA (NETZSCH STA 449F5)
underanAratmosphere.Surfaceinformationonmaterialswascollected
byXPS(ESCALAB250Xispectrometer,ThermoFisherScientific)withan
Al Ka achromatic X-ray source. Microstructural information was
obtained byscanning electron microscopy (TESCANMIRALMS), and
HRTEMimagewereobtainedbyTEM(JEM2100F).TheEDSmapping
wereobtainedbyTEM(FEITalosF200XG2).Theelementalcomposition
ofthematerialswasanalysedthroughaninductivelycoupledplasma
opticalemissionspectrometer(ThermoFisher,ICP-OES).X-rayabsorp-
tionfinestructure(XAFS)spectroscopywascarriedoutusingtheRapid
XAFS 2M (Anhui Absorption Spectroscopy Analysis Instrument Co.,
Ltd.)byfluorescencemodeat20kVand30mA(or10kVand20mA),
andtheSi(533)sphericallybentcrystalanalyzerwitharadiusofcur-
vatureof500mmwasusedforCo,theSi(553)sphericallybentcrystal
analyzerwitharadiusofcurvatureof500mmwasusedforCu,theSi
(531) spherically bent crystal analyzer with a radius of curvature of
500mmwasusedforFe,theSi(440)sphericallybentcrystalanalyzer
witharadiusofcurvatureof500mmwasusedforMn.

Electrochemicalmeasurements
Coincells(CR2032)wereassembledinanargon-filledglovebox(H O
2
andO <0.1ppm)foralltheelectrochemicaltests.Allelectrochemical
2
testswereconductedinsideatemperature-controlledclimaticcham-
ber maintained at 27±1°C with convection heating, in ambient air
atmosphere.Thespecificcurrent(Ag⁻¹/mAg⁻¹)andspecificcapacity
(mAhg⁻¹)valuesreportedthroughoutthisworkarecalculatedbased
onthemassoftheactivematerialaloneinthepositiveelectrode.The
workingelectrodewaspreparedbygrindinginamortarwithauniform
mixtureofactivematerial(80wt.%),polyvinylidenedifluoride(PVDF)
(10wt.%) and Super P carbon (10wt.%) with N-methyl-pyrrolidone
(NMP,≥99.5%,Aladdin)asdispersionsolvent.Theslurrywascoatedto
thesurfaceofaluminumfoilbydoctorbladeinacontrolledenviron-
mentwithRH<30%andusedvacuumdryingovenat80°Cfor12h.
Thearealloadingoftheactivematerialwasabout2.0−3.5mgcm−2.The
electrodeswerecutintocirculardiscswithadiameterof10mmbyan
MTIslicingmachine(MSK-T10).Thevariouselectrochemicalproper-
ties of the electrodes were tested by assembling CR2032 by using
sodium and potassium pieces as the negative electrode. Sodium
(≥99.7%, Aladdin) and potassium (≥99 %, Aladdin) ingots stored in
kerosene were first cleared of surface oxidation using a knife. The
cleaned metals were rolled into thin sheets (<1mm thick) using a
stainless steelrodandcutinto10mmdiameter circularpieces.For
sodium-ionhalf-cells,theelectrolyteis1MNaClO (5%byvolumeof
4
fluoroethylene carbonate (FEC)dissolved in propylene carbonate
(supplier DoDoChem), and separator using by porous glass fiber
(Whatman, Grade GF/C, No.1822-047) to isolate the direct contact
between positive and negative electrodes. Charge–discharge mea-
surementswereperformedinavoltagerangeof2.0−4.0V(versusNa|
Na+)at86.5mAg-1after6hofrelaxationonaLAND(Wuhan,China)
batterytestsystem.FortheKionhalf-cell,theelectrolytesolutionused
inthisstudywas0.8MKPF inethylenecarbonate/diethylcarbonate
6
(1:1byvolume,supplierDoDoChem).Atypicalgalvanostaticcharge-
dischargetestwasperformedinthevoltagerangeof1.5–3.9V(versus
K|K+)forthehalf-cell.Thehardcarbonnegativeelectrodewaspre-
pared by grinding in a mortar with a uniform mixture of the hard
carbon(Kuraray,80wt.%),Super-Pcarbonblack(10wt.%)andpoly-
acrylic acid (dissolved in water, 10wt.%). The resultant slurry was
uniformlypastedontoCufoilusingthedoctorblademethodandthen
carefullydriedat110°Cfor12hundervacuum.Theelectrodeswere
cut into circular discs with a diameter of 12mm by an MTI slicing
machine(MSK-T10).Thearealloadingoftheactivematerialwasabout
1.4−2.5mgcm−2.Toremoveirreversiblecapacityinthefirstcycle,the
hardcarbonnegativeelectrodewasrecycledinthevoltagerangeof
0.01–2.0Vforthreecyclesbeforethefullcellwasfabricated.Fullcell
balancewasachievedbymaintainingthecapacityratioofthenegative
electrodetothepositiveelectrode(N/Pratio)at1.2:1.CVexperiments
wereperformedwithinthesamepotentialrangeat0.1mVs−1.CVwas
carried out on an Autolab electrochemical workstation in a voltage
rangeof2.0–4.0V.Foreachtypeofelectrochemicalexperiment,at
leastthreeindependentcoincellswerefabricatedandtestedtoensure
the reproducibility of the results. The charge-discharge curves and
performancedatapresentedinthemaintextfiguresarefromasingle,
representativecellthatexhibitedperformanceclosesttotheaverage
ofalltestedcells.TheCoulombicefficiency(CE)foreachcyclewas
calculatedastheratioofthedischargecapacitytothechargecapacity
intheprecedingchargecycle.

TheGITTtestwerecarriedoutonaLandCT2001Abatterytest
system(Land,Wuhan,China)byCR2032.IntheGITTtest,thebattery
wascharged/dischargeatacurrentdensityof8.65mAg−1for15min
andrelaxedfor4h,andtheabovestepswererepeatedtoreach4.0/
2.0V.Thevoltagedatawererecordedatasamplingrateof1pointper
20s.Thedetailedcalculationformulaisasfollows:

D Na+ = π 4 τ nV S m 2 Δ Δ E E s 2

Thisformulaisapplicablewhentheworkingcurrentisverysmall.
The τ represents relaxation time; The n represents moles number of
electrodeactivematerial;TheV representsthemolarvolumeofthe
m
electrodematerial;TheΔE representsthecurrentcharging/discharging
t
voltagevariety.TheΔE representsthevoltagechangecausedbythe
s
pulse;TheSrepresentsthecontactareaoftheelectrode/electrolyte.

