Tuning superelasticity in high entropy alloy via a hidden strain order

Domain: neuroscience
Published: 2026-02-03
Editorial outcome: minor_revision

Abstract
Superelasticity–exhibitingeitherHookean(linear)ornon-Hookean(non-linear)recoverablestrainbeyond2%–hasbeenrealizedindistinctmaterialsystemssuchasmetallicglasses,shapememoryalloys,strainglassalloysandGummetals,enablingdiversetechnologicalapplications.Herewedemonstratethat,throughcompositionaltuninginahigh-entropyalloy,theelasticbehaviorcanbecontinuouslyandreversiblymodulatedbetweenHookeansuperelasticity,non-Hookeansuperelasticitywithanultrahighrecoverablestrainof~8%,andbacktotheHookeanregime.Bycombiningatomic-scalestrainmappingandextensivefirst-principlescalculations,werevealthatthistunabilityisgovernedbyahiddenstrainorder,arisingfromfrustratedcrystallizationoftwocompetingphases.Asaresult,locallatticedistortionarises,producingaheterogeneousstrainlandscapethatmodulatesphasestability,phasetransformationpropensity,andelasticresponse.OurfindingsestablishamaterialsdesignstrategyforprogrammingHookeanandnon-Hookeanelasticitybehaviorondemand,withpromisingapplicationsinmicroelectromechanicalsystems,high-precisionactuators,andadaptivedampingdevices.

Introduction
Crystalline alloys (e.g., steel, titanium, aluminum) typically exhibit transformations14,15. In these materials, the crystal lattice undergoes elastic deformation through reversible atomic bond stretching and reversible phase transitions under mechanical loading, enabling shearing1,obeyingHooke’slawwithalinearstress-strainrelationship2. exceptional elasticity without permanent structural damage. Recent Inthesesystems,elasticstrainsaretypicallyconstrainedtobelow1%3,4 discoverieshavepushedtheseboundariesfurther.Xuetal.16reporteda before the activation of plasticity carriers – primarily dislocation lowmodulusstrainglassalloy(SGA)(e.g.,Ti–50.8Ni)exhibitingelastic gliding5anddeformationtwinning6—initiatesirreversibledeformation. strains of ~8%—nearly an order of magnitude beyond conventional Remarkably,certainalloysystemstranscendtheseclassicallimitations Hookean limits. Unlike traditional SMAs where martensitic transfor- throughnonlinearelasticmechanisms.Shapememoryalloys(SMAs) mationsoccurcooperativelyacrosslongranges,SGAsachievesuper- (e.g., NiTi-based, Cu-based, Fe-based alloys)7–10 and Gum metals11–13 elasticitythroughtheactivationofnanoscalemartensiticdomains16,17.

Theadventofhigh-entropyalloys(HEAs)18,19hasrevolutionized thedesignofsuperelasticalloysbyexploitingmulti-principal-element compositions20. Unlike traditional superelastic alloys—including SMAs7–10, Gum metals11–13, and SGAs16,17—HEAs contain more than 4 principalelementswithsignificantatomicsizemismatchesanddiverse chemicalaffinities21,22.Thisuniquecompositiongeneratespronounced chemical and elastic fluctuations at the atomic scale, inducing substantial lattice distortion and heterogenous lattice strains23–27. Remarkably,HEAsexhibitbothHookeanandnon-Hookeanelasticity thatdefyconventionalelasticlimits.Chenetal.observedamassive pseudo-elastic strain of ~15% in Ni Co Fe Ga fibers28, while Gou 25 20 18 27 etal.reported~4%in(TiZrHf) Ni Cu Co Nb singlecrystals17—both 44 25 15 10 6 attributedtostress-inducedphasetransformationsfacilitatedbylat- ticedistortion.Intriguingly,Heetal.discoveredapurelyHookean-type superelasticity with 2–3% recoverable strain in (TiZrHf) Ni Co 50 25 25 alloy,surpassingthetraditional1%limitwhilemaintaininglinearelas- ticity,aneffectalsorootedinlatticedistortion20.Thesefindingsraisea fundamental question: How can severe lattice distortion simulta- neously enable both Hookean and non-Hookean superelasticity in HEAs? Theunderlyingmechanismsremainunresolved,presentinga critical knowledge gap in understanding atomic-scale lattice strain heterogeneityanditsroleinelasticdeformation.Resolvingthispara- dox could unlock new pathways for designing alloys with tailored elasticresponsesbeyondcurrentlimitations.

Inthisstudy,weresolvethisfundamentalquestionthroughsys- tematicinvestigationofthe(TiZrHf) Ni Co HEAsystem.Bypre- 50 50-x x ciselytailoringCo/Niratio,wedemonstratedirectcontroloverlattice distortionandinternalstrainfields—enablingacontinuoustransition between non-Hookean and Hookean superelasticity within a single alloy family. Remarkably,thistransitionoccursthroughminutecom- positional variations (<2at.%), unifying phenomena previously observed only in distinct alloy systems. Our discovery bridges the apparent dichotomy between conventional Hookean elasticity and transformational superelasticity, providing fundamental insights for designingalloyswithtailoredelasticresponses.

Results
Composition-dependentphasetransformationandelastic
response
Figure 1a presents the X-ray diffraction (XRD) patterns of
(TiZrHf) Ni Co (x=15,20,22,23,25)alloys(hereafterdenotedas
50 50-x x
Co15,Co20,Co22,Co23andCo25alloys,respectively;see“Methods”).
TheCo15alloyexhibitsasingle-phaseB19′structure,whereastheCo20
alloy reveals the emergence of B2 characteristic peaks, indicating a
dual-phase (B19′ + B2) microstructure. With further increase in Co
content(Co22,Co23andCo25alloys),thealloystransitiontoasingle-
phase B2 structure. Figure 1b displays the differential scanning
calorimeter (DSC) curves of the (TiZrHf) Ni Co alloys (see
50 50-x x
“Methods”). The Co15 alloy undergoes a martensitic transformation
withamartensitestarttemperature(Ms)of~500K(heating)and~480K
(cooling).AstheCocontentincreases,Msdecreasessharply,andno
martensitictransformation(MT)isobservedfortheCo23andCo25
alloyswithintheDSCdetectionrange(~100–600K).Additionally,the
exothermic/endothermic MT peaks weaken progressively with
increasingCocontent,reflectingacontinuousreductionintransfor-
mationenthalpy(SupplementaryFig.1).Tofurtherprobethepotential
forMTatcryogenictemperatures,weperformedelectricalresistivity
(ER)measurementsoverabroadtemperaturerange(~5–700K)(see
“Methods”).AsshowninFig.1c,thermalhysteresisloopsareevidentin
the Co15, Co20 and Co22 alloys during heating and cooling cycles,
consistentwiththeDSC-observedMTsignatures(Fig.1b).Notably,no
evidenceofMTisobservedintheCo23andCo25alloysevenupon
cooling to ~5K,confirming the complete suppression ofmartensitic
transformationinthesecompositions.

To probe the elastic behavior of these alloys, we conducted
dynamicmechanicalanalysis(DMA)measurementontheCo15,Co22
andCo25alloys(see“Methods”,SupplementaryFig.1d–f).IntheCo15
alloy,thestoragemodulusexhibitsadistinctdipnear490K,accom-
paniedbyacorrespondingpeakininternalfriction—consistentwith
theMTtemperatureidentifiedbyDSCandERmeasurements.Notably,
neitherthepositionofinternalfrictionalpeaknorthestoragemodulus
dipdisplaysfrequencydependence,ahallmarkofconventionalmar-
tensitictransformations29,30.AsimilarDMAresponsewasobservedfor
the Co20 alloy (Supplementary Fig. 2a). In contrast, the Co22 alloy
exhibitsclearfrequency-dependentbehaviorinbothstoragemodulus
and internal friction, with a local modulus minimum and friction
maximumnear200K(Fig.1e),whichresemblesastrainglasstransition
(STG)29.FortheCo23(SupplementaryFig.2b)andCo25alloys(Fig.1f),
neither MT nor STG-like behavior is observed. Instead, these alloys
display a pronounced Elinvar effect—near-invariant elastic modulus
acrossabroadtemperaturerange(130–630K)—aligningwithourprior
finding20.