InsituXRDdiffractionmeasurement
The in situ XRD measurements were performed using an opening
windowcelltoallowtheX-raytocollectthepositivesignalontheAl
foilcollector.TheO3-Na0.67positiveelectrodeandsodiumnegative
electrode were prepared as described in the ‘Electrochemical Mea-
surements’section.Theelectrolytewas1MNaClO₄inPCwith5%FEC.
Aglassfiberseparator(Whatman,GradeGF/C,No.1822-047)wasused.
ThecellwasassembledinanAr-filledglovebox(H₂O/O₂<0.1ppm).

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This work proposes the concept of effective electronegativity entropy weights to understand entropy-dominated phase structure formation. I remain skeptical of the theory the authors proposed. As the electronegativity of the transition metal (TM) increases, the overlap between TM and O orbitals becomes stronger, leading to a shorter dO–TM–O distance. Therefore, we believe that introducing highly electronegative TMs may not effectively increase the dO–TM–O/dO–A–O ratio. Moreover, the use of this ratio as an indicator for the structural preference between P2 and O3 phases is most appropriate for standard Na-layered oxides (such as P2–Na0.67 or O3–Na1). Recent studies have demonstrated that in layered compositions with nonstoichiometric Na contents, the dO–TM–O/dO–A–O ratio is no longer a reliable criterion for distinguishing between P2 and O3-type materials. Together with following concerns, I would not recommend the publication of this manuscript on Nature Communications.\n1. We remain skeptical about the N=6 portion of the data in Fig2e, it is implausible that dO-Na-O/ dO-TM-O= 1.264 was obtained at such a low Na content.\n2. In Fig. 2c, the peak at 2θ = 50° for the sample with N = 5 is not labeled. It does not correspond to either the P2 or O3 phase, indicating that the diffraction pattern is not composed solely of P2 and O3 phases.\n3. In Fig. 3c, are the fine surface particles observed in the SEM image residual Na₂CO₃ formed from alkali precipitation?\n4. In Fig. 4d, it is evident that during the initial stage of charging, the O3 phase first transforms into the O'3 phase, followed by a subsequent transition to the P3 phase.\n5. In Fig. 4f, the x-axis labeling appears to be incorrect, and both the charge and discharge capacities should be significantly higher than 83 mAh g⁻¹.\n6. Based on the initial oxidation states obtained from the XPS fitting in Fig. 5, the composition Na₀.₆₇Ni₀.₁₈Cu₀.₁₈Fe₀.₁₅Co₀.₁₅Mn₀.₁₇Ti₀.₁₇O₂ does not satisfy charge neutrality. Please provide the average oxidation state of each transition metal element.\n7. Please double-check the pristine and charged state of the Fe K edge in Fig5\n8. Fig. 5g shows the presence of Fe²⁺ even after charging to 4 V, which, to our knowledge, has not been reported in previous studies. Moreover, Fe²⁺ is known to be highly unstable and readily oxidizes to Fe³⁺, even upon exposure to air. The persistence of Fe²⁺ at such a high voltage is therefore questionable and appears to be unreasonable.\n9. Co2+/ Co3+ is incorrectly identified in Fig5\n10. Is the unit of the x-axis in Fig. S7 accurate? If yes, the GITT testing duration would be 257 days, which seems unlikely.\n11. Is the unit of the y-axis in Fig. S8 accurate? Is it indeed at the 0.00008 mA level? It is unclear whether such a high-sensitivity measurement instrument was used.\n12. Fig. S10 clearly indicates that Cu is electrochemically active. Please refine the fitting by using thinner lines and more careful correction. Moreover, unless there is an unexpected explanation, the spectra for the charged and discharged states appear to be plotted in reverse.\n13. The signal strength resolution in Fig. S11 is difficult to recognize.\n14. We believe that the improved water and air stability of the high-entropy Na₀.₆₇Ni₀.₁₈Cu₀.₁₈Fe₀.₁₅Co₀.₁₅Mn₀.₁₇Ti₀.₁₇O₂ material is not primarily related to the increased configurational entropy, but is more likely associated with the incorporation of Cu. Relevant discussions can be found in previous studies, such as Advanced Materials, 2015, 27(43): 6928–6933, and Journal of the American Chemical Society, 2017, 139(25): 8440–8443.\n15. Is the performance of the Na₀.₆₇-based material in potassium-ion batteries a unique property of the high-entropy composition? Could other layered oxide compositions also serve as potential K-ion storage materials?", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The authors present a novel theoretical framework termed electronegativity entropy weighting, which integrates effective electronegativity (EEN) and configurational entropy (Sconfig) to establish predictive models for crystal structures in medium- and high-entropy layer oxide materials. This methodology is conceptually innovative and is supported by a combination of experimental and computational evidence. Based on this design principle, the synthesized O3-Na0.67 material shows significantly improved air stability and electrochemical performance. Overall, this work presents compelling findings that are likely to inspire further research in this field, and I recommend it for publication after addressing the following concerns.\n1. The authors report the successful synthesis of an O3-type cathode with ultra-low sodium content (Na0.538); however, the electrochemical performance data are primarily based on the Na0.67 composition. It may mislead the readers. This may cause confusion for readers. The authors should clarify the specific advantages conferred by the low sodium content and, if available, include electrochemical performance data for the Na0.538 sample.\n2. The manuscript proposes that transition metals with higher effective electronegativity (EEN) increase the dO-TM-O/dO-Na-O ratio. How to understand this d ratio, further explanation is required.\n3. The electronegativity entropy weight (Wχ) can be calculated according to Equation 1, which includes the radius of transition metals. And it can be seen from Fig. 1 (c) that some samples with different structures exhibit similar Wχ. How do researchers determine the radius of transition metals with multiple possible valences commonly presents in layered oxides, such as Ni, Co, and Mn?\nGiven that the exact valence states (and hence ionic radii) are often unknown before detailed characterization, how we can better utilize the research findings?\n4. The authors stated that their material exhibits much higher capacity retention than the conventional O3 materials (Page 5). This statement should be supported with specific literature comparisons.\n5. How do disordered ion arrangements delocalize the electronic structure? Can the authors further explain it or proof the statement.\n6. On page 15, it is claimed that the initial Coulombic efficiency (ICE) of 107.7% is significantly higher than the “common ~80%” observed in low Na content systems. The authors should cite relevant references to support this comparison.\n7. The term “configurational entropy”, “configuration entropy”, or “conformational entropy” should be used consistently throughout the paper.", "reviewer_4": "This work presents a truly groundbreaking advancement in the field of sodium-ion batteries. The authors introduce a novel concept—electronegativity entropy weight—to guide the rational design of high-entropy layered oxides, successfully achieving a remarkably stable O3-type structure with the lowest reported sodium content to date. The comprehensive integration of theory, design, synthesis, and multi-scale characterization showcases an exceptional level of scientific rigor and innovation. Notably, the material exhibits outstanding electrochemical performance, structural stability, and even applicability in potassium-ion batteries. This work sets a new benchmark for cathode material development and paves the way for next-generation energy storage technologies. However, some concerns should be addressed before its publication as follows.\n1. The manuscript predicts structural trends in synthesized materials and further investigates the reversible O/P phase transitions during the charge/discharge process. Do the experimentally observed phase transformations under electrochemical conditions align with the predicted structural trends?\n2. Among conformational entropy, electronegativity, and sodium content, which factor exerts the dominant influence on phase structure evolution?\n3. In the hydration test, the three samples exhibit similar XRD patterns. Have you further confirmed the cation ratios? Was any cation lost after soaking in water for 12 hours?\n4. Regarding the full cell measurement, how does the electrochemical performance in this work compare with previously reported results?\n5. Coulombic efficiency results of full cell should be also demonstrated in Fig 6h.\n6. Some recent published references about oxide cathodes for sodium ion batteries are suggested to be cited (10.1002/aenm.202304529; 10.1016/j.cej.2025.160010).", "reviewer_5": "This manuscript presents a conceptual breakthrough in the design of high-performance sodium-ion layered oxide cathodes with an entropy-dominated phase structure. A novel electronegativity entropy weight is proposed to unravel the composition–structure–performance relationships in complex multi-component systems. By integrating electronegativity considerations with conformational entropy analysis, the study successfully deciphers the key interatomic interactions in layered oxides. This innovative approach enables the rational design of an unconventional O3-type cathode material with ultra-low sodium content. The resulting entropy-engineered material demonstrates remarkable stability across multiple functional properties. These findings establish a new entropy-driven design paradigm that effectively bridges compositional complexity with structural predictability in layered oxide development. I recommend this manuscript to be accepted for publication in Nature Communications after some revisions. However, some important aspects require further clarification:\n1. The manuscript introduces a weighting formula for structure prediction based on transition metal layer components. However, in sodium layered oxides, the sodium content typically dictates the phase structure—higher Na concentrations favour O3, while lower concentrations favour P2. For entropy-dominated phase structures, has the influence of sodium content been considered in this weighting formula, and if so, is it quantitatively accounted for?\n2. The weighting formula has been validated across a wide range of materials in this work, but does it perform equally well for non-entropy-dominated structures?\n3. In Figure 2 of the manuscript, various transition metal elements are used to validate the weighting formula. Do certain elements exhibit a stronger tendency to stabilize either P2 or O3 structures?\n4. While numerous studies have demonstrated improved structural stability in high-entropy materials, the underlying mechanisms remain incompletely understood. The manuscript introduces key concepts—multiple redox centers and cationic disordering—as potential drivers of enhanced stability. Please elaborate further to illustrate the mechanism in more detail.\n5. The manuscript convincingly demonstrates that the low-sodium O3-phase material not only exhibits superior stability but also holds promise for potassium-ion battery applications. However, to enhance the impact and utility of this work, a more detailed discussion of future research directions and potential practical applications should be included."}, "author_response": "Response: We sincerely thank the reviewers for their insightful analysis and valuable feedback on the orbital overlap effect. You correctly pointed out that TM electronegativity enhances TM–O orbital overlap, leading to a shorter d distances. We would like to clarify that we use the (OTMO) concept of effective ionic electronegativity, which differs from traditional atomic electronegativity in two key ways: First, we use electronegativity values corresponding to specific valences in an octahedral coordination environment. Second, the effective electronegativity of the transition metal is defined as the difference between the electronegativity of oxygen and the average TM electronegativity, i.e., ∆𝜒 =𝜒 −𝜒 . This value, along with the average electronegativity of the alkali metal layer (𝜒 ) and the content ratio, constitutes the ∏𝜒 value. We have corrected 𝐴 𝐶𝑎𝑡𝑖𝑜𝑛 an error in the previous version where the 𝜒 term was incorrectly included with the alkali metal 𝑂 (𝜒 ) term. We appreciate you bringing this to our attention. The corrected formula shows that, given 𝐴 similar values for 𝑛𝐴 , 𝑟 , and |𝑆 |, as TM electronegativity increases, both ∆𝜒 and 𝑇𝑀 𝑐𝑜𝑛𝑓𝑖𝑔 𝑇𝑀 𝑛𝐶𝑎𝑡𝑖𝑜𝑛 ∏𝜒 decrease. This leads to shorter d distances and a decrease in the 𝑊 value, 𝐶𝑎𝑡𝑖𝑜𝑛 (OTMO) 𝜒 favoring the formation of the P2 phase structure. This conclusion aligns with your theoretical guidance. We have further clarified this concept in the text through a more detailed derivation and explanation of the \"configurational entropy weight\" formula.\nTo further validate our formula, we expanded our dataset to 215 materials and employed machine learning. This analysis confirmed the significance of 𝑟 , ∆𝜒 , and 𝑇𝑀 𝑇𝑀 𝑛𝐴 across the 𝑛𝐶𝑎𝑡𝑖𝑜𝑛 material system, whereas entropy does not exhibit a consistent influence. Specifically, in low-entropy systems (|𝑆 | < 1, Response Fig. 1-1), entropy's influence on structure is negligible. 𝑐𝑜𝑛𝑓𝑖𝑔 However, in systems with |𝑆 | ≥ 1 (Response Fig. 1-1), entropy's impact becomes 𝑐𝑜𝑛𝑓𝑖𝑔 increasingly apparent. This explains the failure of parameters like \" cationic potential \" in predicting high-entropy materials. We have added Fig. S3 and a discussion on the effect of configurational entropy to the revised manuscript.\nSpearman rank correlation analysis quantified the influence of each factor on the structure (Response Fig. 1-3). 𝑊 showed a strong positive correlation with the O3 structure (ρ = 0.82), 𝜒 confirming the reliability of the configurational entropy weight model. Exhaustive analysis of basic operations on several parameters showed that the current formula exhibited outstanding correlation among the 5,488 operations performed. We emphasize that the formula uses thermodynamic quantities and, therefore, cannot describe structural differences resulting from varying synthesis processes. These correlation validation results have been added to Fig. 1e and 1f in the revised manuscript and the limitation is further discussed in the text.