Combiningtheseresultswithadditionalthermogravimetricana-
lysisdata(seeSupplementaryFig.3)spanningawidecompositional
range(TiZrHf) Ni Co (0<x<30),weconstructacomprehensive
50 50-x x
phasediagramforthe(TiZrHf) Ni Co system(Fig.2).AtlowCo
50 50-x x
concentrations (x<15), the alloys stabilize into a high-entropy B2
phaseatelevatedtemperatures,transformingtoahighentropyB19′
phase upon cooling, with the MT temperature decreasing mono-
tonicallywithincreasingCocontent.Intheintermediatecomposition
range (15<x<22), we observe a STG-like behavior, suggesting fru-
strated local transformations31. Remarkably, when the Co content
exceeds that of the Co23 alloy (x>23), the high-entropy B2 phase
persists as the sole stable phase across an exceptionally wide tem-
perature range from ~1000K to ~5K. This complete suppression of
martensitic transformation highlights the profound influence of
compositiontuningonphasestabilityinthismulti-principal-element
alloysystem.

Hookeanversusnon-Hookeansuperelasticity
Conventionalcompressiontestswereconductedtocharacterizethe
elasticresponseofthepolycrystalline(TiZrHf) Ni Co bulkalloys
50 50-x x
(see “Methods”). As illustrated in Fig. 3a, a striking transition from
lineartononlinearelasticity—followedbyareversiontolinearelasti-
city—isobservedastheCocontentincreasesfrom15to25at%.The
single-phaseB19’Co15alloyexhibitsclassicalHookeanelasticity,dis-
playingalinearelasticstress-strainrelationship.Incontrast,theCo20
(B19’ and B2) and Co22 (B2 singlephase) alloys exhibit a nonlinear
elasticbehavior,asevidencedbytheircurvedstress-strainresponses.
Remarkably,furtherCoadditionrestoreslinearelasticityinthesingle-
phase B2 Co23 alloy and Co25 alloy. Cyclic loading-unloading tests
(Fig.3b)confirmidealHookeanelasticityintheCo15alloy,withperfect
overlap between loading and unloading curves. However, the Co20
and Co22 alloys develop mechanical hysteresis, indicting intrinsic
energydissipationconsistentwiththeirnon-Hookeanbehavior.Con-
versely,theCo23andCo25alloysreverttolinearelasticity,demon-
stratingacomposition-dependentrecoveryofHookeanbehavior.

Toinvestigatetheintrinsicelasticityofsingle-crystallinealloys,we
performed microcompression tests on the single-phase B2 Co22,
Co23,Co25,andCo27alloys(see“Methods”).Theinversepolefigure
mapsinSupplementaryFig.4confirmthecrystallineorientationsof
individualmicropillars.AsshowninFig.3c,the[001]-orientedCo22
micropillar exhibits Hookean (linear elastic) behavior until yielding,
whereas [011]- and [111]-oriented micropillars display pronounced
nonlinear superelasticity, indicative of stress-induced martensitic
transformation. The strong anisotropic martensitic transformation
behavior was also reported in other B2 austenite systems, such as
CuZr-based SMAs32,33. The deformation behavior of the B2 phase is
strongly orientation-dependent because the B2 to B19’ martensitic
transformationisactivatedthroughshearalongthe{011}<100> slip
system.Theresolvedshearstressonthesesystemsvariessignificantly
withcrystalorientation33.The[001]axishasanalmostzeroSchmid
factorforalltransformationvariants,suppressingthestress-induced
martensitic transformation and resulting in purely linear elastic
behavior. In contrast, the [011] and [111] orientations possess much
higherSchmidfactors,enablingactivationofthetransformationshear
and giving rise to the observed nonlinear superelasticity. Cyclic
microcompressiontestsrevealrecoverablestrainsof~8%inthe[011]-
orientedCo22micropillars(Fig.3d),withsimilarbehaviorobservedfor
the[111]orientation(SupplementaryFig.5).TheCo23alloyexhibits
analogous orientation-dependent elasticity (Supplementary Fig. 6),
withlinearelasticityalong[001]andnonlinearelasticityalong[011]
and[111].Thisanisotropycanbeattributedtotheabsenceofsufficient
shear strain to drive the B2–B19’ transformation along the [001]
orientation10.Incontrast,Co25andCo27micropillarsexhibitpurely
linearelasticityacrossallcrystallographicorientations(seeref.34and
SupplementaryFigs.7and8),withnoevidenceofmartensitictrans-
formation. These findings suggest that a critical Co concentration
betweenCo23andCo25alloysfullysuppressesmartensitictransfor-
mation,stabilizingtheB2phaseundermechanicalloading.Moreover,
theobserveddifferenceinelasticstrainbetweenbulkandmicropillar
compression is strongly influenced by microstructures. In poly-
crystalline bulk samples, the measured elastic strain represents an
average over multiple grains and grain boundary constrains, which
reduces the apparent elastic limit. In contrast, the micropillar com-
pressionwouldenableustoprobetheintrinsicorientation-dependent
and superelastic behavior within a single crystal free from grain
boundary constraints. Because the transformation strain is highly
anisotropic, the single-crystal micropillars naturally exhibit a larger
recoverable strain than the orientation-averaged bulk material. To
further investigate the temperature dependence of the superelastic
behavior, we performed cyclic micro compression tests on [011]
orientedCo22micropillarsatvarioustemperatures,asshowninSup-
plementaryFig.9.Theresultsclearlydemonstrateatransitionfrom
nonlinear elastic behavior to linear elastic behavior with increasing
temperature,withacriticaltransitionoccurringaround~60°C.This
temperature-dependentevolutionisfullyconsistentwiththeclassical
frameworkfordeformationinSMAs35.

Followingthemethodologyinref.36,weevaluatedthedamping
performanceofbothCo22andCo23alloysinglecrystalsusingtheloss
factorη= ΔW ,whereΔWrepresentstheenergydissipatedperhys-
π(cid:1)W
teresis cycle, m a ax nd W denotes the maximum stored energy. For
max
structuralapplicationsinvolvingelasticloading,thefigureofmeritfor
optimal damping is defined as E1=2(cid:1)η36,37, where E is the Young’s
modulus.AsshowninFig.3eandSupplementaryData1,theCo22and
Co23alloysexhibitexceptionaldampingcharacteristics,withfigures
ofmeritreaching1.1–1.2.Thisperformancesurpassesthatofconven-
tional high-damping materials, including Cu-Al-Ni alloys (maximum
figureofmerit~0.9).Thesuperiordampingcapacityofthesealloys,
combined with their excellent mechanical properties, makes them
particularly promising for microelectromechanical systems. Such
systemsrequirepassivedampingsolutionstocontroloscillationsand
mitigate shocks in micro-resonators, sensors and actuators38,
suggesting significant potential for practical applications of these
alloysinadvancedmicrodevicetechnologies.