\nThe d /d ratio, while a potential predictor of phase structure in stoichiometric (ONaO) (OTMO) systems, has uncertain effectiveness in distinguishing phase preference (P2 vs. O3) in non-stoichiometric systems. Our electronegativity-entropy model, therefore, omits this ratio, instead using electronegativity and configurational entropy to predict phase structure independently of geometric parameters. We have clarified the logic throughout the revised manuscript. We sincerely appreciate your thorough review and expert guidance, which significantly improved the quality of this manuscript.\n1. We remain skeptical about the N=6 portion of the data in Fig2e, it is implausible that d / d O-Na-O O- = 1.264 was obtained at such a low Na content. TM-O\nResponse: We sincerely thank you for your valuable feedback. While the unit cell parameters and atomic coordinates reported in our previous work have been confirmed upon re-examination, we identified and corrected an error in the interlayer spacing calculation. The revised values are d = 3.326 Å and d = 2.139 Å (updated in Response Table 1-1 and revised manuscript (ONaO) (OTMO) Table S10). Consequently, the recalculated ratio d /d = 1.555, which is higher than (ONaO) (OTMO) that of most conventional O3-type materials (Angew. Chem. Int. Ed. 57, 7056–7060 (2018)).\n2. In Fig. 2c, the peak at 2θ = 50° for the sample with N = 5 is not labeled. It does not correspond to either the P2 or O3 phase, indicating that the diffraction pattern is not composed solely of P2 and O3 phases.\nResponse: We sincerely appreciate your careful observation. The X-ray diffraction (XRD) pattern of the N=5 material, presented in Response Fig. 1-4, confirms its biphasic (O3/P2) nature. All diffraction peaks are consistent with reference patterns for both O3 and P2 phases. Specifically, we have identified the diffraction peak at 2θ ≈ 50° as corresponding to the (104) crystallographic plane of the P2 phase (PDF#01-070-3726; space group: P63/mmc). To further clarify the phase identification, complete standard card information for both O3 and P2 phases has been included in the manuscript. Moreover, all characteristic peaks, including the (104) peak, are annotated in the P2 revised manuscript Fig. S4.\n3. In Fig. 3c, are the fine surface particles observed in the SEM image residual Na₂CO₃ formed from alkali precipitation?\nResponse: Thank you for your valuable feedback. To further investigate the composition of these surface particles, the sample was subjected to electron beam irradiation (10 kV, 10 μA) for 60 seconds during SEM characterization. The surface morphology remained largely unchanged following this irradiation (Response Fig. 1-5), suggesting that the surface particles are relatively stable under electron beam exposure. Given that residual alkali species are known to be highly unstable under electron beam irradiation and prone to ablation, this observation suggests that the surface particles are unlikely to be residual alkali. This inference is further supported by the absence of residual alkali-related peaks or peak splitting in the XRD patterns and the uniform elemental distribution revealed by TEM-EDS mapping, which indicates a lack of surface segregation.\n4. In Fig. 4d, it is evident that during the initial stage of charging, the O3 phase first transforms into the O'3 phase, followed by a subsequent transition to the P3 phase.\nResponse: We sincerely appreciate your expert interpretation of the phase transition illustrated in Figure 4d. The evolution and splitting of (104) (J. Am. Chem. Soc. 2022, 144, 18, 8286–8295 and Chemical Engineering Journal 2025, 505, 159207) were amplified and highlighted for clarity (Response Fig. 1-6). We added O'3 transition information to Fig. 4d in revised manuscript with corresponding discussion and included a clearer line segment diagram in the supporting information (Fig. S12).\n5. In Fig. 4f, the x-axis labeling appears to be incorrect, and both the charge and discharge capacities should be significantly higher than 83 mAh g⁻¹.\nResponse：Thank you for your careful review. We have directly annotated the charge and discharge capacities on the revised Figure 4f (Response Fig. 1-7).\n6. Based on the initial oxidation states obtained from the XPS fitting in Fig. 5, the composition Na₀.₆₇Ni₀.₁₈Cu₀.₁₈Fe₀.₁₅Co₀.₁₅Mn₀.₁₇Ti₀.₁₇O₂ does not satisfy charge neutrality. Please provide the average oxidation state of each transition metal element.\nResponse：Thank you for your valuable suggestions. XPS, a surface-sensitive technique with a probing depth < 10 nm, characterizes the local chemical states at the interface, whereas charge balance calculations reflect the average bulk composition. This material was synthesized with a target composition of Na Ni Cu Fe Co Mn Ti O , with the theoretical transition 0.67 0.18 0.18 0.15 0.15 0.17 0.17 2 metal valences, derived from redox couple potentials (Nature Communications 11.1 (2020): 3544), being Na Ni 3+ Ni 4+ Cu 2+ Co 4+Fe 3+ Mn 4+ Ti 4+ O . Based on this theoretical 0.67 0.16 0.02 0.18 0.15 0.15 0.17 0.17 2 ionic valence distribution, the composition was designed, and the ionic ratios were confirmed for subsequent calculations of the electronegativity entropy mixing parameters to predict the structure. To reconcile these differences arising from the assumption of ideal bulk homogeneity in contrast to the inherent complexity of real materials, both XPS and XAFS measurements were employed to validate the multi-redox-center mechanism of the high-entropy material during electrochemical cycling.\n7. Please double-check the pristine and charged state of the Fe K edge in Fig5\nResponse：We sincerely appreciate your meticulous review of the data. To better analyze valence changes, we normalized the ex-situ data, which are now presented in Response Fig. 1-8a and updated in the revised Fig. S16c. The enhanced spectral resolution provides a clearer visualization of edge shifts, with a significant white-line peak shift to higher energy after charging (Adv. Energy Mater. 2021, 11, 2100479). First-derivative analysis of the Fe K-edge XANES spectra was used to identify the absorption edge energy (E ) (Response Fig. 1-8b). Upon charging, E shifted to a edge edge higher 7113.3 eV, and after discharging, E returned to its original 7112.0 eV. Combined with edge XPS data, these results indicate a clear valence change of Fe during the first charge-discharge cycle.\n8. Fig. 5g shows the presence of Fe²⁺ even after charging to 4 V, which, to our knowledge, has not been reported in previous studies. Moreover, Fe²⁺ is known to be highly unstable and readily oxidizes to Fe³⁺, even upon exposure to air. The persistence of Fe²⁺ at such a high voltage is therefore questionable and appears to be unreasonable.\nResponse: We sincerely appreciate your valuable comments. To ensure the rigor of our experimental conclusions, we have re-conducted XPS measurements on the Fe species re-fitted the peaks, as shown in Response Figure 1-9. The peak area ratio of Fe4+/Fe3+ dynamically evolves during charge and discharge: it increases during charging, indicating Fe oxidation, and decreases during discharging, indicating reduction. This trend aligns with XANES results, cross-validating Fe's role as a redox center in the reaction. The re-tested data is included in Fig. S18 of the revised manuscript.\n9. Co2+/ Co3+ is incorrectly identified in Fig 5.