Atomic-scalestructuralvariationandlatticestrain
To elucidate the atomic-scale mechanisms governing the transition
from Hookean to non-Hookean superelasticity, we conducted a
detailedinvestigationofthecrystallineandlocalatomicstructuresin
therepresentativeCo15,Co22,andCo25alloys.AsshowninSupple-
mentaryFig.10,theCo15alloyadoptsthemartensiticB19′structure.In
contrast,theCo22alloymaintainsasingle-phaseB2structure(Sup-
plementaryFig.11a).Notably,theCo25alloymaintainsasingle-phase
B2structure(SupplementaryFig.11b–d)withoutanydetectablemar-
tensiticvariantsevenat90K39,indicatingexceptionalstabilityoftheB2
phase across the entire temperature range probed. Atomic-scale
structural and chemical evolution across these compositions is
revealed by aberration-corrected scanning transmission electron
microscopy high-angle annular dark-field (STEM-HAADF) imaging
(Fig.4a–c).Theimagesshowdistinctcontrastvariations,indicativeof
chemical heterogeneity inherent to these multi-principal-element
alloys. The corresponding atomic intensity line profiles (Fig. 4d–f),
extractedfromtheboxedregionsintheSTEM-HAADFimages,quan-
titativelycorroboratethesecompositionalfluctuations.TheCo22and
Co25alloysexhibitmorepronouncedintensityvariationsthanCo15
alloy, signifying enhanced chemical short-range ordering and local
elemental partitioning with increasing Co content. This chemical
evolution is accompanied by a clear structural progression, as con-
firmedbyselected-areaelectrondiffractionpatterns(Fig.4g–i).

Criticalinsightsintolatticestrainwererevealedthroughatomic-
scalestrainmappingbasedongeometricphaseanalysis(GPA)ofhigh-
resolutionSTEMimages.ThevonMisesstraindistributions(Fig.4j–l)
exhibit striking variations across the three alloys. The Co15 alloy
exhibitsuniform,low-magnitudestrainfields,withanarrowdistribu-
tion (inset histogram) peaked near zero—a signature of its
homogeneous, low-strain martensitic (B19′) structure. In stark con-
trast,theCo22alloydisplaysasubstantiallyhigherandheterogeneous
strain distribution, with a broad peak extending to elevated values.
This signifies pronounced lattice distortion, which we attribute to
strongchemicalfluctuationsandlocalelasticmisfitwithinthehigh-
entropyB2phase.Notably,theCo25alloyexhibitsastraindistribution
that isreduced inmagnitude and heterogeneity compared to Co22
alloy,indicatingthatfurtherCoadditionbeyondacriticalconcentra-
tionalleviates, rather than enhances, the lattice strain. This non-
monotonicevolutionofstrain—peakingatanintermediatecomposi-
tion—isakeypredictoroftheanomaloussuperelasticbehavior.

Mechanisticunderstandingthroughfirst-principlescalculation
To elucidate the atomic-scale mechanisms governing composition-
dependent elastic transitions in (TiZrHf) Ni Co alloys, we per-
50 50-x x
formed first-principles density functional theory (DFT) calculations
(see“Methods”).StructuralmodelsofB2(cubic)andB19′(monoclinic)
phases—keytounderstandingdivergentsuperelasticbehaviors—were
constructed and relaxed. Figure 5a reveals distinct atomic packing
geometries in these phases at the equiatomic Ni:Co ratio (25:25),
visualized along major crystallographic orientations. DFT-derived
formation enthalpies (ΔH) (Fig. 5b) exhibit a critical composition-
dependentcrossover.Below25%Co,theB19′structureisenergetically
favored(ΔH B19′<ΔH
B2
);whilebeyondthisthreshold,theB2structure
becomesthermodynamicallypreferred.Thistrend,corroboratedby
theTOTENenergycalculations(SupplementaryFig.12),persistseven
withoutconfigurationalentropycontributions.Theenthalpyreversal
at x≈25 aligns with experimental phase stability observations and
implies a fundamental link between Co content and the B2↔B19’
structuralenergetics.

Figure 5c, d presents the calculated von Mises and volumetric
strain distributions as a function of Ni:Co ratio (see “Methods”),
resultingfromlatticedistortionsintheB2andB19′phases.IntheB2
phase,boththevonMisesstrainandatomicdisplacements(Supple-
mentaryFig.13)decreasemonotonicallywithincreasingCocontent.
In contrast,theB19′phaseexhibitstheoppositetrend,withvonMises
strainincreasingasCocontentrises(Fig.5c).Giventhatlatticestrain
correlates with system potential energy and enthalpy23, these strain
variationsalignwiththecomputedenthalpiesofbothphasesacross
differentCoconcentrations.Notably,theseresultsuncoverahidden
strainorderimposedbyCothatinfluencestheB2–B19′transformation
andsuperelasticbehavior.AtlowCocontent,theB19′phaseisless
distorted than B2, thermodynamically favoring the transformation
fromB2toB19’.ThispreferencereversesathighCocontent,where
B19’becomesmorestrained.Thecrossoverpoint—wherebothphases
experiencecomparablelatticedistortion—isparticularlysignificant,as
itsuggestsageometrically“frustrated”statethatmayinhibitcoordi-
nated phase transition. Crucially, this transition can be precisely
modulatedbyadjustingtheNi:Coratio,asdemonstratedexperimen-
tallyinFig.2.Incomparison,volumetricstrainremainslargelyinsen-
sitive to Co content in both phases, indicating a secondary role in
strain-governedphasetransformation.

To further elucidate the influence of the Ni:Co ratio, we per-
formed detailed electronic structure calculations (see “Methods”).
GiventhatTi,ZrandHfsharethesamevalenceelectronconfiguration,
Zrwasselectedasarepresentativemodelsystemtosimplifythepre-
sentation of electronic structure results. The electron localization
function (ELF) on the (100) plane of the B2 phase (Fig. 5e) reveals
enhancedelectronlocalizationbetweenZratomsinZr-Copairsrela-
tivetoZr-Nipairs.ThissuggeststhatCoformsstrongercovalent-like
bondswithZr,therebystabilizingtheZr-occupiedB2sublatticeand
reducinglatticedisplacementandlatticedistortion.Consistentwith
this,thedisplacementsofTiandHfatomsalsodecreasesystematically
withincreasingCocontent(SupplementaryFig.13).Incontrast,the
ELF distribution on the (001) plane of the B19′ phase exhibits the
oppositebehavior(Fig.5e):substitutionofNiwithCoweakenselec-
tronlocalization,resultinginamorecompliantZrsublatticewithlar-
ger atomic displacements. To assess the influence of Ti and Hf
elements,we further performed DFT calculations for TM-Xsystems
(TM=TiandHf,andX=NiandCo).OurcalculationsshowthatCocan
induceaBCC-likeatomicordernotonlyinZrCobutalsoinTiCoand
HfCo.Ni,however,doesnotproducethiseffectinanyofthethree
systems (see Supplementary Fig. 14). Notably, the Ti-Co system
undergoes the most sensitive transformation, fully converting to a
standardB2phase.AthigherCocontent,thispromotesatomic
slipalongthe[100]directionandfacilitatestheformationofB2-like
clusterswithintheB19′matrix(SupplementaryFig.15a).Theseelec-
tronic and structural changes align with the calculated enthalpies
(Fig.5b),whichindicatethattheB2phaseismorestablethanB19′ata
Ni:Coratioof0:50.NosuchB2-likeclusteringisobservedinB19′ata
Ni:Coratioof50:0afterstructuralrelaxation(SupplementaryFig.15b).
Boththemagnitudeofatomicdisplacements(SupplementaryFig.15c)
andtheextentofB2-likeclustering(SupplementaryFig.15d)increase
withCocontentinB19′,indicatingagrowingtendencyforB19’-to-B2
reversionathigherCoconcentrations.

To further probe the electronic origins of phase stability, we
comparedthetotaldensityofstates(TDOS)foralloyswithNi:Coratios
of50:0,25:25,and0:50beforeandafterstructuralrelaxation,witha
focusonorbitalhybridization.IntheB2structure,theTDOSofthe
Ni:Co=50:0 alloy undergoes a substantial reshaping after relaxation
(Supplementary Fig. 16). This is attributed to significant lattice dis-
tortion,whichdisruptsthecrystalfieldandpromotesdiverseorbital
hybridization. In contrast, the TDOS profile of the Ni:Co=0:50 alloy
remainslargelyunchanged,consistentwithitsminimallatticedistor-
tion.Notably,anadditionalhybridizationpeakemergesinthebonding
statesneartheFermilevelintheCo-richalloy,correspondingtoCod-
eg—d-eginteractions(SupplementaryFig.17),whichfurtherenhances
structuralstability.FortheB19′structure,theNi:Co=50:0alloyexhibits
astableTDOScurveafterrelaxation,withtheFermilevelpositionedat
thebottomofapseudogap—asignatureofelectronicstabilityandlow
distortion(SupplementaryFig.18).ThiscontrastssharplywiththeCo-
richB19’alloy(Ni:Co=0:50),whichshowsgreaterelectronicdisorder,
reflectingitsstructuralinstabilityandpropensityfortransformation.