\nResponse：We sincerely appreciate your valuable critique regarding the Co valence state assignment in Figure 5. We have re-performed the XPS measurements and peak fitting (Response Fig. 1-10), where the binding energy of Co³⁺ 2p is 1-2 eV lower than that of Co²⁺. Quantitative analysis of the fitted peak areas indicates that the Co oxidation state increases during charging, with the Co²⁺/Co³⁺ ratio decreasing from 0.96 to 0.76. Upon discharge, the Co reduction leads to a decrease in valence, and the ratio recovers to 1.11. The same redox behavior, with valence increasing then decreasing, is observed during the second cycle. The re-measured data are now included in the revised manuscript as Fig. S17c.\n10. Is the unit of the x-axis in Fig. S7 accurate? If yes, the GITT testing duration would be 257 days, which seems unlikely.\nResponse: Thank you sincerely for your careful review. We have corrected the data units to minutes in the revised manuscript Fig. S13 (Response Fig. 1-11).\n11. Is the unit of the y-axis in Fig. S8 accurate? Is it indeed at the 0.00008 mA level? It is unclear whether such a high-sensitivity measurement instrument was used.\nResponse：We sincerely thank you for your thorough review and valuable suggestions. We have unified the units to \"A\" (Response Fig. 1-12), which has been corrected in the revised manuscript Fig. S14. We also conducted a systematic check of the entire manuscript to ensure accuracy in every detail. Your high standards and attentive review have greatly enhanced the quality of this paper, for which we are deeply grateful.\n12. Fig. S10 clearly indicates that Cu is electrochemically active. Please refine the fitting by using thinner lines and more careful correction. Moreover, unless there is an unexpected explanation, the spectra for the charged and discharged states appear to be plotted in reverse.\nResponse: We sincerely appreciate your insightful critique regarding the electrochemical activity of Cu in Fig. S10. In response to your concern, we have re-plotted the Cu K-edge XANES spectra using finer lines (Fig. S19). Analysis of these spectra reveals a minimal shift of approximately 0.3 eV in the pre-edge feature peak intensity between the pristine, charged, and discharged states. This shift is significantly smaller than the characteristic shift exceeding 1 eV typically observed in Cu redox reactions within sodium layered oxides (Adv. Funct. Mater. 2025, 2504642). Furthermore, literature reports (Adv. Energy Mater, 2019, 36(9):1901785 and J. Mater. Chem. A 3, 22846–22852 (2015)) indicate that the Cu²⁺/Cu³⁺ redox potential exceeds 4.2 V, which is beyond the 2-4 V operating voltage window of this study. Further supporting the electrochemical inertness of Cu within our system are the XPS results presented in Response Fig. 1-13. Your rigorous review standards have prompted us to conduct a more thorough verification of this phenomenon, and we express our sincere gratitude for your expert feedback.\n13. The signal strength resolution in Fig. S11 is difficult to recognize.\nResponse: We sincerely appreciate your valuable feedback. To ensure rigorous and scientific experimental results, we repeated the XPS measurements. The Cu 2p and Ti 2p XPS results, shown in Response Figure 1-14, indicate no significant shifts in binding energy peak positions during the two cycling processes, confirming that Cu and Ti do not undergo redox reactions during charge and discharge, consistent with our original data. Furthermore, XANES results align with the XPS-observed valence state evolution. We have replaced the original data with the results from this retest (added as Fig. S20 in the revised manuscript).\n14. We believe that the improved water and air stability of the high-entropy Na Ni Cu Fe Co Mn Ti O material is not primarily related to the increased 0.67 0.18 0.18 0.18 0.18 0.18 0.18 2 configurational entropy, but is more likely associated with the incorporation of Cu. Relevant discussions can be found in previous studies, such as Advanced Materials, 2015, 27(43): 6928–6933, and Journal of the American Chemical Society, 2017, 139(25): 8440–8443.\nResponse: We sincerely appreciate your insightful perspective on stability mechanisms. While acknowledging the role of Cu in enhancing stability, our experimental evidence demonstrates an independent entropy stabilization effect. To isolate this effect, we synthesized a Cu-free control material, O3-Na Ni Li Sn Fe Co Mn Ti O , and subjected it to the same rigorous 0.67 0.18 0.12 0.06 0.15 0.15 0.17 0.17 2 testing protocol. Specifically, after 12 hours of water exposure, XRD analysis revealed no evidence of impurity or hydrate phase formation (Response Fig. 1-15a), and the material exhibited only a minimal initial capacity loss of 6.4 mA h/g (Response Fig. 1-15b). Furthermore, following 18 hours of air exposure, the charge/discharge profiles remained virtually unchanged compared to the pristine material, and the material demonstrated comparable rate performance and capacity retention after 100 cycles (Response Fig. 1-15c and d). These findings suggest that the observed air and water stability can be attributed to the high-entropy characteristics of the low-sodium O3 material, rather than solely relying on Cu-induced structural stabilization. We have included these supporting data in Fig. S22 and have provided further clarification in the revised manuscript, as per your valuable suggestion.\n15. Is the performance of the Na -based material in potassium-ion batteries a unique property of 0.67 the high-entropy composition? Could other layered oxide compositions also serve as potential K-ion storage materials?\nResponse: To evaluate the potassium-ion storage capabilities of other layered oxides, we synthesized conventional P2-Na Ni Mn O (P2-NM) and O3-NaNi Fe Mn O (O3-NFM) 2/3 1/3 2/3 2 1/3 1/3 1/3 2 (Response Fig. 1-16a) and conducted half-cell potassium-ion battery tests. The initial discharge specific capacities of P2-NM and O3-NFM were 87.3 and 89.0 mA h/g, respectively (Response Fig. 1-16b). However, O3-NFM exhibited a lower capacity retention of only 72.42% after 15 cycles (Response Fig.1-16c), which can be attributed to its narrower interlayer spacing causing greater structural disruption during K+ insertion/extraction. In contrast, P2-NM demonstrated superior cycling stability, albeit with inferior rate performance, showing almost no capacity at a current density of 5 C (Response Fig. 1-16d). Considering the characteristics of both O3 and P2 materials, our designed low-sodium O3-Na0.67 material demonstrates improved overall performance (Fig. 6f and S23 in the revised manuscript). The larger ionic radius and mass of K+ compared to Na+ typically lead to diminished cycling stability and ion dynamics when K+ is intercalated into sodium-based layered structures. Therefore, this work offers a novel approach to achieving enhanced K-storage performance in sodium-based layered oxide cathodes compared to traditional materials.\nResponse: We sincerely appreciate the reviewer for recognizing the novelty of our electronegativity entropy weighting framework and its value in guiding the design of high-entropy layered oxides. Their expert guidance has significantly strengthened both the theoretical basis and practical applications of this approach. We have carefully addressed each point through rigorous revisions.