Methods
Samplepreparation
The present (TiZrHf) Ni Co alloys were fabricated by an arc-
50 50-x x
melting furnace in Ti-gettered high-purity argon atmosphere. The
master alloys were papered from commercially pure elements with
puritiesatleast99.9wt.%.Theingotswereturnedandremeltedatleast
fourtimestoensurethechemicalhomogeneity,andthendropcast
into a water-cooled copper plate mold with dimension of
5×10×50mm3. The as-cast ingots were encapsulated into vacuum
quartz tubes and thermal annealed at 1000°C for 6h with water
quenchingtoeliminatepossiblechemicalinhomogeneities.

Structuralcharacterization
The crystalline structures of the present alloys were determined
throughanXRDequipment(D8ADVANCEDaVinci,Bruker)usingCu-
Kαradiationwithwavelengthof1.5418Å.Themicrostructurechar-
acterizationwasconductedinascanningelectronmicroscope(SEM,
LYRA3 GMU, TESCAN) equipped with electron backscatter diffrac-
tion (EBSD, Nordlys Max3, Oxford Instruments) detector for crys-
tallographicanalysis.TheEBSDsampleswerepaperedbymechanical
grindingusingSiCsandpapersandthenpolishedstepbystepusing
diamondandaluminaoxidationsuspension.Thedetailedstructure
analysiswascarriedoutinaTEMequipment(FEITalosF200XG2,
Thermofisher).WhereastheatomicscaleSTEM-HAADFanalysiswas
conductedonthesphericalaberrationcorrectedTEM(FEISpectra
300,Thermofisher).TheGPAwasperformedusingtheopen-source
software Strain++44, which enables the determination of various
strain components in the atomic strain field from high-resolution
TEMimages.Thecryogenicstructureanalysiswascarriedoutona
TEMequipment(JEOL2100F)equippedwithacryogenicTEMsample
holder.TheTEMsampleswerepreparedfollowingtwomethods,i.e.,
fabricationusingionmillingandfocused-ionbeam(FIB).Forthese
ionmillingsamples,thesheetTEMfoilsweremechanicallygrindedto
athicknessabout40μmandthenpunchedintodiscswithdiameter
of3mm.TheTEMfoilswerefurtherdimpledandthinnedusingion
milling in a Precision Ion-beam Polish System (PIPS, PIPS II 695,
Gatan). For the FIB-fabricated TEM samples, a 2μm-thick
protectivelayerofPtwasfirstdepositedovertheareaofinterest.The
lamellas with dimension about 10×7×1.5μm3 were then
extractedandattachedtoacopperTEMgrid.Finally,thelamellawas
thinnedtobelow100nmbyalternatelymillingeachsideattiltangles
of±1.2°.

Mechanicalcharacterization
The macroscopiccompression tests were conducted on a universal
testmachine(MTEST5000WTensileStage,GATAN)withquasi-static
strainrateof1×10−3s−1.Thecylindricalcompressionsamples(3.5mm
indiameterand7mminheight)werepreparedbywirecutting,fol-
lowedbymechanicallygrindingandpolishingtoamirrorsurface.A
digitalimagecorrelated(DIC)systemwasusedforthein-situstrain
analysis(Vic-2D,CorrelatedSolution).Themicropillarsampleswere
preparedusingtheSEM/FIBsystemusingtheannualmillingmethods
withadiameterabout1μmandheightabout2μm.Themicropillar
compressiontestswerecarriedoutonaHysitronTI950TriboIndenter
system. The high-temperature micropillar compression tests were
carried out on the Hysitron TI 950 TriboIndenter system equipped
withaheatingstage.

Phasetransformationcharacterization
Latentheatandcharacteristictemperaturesassociatedwithmarten-
sitictransformationsweredeterminedbyaDSC(TA-Q200)atacool-
ing/heating rate of 10K/min. Electrical resistivity (ER) curves were
detectedbyafour-probemethodunderaconstantcurrentof100mA
andatacooling/heatingrateof3K/min.Storagemodulusandinternal
frictioncurvesweremeasuredbyadynamicmechanicalanalyzer(TA-
Q800)inasinglecantilevermodewithacoolingrateof2K/minanda
frequencyrangefrom0.2to20Hz.

DFTcalculations
DFTcalculationswereconductedusingtheViennaAb-initioSimula-
tion Package45 to investigate the influence of Co content on lattice
strains in the (TiZrHf) Ni Co alloy system. To accurately model
50 50-x x
thesecompositions,whicharehighlysensitivetotheNi/Coratio,we
constrained the special quasi-random structures (SQS) supercell to
100 atoms. For the B2 alloys, SQS were generated within
5×5×2supercells,whiletheB19′alloysweremodeledusing4×1×5
SQSsupercells.TakingtheNi:Co=1:1compositionasarepresentative
case, we performed volume-energy fitting using more isotropic
supercells,a2×2×2supercellforB2anda3×2×2supercellforB19’.
AsshownintheTable S1,theresultinglatticeconstants,when nor-
malized totheirconventionalunitcells,deviated bylessthan 0.3%.
Thisexcellentagreementconfirmsthatthesystematicbiasfromthe
anisotropic100-atomsupercellsisnegligible.Todeterminetheequi-
libriumlatticeparameters,theuniformscalingfactorofeachstructure
wassystematicallyvariedfrom0.94to1.05inincrementsof0.01,and
single-pointtotalenergieswerecomputedforeachoftheresulting12
configurations. The energy–volume data were subsequently fitted
usingtheBirch–Murnaghanequationofstate,yieldingoptimizedlat-
ticeconstantsforeachalloycomposition.Followingthis,fullstructural
relaxationswereperformed,allowingatomicpositionstorelaxfreely
whileconstraininglatticeshapedeformations.Forthelower-symmetry
B19’supercells,usingtheNi:Co=1:1compositionasarepresentative
example,wefirstappliedindependent−1%to+1%perturbationstothe
threelatticeparametersoftheinitialstructure.Thisprocessconfirmed
thatusingauniformscalingfactorprovidesthepathwayofsteepest
energydescent(SupplementaryFig.19a).Withtheoptimizedlattice,
wefurtherappliedanothersetofindependent−2%to+2%perturba-
tions to the three lattice constants. This step confirmed that the
optimizedstructureislocatedatthebottomofthepotentialenergy
surface, thereby validating the uniform scaling approach (Supple-
mentary Fig. 19b). Periodic boundary conditions were applied
throughout, and the projector augmented-wave method46 was
employedinconjunctionwiththePerdew–Burke–Ernzerhofgeneral-
izedgradientapproximationforexchange-correlationinteractions47.
Geometryoptimizationswerecarriedoutusingtheconjugategradient
algorithm,withconvergencethresholdssetto1×10−5eV/atomfortotal
energyand0.01eV/Åforresidualatomicforces.Aplane-waveenergy
cutoffof400eVwasadoptedforbothB2andB19′phases.Brillouin
zonesamplingwasperformedusingMonkhorst–Packk-pointgridsof
3×3×3forB2and2×4×2forB19′structures.Formationenergyis
definedastheenergydifferencebetweenthecompoundanditscon-
stituent elements in their standard states. Thesecomputational set-
tings were also applied to the electronic structure calculations of
binaryB19′ZrCoandZrNicompounds,whereinbothlatticeshapeand
atomicpositionswerefullyrelaxed.TheB2-likeorderingintherelaxed
B19′ structural (TiZrHf) Ni Co alloy is analyzed by Common
50 50-x x
NeighborAnalysis(CNA)moduleinOVITOsoftware.Thevolumetric
straintensorηVolumeandVonMisesshearstraintensorηMisessinthiswork
werecalculatedaccordingtothefollowingformulations48:

ηVolume=
η xx+η yy+η
zz (1)
i 3

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u u t (cid:3) η yy (cid:3)η zz (cid:4) 2 + (cid:5) η xx (cid:3)η zz (cid:6) 2+ (cid:3) η xx (cid:3)η yy (cid:4) 2
ηM i ises= η2 yz+η2 xz+η2 xy+ 6

(2)

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors present a comprehensive study on the tunability of superelastic behavior in a (TiZrHf)50Ni50-xCox high entropy\nalloy system. This work stands out for its elegant demonstration of continuous and reversible transitions between Hookean\nand non-Hookean superelasticity, achieved through remarkably minor compositional variations (<2 at.%), unifying the two\nphenomena previously observed only in different alloy systems. By systematically varying the Co content, a reversible\ntransition between Hookean and non-Hookean superelasticity was achieved, with recoverable strains up to ~8%. The\ncombination of sophisticated experimental characterization and thorough theoretical calculations provides a convincing\nphysical understanding of the underlying “hidden strain order” governed superelastic mechanism.\nHere are a few technical comments for the authors:\n1. In the phase diagram presented in Figure 2, what is denoted by the blue dashed line? A brief note in the caption would be\nbeneficial.\n2. Based on the results shown in Figure 3, it can be observed that crystal orientation has a significant influence on\ndeformation behavior. Why do [001] orientated single crystals exhibit linear elastic deformation, while those with [011] and\n[111] orientations demonstrate nonlinear superelastic behavior? What is the underlying mechanism behind the effect of\ncrystal orientation on deformation behavior?\n3. The DFT models (SQS) are well-justified, however the binary-like models (ZrNi/ZrCo) are used to represent the full HEA\nsystem in Fig. 5. The authors should briefly discuss the influence of other elements such as Ti and Hf.\n4. It's better to ensure consistent use of the alloy naming convention. The text primarily uses “Co15, Co20...”, but in some\ncases (e.g., Page 3, “Co23 and Co25 alloys”), the “alloy” suffix is dropped. A consistent style (e.g., always using “Co25 alloy”\nor simply “Co25”) improves readability.", "reviewer_2": "In the manuscript titled “Tuning superelasticity in high entropy alloy via a hidden strain order,” Yang and colleagues have\nfabricated (TiZrHf)50Ni50-xCox high-entropy superelastic, characterized the transformation behaviors, superelastic stress,\nrecovery strain, and carried out microstructural analysis and DFT calculations. Overall, the authors have gained solid and\nuseful data and conducted the analysis. However, the following issues exist and need to be addressed.\n1. Justify the phase diagram. Based on the limited dataset from Figure 1, the authors propose a composition-temperature\nphase diagram. The readers may wonder about the validation of the phase diagram, although the variable is set to be the\ncomposition of Co. The phase diagram should have been constructed from a well-supported dataset, either experiments or\nsimulations. If possible, the authors are advised to add relevant experiments or discussions.\n2. Clarify the discrepancy between the stress-strain curves. In Figure 3, the macroscopic stress-strain curves show an elastic\nstrain of ~5% and the micropillar stress-strain curves show an elastic strain of ~10%. The discrepancies and connections\nought to be well ascertained with microstructural features. Also, the impact of different testing routes should be explained\nwell. In particular, the artifacts associated with the micropillar test should be cautioned.\n3. Reconcile the temperature-dependent stress hysteresis. The authors have done a good job of showing the characteristic\nsuperelastic behaviors. From the results of Figures 1 and 2, the readers may wonder how the superelastic behaviors vary in\nthe wide temperature regime, and in particular, how the stress hysteresis depends on the temperature. The authors are\nexpected to explain, and even better, provide an experimental pathway to justify.\n4. Strengthening the connection between atomic-scale strain and atomic-size mismatch. The authors have provided in-situ\nTEM observation of lattice strain through atomic-scale strain mapping. Later, the authors have claimed the complex interplay\nof atomic-size mismatch and chemical ordering to be the main factor in the fundamental mechanism, but the connection is\nweak. The authors are advised to strengthen the connection, for example, by in situ correlation experiments.\n5. Assess the reversibility. Reversibility and stability are of great importance for the applications of superelastic materials.\nBecause the fatigue life is closely related to stress hysteresis and the (TiZrHf)50Ni50-xCox high-entropy alloy has quite a\nlarge stress hysteresis (depending on the temperature), the audience may wonder what the reversibility and stability of the\nhigh-entropy superelastic alloy would look like. If possible, the authors are advised to add relevant experiments or\ndiscussions.\n6. Minors. (1) In the Abstract, the mechanism should be expounded in an information-rich manner. (2) Please ensure the\nfonts in Figures are legible and consistent in size.", "reviewer_3": "Referee's Comments on \"Tuning Superelasticity in High Entropy Alloy via a Hidden Strain Order.\"\nThis paper presents an interesting study of the mechanical properties of a class of B2-B19' high entropy alloys. The authors\nfind that by tuning the composition, they can tune the properties of the martensitic transformation. The ability to tune the MT\nis attributed to changes in the stress fluctuations associated with the composition fluctuations inherent in an HEA.\nOverall, I find the paper interesting and worthy of publication. I do, however, have a few questions/observations that I would\nlike the authors to address before publication.\n(1) Figure 2. I think I understand the origin of the plot symbols and most of the lines. I think I even understand why the blue\nline is dashed above 22% Co. Nevertheless, the figure would be more useful if the origin of the various features within it\nwere described in the caption.\n(2) With respect to fig. 3, I presume the stress vs. strain curves were obtained at room temeperature. If so, this should be\nstated in the manuscript.\n(3) For the geometric phase analysis, I presume the authors need to choose a reference state from which to measure the\nstrain. How was this chosen? Does this choice affect the computed von Mises strains?\n(4) The DFT calculations use cells that are quite anisotropic in shape. For example, the B2 unit cells extend much more in\nthe x and y directions than they do in the z directions. It seems that these will insure that one direction is different than the\nother two directions (at least for the B2 phase). Why was this choice made? Also, the description of the minimization\nprocedure makes sense for the B2 alloys, but for the B19' structure, one needs to vary the lattice parameters independently.\nIs this what was done? If so, for the B19' structure, I would expect an unusually large number of structures (over 1700 for a\nsingle composition) would be necessary. The authors should explain this procedure more carefully with respect to the B19'\nstructure.\n(5) Supplementary figure S3 shows the orientation of the grains for four samples. The figure also shows that the grain size is\ndependent upon Co composition. In particular, the Co22 structure appears to have a much larger grains size, on average,\nthan the higher Co concentration alloys. The author should comment on this, and assess to what extent the larger grain size\nmight impact their conclusions.\n(6) Figure S10 does not have a key telling the reader which atoms are which. This should be fixed."}, "author_response": "General Responses\nDear Reviewers,\nWe extend our sincere gratitude for your insightful comments and constructive suggestions, which\nhave been invaluable in enhancing the quality of our manuscript. In response to your feedback, we\nhave undertaken significant revisions.\nFor Reviewer #1, we have clarified the phase diagram annotations, provided a detailed explanation\nof the crystallographic anisotropy governing deformation, and supplemented our DFT calculations\nto elucidate the roles of Ti and Hf. For Reviewer #2, additional TGA data has been provided to\nfurther validate the phase diagram. We have also explained the discrepancy in elastic strain between\nbulk and micropillar tests, conducted new temperature-dependent cyclic tests to clarify hysteresis\nevolution, and strengthened the discussion on the connection between chemical short-range order\nand lattice strain. For Reviewer #3, we have optimized figure captions for clarity, specified testing\nconditions, justified the reference selection for geometric phase analysis, validated our DFT\nsupercell approach, and clarified the influence of grain size.\nAll suggestions have been carefully addressed, and the corresponding revisions have been\nthoroughly incorporated into the main text and supplementary materials. Our detailed point-by-point\nresponses follow below.\nThank you again for your time and expertise.\nBest Regards,\nProf. Y. Yang, Prof. S.J. Zhao, Prof. J.F. Gu\nOn behalf of all co-authors\nPoint-by-Point Responses\nReviewer #1 (Remarks to the Author):\nThe authors present a comprehensive study on the tunability of superelastic behavior in a\n(TiZrHf) Ni Co high entropy alloy system. This work stands out for its elegant demonstration of\n50 50-x x\ncontinuous and reversible transitions between Hookean and non-Hookean superelasticity, achieved\nthrough remarkably minor compositional variations (<2 at.%), unifying the two phenomena\npreviously observed only in different alloy systems. By systematically varying the Co content, a\nreversible transition between Hookean and non-Hookean superelasticity was achieved, with\nrecoverable strains up to ~8%. The combination of sophisticated experimental characterization and\nthorough theoretical calculations provides a convincing physical understanding of the underlying\n“hidden strain order” governed superelastic mechanism.\nResponse: We sincerely appreciate the reviewer’s insightful and positive comments on our work.\nWe would like to address the concerns raised and provide the following responses.\nHere are a few technical comments for the authors:\n1. In the phase diagram presented in Figure 2, what is denoted by the blue dashed line? A brief note\nin the caption would be beneficial.\ndiagram (Figure 2) have been added in the revised manuscript to avoid any possible\nmisunderstanding.\nIn the revised captions:\n“The solid black squares and open blue circles are experimental data set. The black solid line\ndenotes the martensite start temperature M, while the solid and dashed blue lines indicate the strain\ns\nglass transition temperature T .”\ng\n2. Based on the results shown in Figure 3, it can be observed that crystal orientation has a\nsignificant influence on deformation behavior. Why do [001] orientated single crystals exhibit linear\nelastic deformation, while those with [011] and [111] orientations demonstrate nonlinear\nsuperelastic behavior? What is the underlying mechanism behind the effect of crystal orientation on\ndeformation behavior?\nResponse: We thank the reviewer for this insightful question. The martensitic transformation (MT)\nis well known to exhibit strong crystallographic anisotropy, as widely reported in the literature [1–\n2]. The orientation dependence observed in our Co22 alloy is consistent with the transformation\ncharacteristics of other B2 austenite systems, such as CuZr-based SMAs [1–2]. In B2 austenite, the\nB2 to B19’ martensitic transformation proceeds through a lattice shear associated with the\n{011}<100> shear system [3]. The activation of this transformation is therefore governed by the\nB2\nresolved shear stress on these transformation systems, quantified by the Schmid factor\n. As shown in Fig. R1, the Schmid factor reaches a high value (~0.5) along the\n𝑚 =\n<111> direction, decreases toward <011> , and drops sharply to nearly zero when approaching\nB2 B2\n𝑐𝑜𝑠(𝜑)∙𝑐𝑜𝑠(𝜆)\nthe <001> axis. The [001] loading direction is nearly perpendicular to the transformation shear\nB2\ndirections, resulting in a very low Schmid factor for all transformation variants. As a result, the\nstress-induced MT is effectively suppressed, and the deformation is dominated by purely elastic\ndeformation, yielding a linear elastic response. In contrast, the [011] and [111] orientations exhibit\nsignificantly larger Schmid factors, allowing efficient activation of transformation shear. This\nfavorable geometric alignment promotes the nucleation and growth of martensitic variants, giving\nrise to pronounced nonlinear superelasticity with characteristic transformation-induced strain and\nhysteresis. To clarify this point, we added more discussion on the orientation-dependent elastic\nresponse in the revised manuscript.\n2\n[Figure Redacted]\nFigure R1. (a)-(b) The side and top views of SEM micrographs, respectively, showing a transformed\npillar via shearing on a specific plane and along a specific direction. (c) A unit stereographic triangle\nshowing the distribution of Schmid factor, calculated with respect to the {011}<100> shear system.\nB2\n(d) The measured critical stress for the onset of MT as a function of the calculated Schmid factor\nwith respect to the {011}<100> shear system. [1]\nB2\nIn revised manuscript:\n“As shown in Fig. 3(c), the [001]-oriented Co22 micropillar exhibits Hookean (linear elastic)\nbehavior until yielding, whereas [011]- and [111]-oriented micropillars display pronounced\nnonlinear superelasticity, indicative of stress induced martensitic transformation. The strong\nanisotropic martensitic transformation behavior was also reported in other B2 austenite systems,\nsuch as CuZr-based SMAs32,33. The deformation behavior of the B2 phase is strongly orientation-\ndependent because the B2 to B19’ martensitic transformation is activated through shear along the\n{011}<100>B2 slip system. The resolved shear stress on these systems varies significantly with\ncrystal orientation33. The [001] axis has an almost zero Schmid factor for all transformation\nvariants, suppressing the stress-induced martensitic transformation and resulting in purely linear\nelastic behavior. In contrast, the [011] and [111] orientations possess much higher Schmid factors,\nenabling activation of the transformation shear and giving rise to the observed nonlinear\nsuperelasticity.”\nReference:\n[1]Dong, Jie, Yan Huang, Yibo Zhang, Baoan Sun, Ming Yang, Xuerui Wei, Zhichao Lu, Fan Zhang,\nZhiyuan Liang, Jinkui Zhao, Wenli Song, Yuan Wu, Zhaoping Lu, Xun-Li Wang, and Dong Ma.\n\"Anisotropic Martensitic Transformation in B2-Cuzr-Structured Crystallites.\" Acta Materialia 289\n(2025). https://dx.doi.org/10.1016/j.actamat.2025.120872.\n[2] Huang, Yan, Jie Dong, Ming Yang, Yibo Zhang, Zhichao Lu, Xuerui Wei, Jinkui Zhao, Wenli\nSong, Xiongjun Liu, Hui Wang, Xiaobin Zhang, Zhaoping Lu, Xun-Li Wang, and Dong Ma.\n\"Frictional Shear Stress-Induced Incomplete Martensitic Transformation in Mono-Crystalline B2-\nCuzr Spherulites.\" Acta Materialia 267 (2024). https://dx.doi.org/10.1016/j.actamat.2024.119705.\n[3] Otsuka, K. and X. Ren. \"Physical Metallurgy of Ti–Ni-Based Shape Memory Alloys.\" Progress\nin Materials Science 50, no. 5 (2005): 511-678. https://dx.doi.org/10.1016/j.pmatsci.2004.10.001.\n3. The DFT models (SQS) are well-justified, however the binary-like models (ZrNi/ZrCo) are used\n3\nto represent the full HEA system in Fig. 5. The authors should briefly discuss the influence of other\nelements such as Ti and Hf.