\n1. The authors report the successful synthesis of an O3-type cathode with ultra-low sodium content (Na0.538); however, the electrochemical performance data are primarily based on the Na0.67 composition. It may mislead the readers. This may cause confusion for readers. The authors should clarify the specific advantages conferred by the low sodium content and, if available, include electrochemical performance data for the Na0.538 sample.\nResponse：We sincerely appreciate your insightful comments regarding the sodium content expression. The composition Na0.67 was specifically chosen to facilitate a direct comparison with traditional P2-type materials, which also possess a sodium content of 0.67, thereby better illustrating the impact of entropy. To avoid potential reader confusion, we have included the electrochemical data for Na0.538 in the revised manuscript (Fig. S11). As shown in Response Fig. 3-1, Na0.538 exhibits comparable cycling stability and rate capability to Na0.67, with a capacity retention of 91.60% after 100 cycles at 0.5 C and 58.95% at 10 C, confirming that a lower sodium content does not compromise these attributes. We have added corresponding discussions in the revised manuscript. While traditional O3-type layered oxide cathode materials offer the advantage of high specific capacity, their sluggish ion kinetics and complex phase transition behavior severely hinder their practical application. In this study, we successfully synthesized a low-sodium O3-type structure material using a non-stoichiometric high-entropy strategy. The pre-existing sodium vacancies in this structure effectively promote the establishment of rapid ion diffusion channels and significantly enhance the structural stability of the material. Unlike the P2 structure, which transforms into the O phase during charging, thereby hindering K+ re-intercalation, the low-sodium O3 structure can rapidly transform into a P-type phase with wider channels and superior diffusion performance upon charging. This enables the application of low-sodium O3 materials as cathodes for potassium-ion batteries. Importantly, this low-sodium O3 material demonstrates a unique phase transition advantage: it can stably maintain the P-type structure during 86.35% of the charge-discharge process, while also avoiding the low first-cycle Coulombic efficiency issue commonly associated with the sodium-poor P phase, thus better meeting the practical requirements of full-cell applications.\n2. The manuscript proposes that transition metals with higher effective electronegativity (EEN) increase the d /d ratio. How to understand this d ratio, further explanation is required. O-TM-O O-Na-O\nResponse： We thank the reviewer for the insightful comment. In the OTMOAO configuration of the layered oxide, oxygen atoms are simultaneously subjected to Coulombic attraction from the transition metal and alkali metal in opposite directions. In the TMOA structure, increasing the IEN value of TM reduces the electronegativity difference ∆𝜒 between TM and O, which enhances their orbital overlap and promotes more covalent TMO bonding with stronger binding and shorter d distances. This strengthened TMO interaction concurrently weakens the NaO bonding in O-TM-O the same TMOA configuration, yielding more open AO structural arrangements with expanded 6 d spacing. We have incorporated additional descriptions in the revised manuscript to further OAO clarify this mechanism.\n3. The electronegativity entropy weight (Wχ) can be calculated according to Equation 1, which includes the radius of transition metals. And it can be seen from Fig. 1 (c) that some samples with different structures exhibit similar Wχ. How do researchers determine the radius of transition metals with multiple possible valences commonly presents in layered oxides, such as Ni, Co, and Mn?\nGiven that the exact valence states (and hence ionic radii) are often unknown before detailed characterization, how we can better utilize the research findings?\nResponse：We sincerely appreciate the reviewer for insightful comments, which prompted us to provide a more detailed explanation of our theoretical composition design methodology. Building upon literature insights (Nature communications 11.1 (2020): 3544), we determined the composition Na Ni Cu Fe Co Mn Ti O by integrating redox potentials of transition metal 0.67 0.18 0.18 0.15 0.15 0.17 0.17 2 couples with charge balance principles. Given fixed +1 and -2 valence states for Na and O respectively, overall charge neutrality necessitates specific transition metal valences. Following the oxidation sequence of redox pairs: Ti3+/4+, Mn3+/4+, Co3+/4+, Ni2+/3+/+4, Fe3+/4+, Cu2+/3+, we derived the valence distribution: Ni 3+Ni 4+Cu 2+Co 4+Fe 3+Mn 4+Ti 4+. The effective ion radius 0.16 0.02 0.18 0.15 0.15 0.17 0.17 and electronegativity of different valence states were taken into consideration and the electronegativity entropy weight value based on the Equation 1 was calculated. Although sintered materials may show deviation from theoretical valences, this methodology provides critical pre-characterization guidance for predicting phase stability (O3 or P2), optimizing elemental substitution through electronegativity modulation, and streamlining synthesis workflows.\n4. The authors stated that their material exhibits much higher capacity retention than the conventional O3 materials (Page 5). This statement should be supported with specific literature comparisons.\nResponse：Thank you for pointing out the need to support our claim of superior capacity retention with a direct comparison to existing literature. We have now included a specific comparison of our material's capacity retention with several conventional O3-type materials in Response Table 3-1 and Table S21 in the manuscript. The results demonstrate significantly higher capacity retention for our material.\n5. How do disordered ion arrangements delocalize the electronic structure? Can the authors further explain it or proof the statement.\nResponse: We appreciate the reviewer's insightful question regarding the mechanism of electron delocalization induced by disordered ionic arrangements. In multi-component TM systems, the random occupation of equivalent crystallographic sites by ions with differing electronegativities and ionic radii disrupts translational symmetry within the TM layers, leading to a diverse range of electronic configurations. To elucidate this effect, we performed complementary DFT calculations on both multi-component and mono-component TM systems. Analysis of the projected density of states (PDOS) for O 2p orbitals reveals a significant bandwidth broadening in the multi-component systems compared to their monometallic counterparts (Response Fig. 3-2). This broadening, now illustrated in Fig. 2d of the revised manuscript, demonstrates enhanced energetic delocalization across the occupied energy range, indicating that the high-entropy multi-component system promotes a more delocalized electronic structure in the disordered ionic arrangement. The relevant discussion has also been highlighted in the revised manuscript.\n6. On page 15, it is claimed that the initial Coulombic efficiency (ICE) of 107.7% is significantly higher than the “common ~80%” observed in low Na content systems. The authors should cite relevant references to support this comparison.