\nResponse: We appreciate the reviewer’s suggestion. Here we adopt the binary-like models to\nelucidate the dominant factors influencing the structural stability and phase transitions. In addition\nto the quinary TiZrHfCoNi models, we further performed supplementary DFT calculations for TM-\nX binary systems (TM = Ti, Zr and Hf, and X = Ni and Co)to address the influence of the individual\nelements. The results are presented in Fig. S14. Our calculations show that Co can induce a BCC-\nlike atomic order not only in ZrCo but also in TiCo and HfCo, while Ni does not produce this effect\nin any of the three systems. Notably, the Ti-Co system undergoes the most sensitive transformation,\nfully converting to a standard B2 phase. This finding is highly consistent with observations in the\nalloys with the B19’ structure, where B2-like atomic order regions containing TiCo are most\nprominently observed.We have added the following discussion to the revised manuscript.\nIn revised manuscript:\n“Our calculations show that Co can induce a BCC-like atomic order not only in ZrCo but also in\nTiCo and HfCo. Ni, however, does not produce this effect in any of the three systems (see Fig. S14).\nNotably, the Ti-Co system undergoes the most sensitive transformation, fully converting to a\nstandard B2 phase.”\nFigure S14. Relaxed atomic structures of TM-X (TM=Ti, Zr, Hf; X=Ni, Co) systems with the B19'\nstructure.\n4. It's better to ensure consistent use of the alloy naming convention. The text primarily uses “Co15,\nCo20...”, but in some cases (e.g., Page 3, “Co23 and Co25 alloys”), the “alloy” suffix is dropped.\nA consistent style (e.g., always using “Co25 alloy” or simply “Co25”) improves readability.\nResponse: Thank you for pointing this out. We have corrected it in the revised manuscript according\nto the reviewer’s suggestion.\nReviewer #2 (Remarks to the Author):\nIn the manuscript titled “Tuning superelasticity in high entropy alloy via a hidden strain order,”\n50 50-x x\nthe transformation behaviors, superelastic stress, recovery strain, and carried out microstructural\nanalysis and DFT calculations. Overall, the authors have gained solid and useful data and\nconducted the analysis. However, the following issues exist and need to be addressed.\nResponse: Thank you for the positive comments on our manuscript, we would like to address the\nraised concerns and make the detailed revisions as follows.\n1. Justify the phase diagram. Based on the limited dataset from Figure 1, the authors propose a\ncomposition-temperature phase diagram. The readers may wonder about the validation of the phase\ndiagram, although the variable is set to be the composition of Co. The phase diagram should have\nbeen constructed from a well-supported dataset, either experiments or simulations. If possible, the\nauthors are advised to add relevant experiments or discussions.\nResponse: We thank the reviewer for raising this important point. For the Co0, Co5, and Co10\nalloys, the martensite start temperatures (Ms) were determined from our thermogravimetric analysis\n(TGA) measurements. We have now added the original TGA curves to Fig. S3 in the revised\nmanuscript for completeness. We would like to emphasize that all data points presented in the phase\ndiagram of Figure 2 are experimentally measured. The combined DSC, TGA, and electrical\nresistivity measurements now form a consistent and well-supported experimental basis for\ndetermining the phase boundaries across the full Co composition range. We have updated the\nmanuscript accordingly to ensure that the construction of the phase diagram is fully justified and\ntransparent to the reader.\nIn revised manuscript:\n“Combining these results with additional thermogravimetric analysis (TGA) data (see Fig. S3)\nspanning a wide compositional range (TiZrHf)50Ni50-xCox (0< x < 30), we construct a\ncomprehensive phase diagram for the (TiZrHf)50Ni50-xCox system (Fig. 2).”\nFig. S3 was added in the revised Supplementary Materials:\nFigure S3. The thermogravimetric analysis curves of Co0, Co5 and Co10 alloys demonstrating the\n5\nmartensitic transformation temperature variations with Co content.\n2. Clarify the discrepancy between the stress-strain curves. In Figure 3, the macroscopic stress-\nstrain curves show an elastic strain of ~5% and the micropillar stress-strain curves show an elastic\nstrain of ~10%. The discrepancies and connections ought to be well ascertained with\nmicrostructural features. Also, the impact of different testing routes should be explained well.\nIn particular, the artifacts associated with the micropillar test should be cautioned.\nResponse: Thank you for the comments. The macroscopic samples are polycrystalline, and their\nelastic response represents an average over many grains with different orientations and grain\nboundaries. As discussed in our response to Reviewer #1, the martensitic transformation in B2\naustenite is highly orientation-dependent. In a polycrystal, grains that are unfavorably oriented for\ntransformation (e.g., near [001]) would suppress the transformation-induced strain, thereby\nlowering the apparent macroscopic elastic strain. In contrast, the micropillar compression would\nenable us to probe the intrinsic superelastic behavior within a single crystal free from grain boundary\nconstraints. Because the transformation strain is highly anisotropic, the single crystal micropillars\nnaturally exhibit a larger recoverable strain than the orientation-averaged bulk material. What’s\nmore, micro pillar compression is a standard approach which was widely adopted in the mechanical\nbehavior in the SMAs [1-5]. Numerous studies on NiTi [1-2], CuZr [3], CuAlNi [4-5] SMAs and\nhigh-entropy superelastic alloys [6] have demonstrated that micropillar testing reliably captures the\nfundamental stress-induced martensitic transformation behavior and often reveals higher elastic or\nrecoverable strains compared with bulk tests due to the removal of microstructural constraints.\nTherefore, the larger elastic strain measured in micropillars is fully consistent with prior literatures\nand reflects the intrinsic mechanical behavior. In the revised manuscript, we have added further\ndiscussion to clarify this issue and its impact on the observed differences between macroscopic and\nmicropillar compression.\nIn the revised manuscript:\n“Moreover, the observed difference in elastic strain between bulk and micropillar compression is\nstrongly influenced by microstructures. In polycrystalline bulk samples, the measured elastic strain\nrepresents an average over multiple grains and grain boundary constrains, which reduces the\napparent elastic limit. In contrast, the micropillar compression would enable us to probe the\nintrinsic orientation dependent and superelastic behavior within a single crystal free from grain\nboundary constraints. Because the transformation strain is highly anisotropic, the single crystal\nmicropillars naturally exhibit a larger recoverable strain than the orientation-averaged bulk\nmaterial.”\nReference:\n[1] Hua, P., M. Xia, Y. Onuki, and Q. Sun. \"Nanocomposite Niti Shape Memory Alloy with High\nStrength and Fatigue Resistance.\" Nat Nanotechnol 16, no. 4 (Apr 2021): 409-13.\nhttps://dx.doi.org/10.1038/s41565-020-00837-5.\n[2] Hua, Peng, Kangjie Chu, Fuzeng Ren, and Qingping Sun. \"Cyclic Phase Transformation\nBehavior of Nanocrystalline Niti at Microscale.\" Acta Materialia 185 (2020): 507-17.\nhttps://dx.doi.org/10.1016/j.actamat.2019.12.019.\n6\n[3] Dong, Jie, Yan Huang, Yibo Zhang, Baoan Sun, Ming Yang, Xuerui Wei, Zhichao Lu, Fan Zhang,\nZhiyuan Liang, Jinkui Zhao, Wenli Song, Yuan Wu, Zhaoping Lu, Xun-Li Wang, and Dong Ma.\n\"Anisotropic Martensitic Transformation in B2-Cuzr-Structured Crystallites.\" Acta Materialia 289\n(2025). https://dx.doi.org/10.1016/j.actamat.2025.120872.\n[4] Gomez-Cortes, J. F., M. L. No, I. Lopez-Ferreno, J. Hernandez-Saz, S. I. Molina, A. Chuvilin,\nand J. M. San Juan. \"Size Effect and Scaling Power-Law for Superelasticity in Shape-Memory\nAlloys at the Nanoscale.\" Nat Nanotechnol 12, no. 8 (Aug 2017): 790-96.\nhttps://dx.doi.org/10.1038/nnano.2017.91.\n[5] San Juan, J., M. L. No, and C. A. Schuh. \"Nanoscale Shape-Memory Alloys for Ultrahigh\nMechanical Damping.\" Nat Nanotechnol 4, no. 7 (Jul 2009): 415-9.\nhttps://dx.doi.org/10.1038/nnano.2009.142.\n[6] Gou, Junming, Guoxin Liu, Tianzi Yang, Xiaolian Liu, Yun Pan, Chang Liu, Yu Qian, Yao Liu,\nYing Chen, Xuefeng Zhang, Tianyu Ma, and Xiaobing Ren. \"A High-Entropy Alloy Showing\nGigapascal Superelastic Stress and Nearly Temperature-Independent Modulus.