\nResponse: We sincerely appreciate your valuable comments. We have incorporated references [42-45] for P′2-Na MnO , P2-Na [Ni Fe Mn ]O , P2-Na Mn Fe O , 0.67 2 0.55 0.1 0.1 0.8 2 0.67 0.65 0.35 2 Na Mn Ni Co O , and Na Cu Ni Mn O materials to substantiate our comparative 0.67 0.65 0.2 0.15 2 0.50 0.15 0.20 0.65 2 analysis of Coulombic efficiency.\n7. The term “configurational entropy”, “configuration entropy”, or “conformational entropy” should be used consistently throughout the paper.\nResponse: We sincerely appreciate the reviewer's meticulous review. We have thoroughly reviewed the entire manuscript and standardized the term to \" configurational entropy\".\nResponse: We express our profound gratitude for the reviewer's emphasis on the originality of the electronegativity entropy weight strategy and its role in achieving unprecedented structural stability at ultralow Na content. All suggested improvements have been rigorously implemented, with revisions marked in yellow in the manuscript. These enhancements have strengthened the mechanistic discussion and practical implications of our electronegativity-driven entropy engineering strategy, further solidifying its value for next-generation battery materials development.\n1. The manuscript predicts structural trends in synthesized materials and further investigates the reversible O/P phase transitions during the charge/discharge process. Do the experimentally observed phase transformations under electrochemical conditions align with the predicted structural trends?\nResponse: We appreciate the reviewer's insightful question concerning the consistency between our predicted structural trends and the experimentally observed phase transitions. Indeed, the structural changes occurring during the electrochemical process align well with our predictions. Specifically, during charging, the progressive extraction of sodium leads to a reduction in the sodium content. Concurrently, the transition metal ions undergo oxidation, resulting in a change in their valence states, radii, and electronegativity as they lose electrons. To quantitatively assess these changes, we calculated the electronegativity entropy weight (𝑊 ) for materials with the same transition metal 𝜒 composition but varying sodium content (ranging from 1.0 to 0.4), as summarized in Response Table 4-1. Our model predicts that as the sodium content decreases, both 𝑛𝐴 and ∆𝜒 𝑇𝑀 𝑛𝐶𝑎𝑡𝑖𝑜𝑛 continuously decrease, causing 𝑊 to diminish towards a critical value of 0.6445. Experimentally, 𝜒 when the sodium content is reduced to 0.4, 𝑊 falls below this critical value, decreasing to 0.5143. 𝜒 The configurational entropy weight model we proposed predicts a P phase structure when 𝑊 is 𝜒 below this threshold, which is consistent with the observed O to P phase transition documented by in situ XRD in the manuscript.\n2. Among conformational entropy, electronegativity, and sodium content, which factor exerts the dominant influence on phase structure evolution?\nResponse: We sincerely thank the reviewers for their insightful questions regarding the dominant factors controlling phase evolution. In sodium layered oxides Na TMO , sodium content primarily x 2 drives phase transitions during charge-discharge cycling. The weakening of NaO electrostatic attraction as Na+ de-/intercalates from the alkali metal layers directly induces structural rearrangements. Thus, sodium content is central to determining the type of phase transition, while electronegativity and configurational entropy synergistically influence bonding strength and structural stability. In summary, sodium content dictates the phase transition pathway, electronegativity modulates bonding behavior, and configurational entropy stabilizes the structure.\n3. In the hydration test, the three samples exhibit similar XRD patterns. Have you further confirmed the cation ratios? Was any cation lost after soaking in water for 12 hours?\nResponse：We sincerely thank the reviewers for their insightful questions regarding cation stability. To address these concerns directly: inductively coupled plasma (ICP) analysis was performed on soaked samples to quantitatively confirm cation ratios. After 12 hours of soaking, negligible cation loss was observed, as evidenced by the nearly identical elemental composition (Response Table 4-2). These results demonstrate that all samples retained their original cation stoichiometry within experimental error, confirming the excellent water stability of our materials. The complete ICP data is provided in the Supporting Information as Table S22.\n4. Regarding the full cell measurement, how does the electrochemical performance in this work compare with previously reported results?\nResponse：Thank you for this valuable comment. As systematically compared in Response Table 4-3 and revised manuscript Table S23, our work demonstrates competitive electrochemical properties against previously reported results sodium-ion full cells.\n5. Coulombic efficiency results of full cell should be also demonstrated in Fig 6h.\nResponse： Thanks to the reviewer for this careful comment. The Coulombic efficiency results for the full cell have now been incorporated into revised manuscript Fig. 5h (Response Fig. 4-1). This addition provides critical insights into the electrochemical reversibility of our Na-ion full cell system.\n6. Some recent published references about oxide cathodes for sodium ion batteries are suggested to be cited (10.1002/aenm.202304529; 10.1016/j.cej.2025.160010).\nResponse: Thank you for this valuable comment. The recommended references (10.1002/aenm.202304529; 10.1016/j.cej.2025.160010) have been carefully studied and cited as references [16] and [27] in the revised manuscript.\nResponse：We are deeply honored by the reviewer’s recognition of this work as a \"conceptual breakthrough\" establishing a \"new entropy-driven design paradigm\". We express profound gratitude for the reviewer’s expert guidance in elevating the work’s conceptual rigor and practical relevance. We have rigorously addressed all concerns through substantive revisions summarized below, with detailed point-by-point responses.\n1. The manuscript introduces a weighting formula for structure prediction based on transition metal layer components. However, in sodium layered oxides, the sodium content typically dictates the phase structure—higher Na concentrations favour O3, while lower concentrations favour P2. For entropy-dominated phase structures, has the influence of sodium content been considered in this weighting formula, and if so, is it quantitatively accounted for?\nResponse：We sincerely appreciate the reviewer's profound insight regarding the interplay between sodium content and configurational entropy in phase stabilization. The weighting formula explicitly incorporates sodium content through the 𝑛𝐴 term, which serves as a quantitative descriptor of 𝑛𝐶𝑎𝑡𝑖𝑜𝑛 NaO bond strength evolution. An increase in sodium content enhances the electrostatic attraction of NaO and thermodynamically stabilizes the O3 phase. When the sodium content increases, 𝑛𝐴 increases. When other parameters remain unchanged, the calculated value of 𝑊 also 𝜒 𝑛𝐶𝑎𝑡𝑖𝑜𝑛 increases, and the predicted materials more inclined to form the O3 phase. On the contrary, it tends to form a P2 structure.\n2. The weighting formula has been validated across a wide range of materials in this work, but does it perform equally well for non-entropy-dominated structures?\nResponse：We appreciate the reviewer's insightful comments regarding the applicability of our weighting model in non-entropy-dominated systems. To address this, we calculated the configurational entropy for low-entropy P2/O3 materials (|𝑆 |<1 , typically with ≤ 2 𝑐𝑜𝑛𝑓𝑖𝑔 transition metals) using the configurational entropy weight formula. These results are now included in the revised manuscript as Figure 1d and Table S2. While the calculated weight values (𝑊 ) still 𝜒 align with the structural preferences observed in P2/O3 structures, a Spearman's rank correlation analysis of all parameter pairs (Response Fig. 5-1) reveals that the alkali metal ratio 𝑛𝐴 𝑛𝐶𝑎𝑡𝑖𝑜𝑛 exhibits the strongest correlation (ρ = 0.85) with the weighting formula's factors, followed by ∆𝜒 𝑇𝑀 (ρ = 0.78), while the influence of |𝑆 | is negligible (ρ = 0.09). This suggests that |𝑆 | 𝑐𝑜𝑛𝑓𝑖𝑔 𝑐𝑜𝑛𝑓𝑖𝑔 exerts minimal influence on the structure in non-entropy-dominated systems. Although Hu et al. developed a model for the O3/P2 structural competition based on cationic potential, it is unable to predict structures in entropy-dominated systems. In these systems, increased disorder in the transition metal arrangement leads to a more \"averaged\" transition metal layer, enhancing the impact of entropy on structure formation and increasing the number of factors governing the interaction between alkali metal layers (O–Na–O) and transition metal layers (O–TM–O). By integrating both entropy and non-entropy terms, our model offers a unified predictive framework for both medium- and high-entropy systems.\n3. In Figure 2 of the manuscript, various transition metal elements are used to validate the weighting formula. Do certain elements exhibit a stronger tendency to stabilize either P2 or O3 structures?\nResponse：We appreciate the reviewer's insightful inquiry regarding element-specific phase stabilization tendencies. As evidenced by the XRD patterns presented in Figure 2, materials synthesized with component 5 exhibit diverse phase behaviors. Specifically, the NO Mn material displays two distinct O3 phases. In contrast, NO Ni, NO Co, NO Fe, and NO Ti materials adopt a two-phase structure consisting of both P2 and O3 phases, while NO Cu exhibits a single, pure P2 phase. To investigate the underlying factors governing these phase preferences, we calculated and quantified the 𝑊 parameter for each material and correlated it with the proportion of the O3 phase. 𝜒 As detailed in Response Table 5-1, an examination of the individual data reveals no direct correlation between any single factor and the O/P phase transition. However, analysis using the 𝑊 𝜒 formula demonstrates a clear trend: an increase in the 𝑊 value corresponds to an increased 𝜒 proportion of the O3 phase. This observation suggests that the O/P structure is not determined by a single dominant factor, but rather emerges from the synergistic interplay of multiple elemental influences.\n4. While numerous studies have demonstrated improved structural stability in high-entropy materials, the underlying mechanisms remain incompletely understood. The manuscript introduces key concepts—multiple redox centers and cationic disordering—as potential drivers of enhanced stability.\nResponse: We acknowledge the reviewer's request for a more in-depth mechanistic explanation. The enhanced structural stability observed in our high-entropy oxides arises from two interconnected mechanisms. First, the compositional complexity inherent in high-entropy materials, specifically the presence of diverse transition metal ions, leads to a disordered ionic arrangement. This disorder reduces the average ionic electronegativity of the transition metals, thereby increasing the ionicity and bond length of the TM–O bonds. This, in turn, mitigates lattice distortions induced by local ionic distortions, such as those arising from the Jahn-Teller effect. Second, the coexistence of more than five transition metals creates a network of multi-level redox centers. These centers facilitate step-wise redox reactions, preventing the excessive accumulation of local charge and avoiding phase transition stresses that could result from abrupt voltage changes associated with single-element redox behavior. Our DFT calculations corroborate these synergistic effects, demonstrating that the anisotropy of the high-entropy structure, in combination with the presence of multiple redox centers and stabilizing \"pillar\" elements, significantly diminishes local structural changes within the system. This reduced structural dynamism is ultimately responsible for the observed exceptional long-term cycling stability. We have emphasized this discussion further in the revised manuscript.\n5. The manuscript convincingly demonstrates that the low-sodium O3-phase material not only exhibits superior stability but also holds promise for potassium-ion battery applications. However, to enhance the impact and utility of this work, a more detailed discussion of future research directions and potential practical applications should be included.\nResponse: In response to the reviewer's insightful suggestions concerning practical applications, we have expanded upon the significance of our low-sodium O3-phase discovery. Specifically, we have developed a computational descriptor for entropy-dominated structures, integrating key parameters, including electronegativity difference, ionic radius, configurational entropy, and the alkali-to-transition-metal ratio. This descriptor enabled the construction of an O3/P2 phase stability database. Consequently, we can now leverage neural networks to predict promising next-generation battery material candidates. This represents a clear trajectory from fundamental descriptor development towards large-scale industrial deployment, a point we have emphasized in the revised conclusion."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have well addressed my concerns, I would recommend acceptance as it is.", "reviewer_2": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_3": "The authors have thoroughly addressed all reviewer concerns through rigorous revisions. The revised manuscript convincingly validates the proposed electronegativity–entropy weighting formula with comprehensive supporting evidence. In particular, the control experiments excluding Cu and the expanded machine-learning validation strongly substantiate their claims. The inclusion of DFT-supported electronic structure analysis, together with comparative performance tables, further reinforces both the mechanistic interpretation and the practical relevance of the study.Therefore, I recommend the manuscript for acceptance in Nature Communications.", "reviewer_4": "This revised has addressed my comments and thus should be accepted as is.", "reviewer_5": "The authors have addressed all my comments and concerns. I am satisfied with the authors' responses and elucidations. Therefore, I recommend this manuscript to be accepted for publication in Nature Communications."}, "author_response": ""}]

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