\" Nature\nCommunications 16, no. 1 (2025). https://dx.doi.org/10.1038/s41467-025-56580-9.\n3. Reconcile the temperature-dependent stress hysteresis. The authors have done a good job of\nshowing the characteristic superelastic behaviors. From the results of Figures 1 and 2, the readers\nmay wonder how the superelastic behaviors vary in the wide temperature regime, and in particular,\nhow the stress hysteresis depends on the temperature. The authors are expected to explain, and even\nbetter, provide an experimental pathway to justify.\nResponse: We thank the reviewer for this important comment. To clarify the temperature\ndependence of superelasticity and stress hysteresis, we performed additional cyclic micro\ncompression tests on [011]-oriented Co22 micropillars using a TI950 nanoindenter equipped with a\nheating stage. The results, now included in Fig. S9, reveal a clear and systematic evolution of the\ndeformation behavior with temperature. At low temperatures, the Co22 alloy exhibits pronounced\nnonlinear superelasticity accompanied by a well-defined hysteresis loop, consistent with stress-\ninduced martensitic transformation. As the temperature increases, both the nonlinearity and the\nhysteresis gradually decrease. When temperature above ~60 °C, the micropillars display fully linear\nelastic behavior with negligible hysteresis, indicating that the deformation mechanism transitions\nfrom transformation dominated to slip dominated.\nThis trend is consistent with the classical framework for deformation in shape memory alloys\nas shown in Fig. R2 [1-2], in which the deformation mechanism is governed by the competition\nbetween the critical stress for slip ( ) and the critical stress for transformation ( ). The\ntransformation stress follows the Clausius–Clapeyron relation, , where\n𝜎𝑠 𝜎𝑇𝑟\nL=H -H is the latent heat (typically negative), implying that increases with increasing\nM A 𝑑𝜎𝑇𝑟⁄𝑑𝑇=−𝐿⁄𝜀𝑇𝑇\ntemperature. As temperature approaches and exceeds the martensite deformation limit temperature\n𝜎𝑇𝑟\nM , surpasses , leading to the deformation mode shift from martensitic transformation to\nd\ncrystallographic slip. This mechanistic transition is fully consistent with the experimentally\n𝜎𝑇𝑟 𝜎𝑠\nobserved evolution from nonlinear superelasticity at low temperatures to linear elasticity at elevated\ntemperatures in the Co22 alloy. We have incorporated this additional discussion and the\nsupplementary figure in the revised manuscript and SI.\n“To further investigate the temperature dependence of the super elastic behavior, we performed\ncyclic micro compression tests on [011] oriented Co22 micropillars at various temperatures, as\nshown in Fig. S9. The results clearly demonstrate a transition from nonlinear elastic behavior to\nlinear elastic behavior with increasing temperature, with a critical transition occurring around\n~65°C. This temperature-dependent evolution is fully consistent with the classical framework for\ndeformation in shape memory alloys35.”\nIn the revised method part:\n“The high temperature micropillar compression tests were carried out on the Hysitron TI 950\nTriboIndenter system equipped with a heating stage.”\nFigure S9. The progressive loading-unloading stress-strain curves of [011] oriented Co22\nmicropillars at different temperatures (a) 30°C, (b) 40°C, (c) 50°C, (d) 55°C, (e) 60°C, (f) 65°C, (g)\n70°C, (h) 100°C, respectively. The results indicate that the Co22 alloy transform from non-linear\nelastic behavior to linear elastic behavior with the increasing temperature.\n8\n[Figure Redacted]\nFigure R2. Schematic representation for the appearance of shape memory effect and superelasticity\nin temperature–stress space. [1-2] The M indicates the critical temperature, at which the critical\nd\ntransformation stress equals the yield stress of the alloy.\nReference:\n[1]Wang, Xiebin, Xiayang Yao, Dominique Schryvers, Bert Verlinden, Guilong Wang, Guoqun\nZhao, Jan Van Humbeeck, and Sergey Kustov. \"Anomalous Stress-Strain Behavior of Niti Shape\nMemory Alloy Close to the Border of Superelastic Window.\" Scripta Materialia 204 (2021/11/01/\n2021): 114135. https://dx.doi.org/https://doi.org/10.1016/j.scriptamat.2021.114135.\n[2]https://indico.cern.ch/event/314484/contributions/1689719/attachments/602948/829769/SMAs\n_Overview_and_TWSMA_Sleeve_Seminar_F.Niccoli_07_11_2014.pdf\n4. Strengthening the connection between atomic-scale strain and atomic-size mismatch. The authors\nhave provided in-situ TEM observation of lattice strain through atomic-scale strain mapping. Later,\nthe authors have claimed the complex interplay of atomic-size mismatch and chemical ordering to\nbe the main factor in the fundamental mechanism, but the connection is weak. The authors are\nadvised to strengthen the connection, for example, by in situ correlation experiments.\nResponse: We thank the reviewer for the insightful comment. We would like to clarify that the\natomic-scale strain in this work was obtained from high-resolution STEM images using geometric\nphase analysis rather than in-situ TEM, and we apologize if this point was not sufficiently clear. The\nconnection between chemical fluctuation, chemical short-range order, and lattice distortion is well\nestablished in chemically complex alloys [1-5] and is directly supported by our experimental\nobservations. In multi-principal-element systems, the large atomic-size mismatch among constituent\nelements generates local elastic misfit, which manifests as heterogeneous atomic-scale strain fields\n[1-3]. Chemical short-range ordering emerges as atoms locally rearrange to minimize this elastic\nmisfit and reduce the local strain energy [4-6]. As widely reported in the HEA literature (e.g., Ding\net al., Nature 2019; Moniri et al., Nature 2023; Li et al., PNAS 2022) [1-3], regions with stronger\nCSRO tend to exhibit reduced lattice distortion because preferred atom pairs/clusters better\naccommodate the size mismatch, whereas local chemical frustration regions amplify local distortion.\nOur own results also show this trend. As demonstrated by the HAADF-STEM intensity profiles and\nGPA strain maps in Fig. 4, Co22 and Co25 alloys exhibit more pronounced chemical fluctuation\ncompared with Co15, and this correlates with their broadened and intensified von Mises strain\ndistributions. This connection is further supported by our previous study on Co Ni (TiZrHf)\n25 25 50\n(He et al., Nature 2022) [6], where controlled modification of chemical ordering systematically\nreduced lattice distortion and elastic strain energy. We added more discussions in the revised\nmanuscript to strengthen the connection between chemical ordering and lattice distortions.\nIn the revised manuscript:\n“The connection between chemical fluctuation, chemical short-range order, and lattice distortion is\nwell established in chemically complex alloys22,25,26. Atomic-size mismatches among constituent\nelements generate local lattice strains, while the specific arrangement of atoms i.e., chemical short-\nrange ordering, modulates both the magnitude and distribution of these strains20. Regions with\nstronger chemical ordering can locally accommodate size differences more efficiently, reducing\nlattice distortion, whereas regions with weaker or frustrated ordering amplify local strains. This\nreciprocal interplay governs the heterogeneity of the atomic-scale strain field, providing a\nfundamental basis for the tunable Hookean and non-Hookean superelasticity observed in the\n(TiZrHf) Ni Co alloys. By adjusting the Ni/Co ratio, the balance between chemical ordering and\n50 50-x x\nlattice distortion can be finely controlled, resulting in a continuous strain-field landscape that can\nbe precisely tuned through minor compositional variations (<2 at.%), unlike binary or ternary\nsystems where similar adjustments often induce discrete phase transitions.”\nReference:\n[1] Ding, Qingqing, Yin Zhang, Xiao Chen, Xiaoqian Fu, Dengke Chen, Sijing Chen, Lin Gu, Fei\nWei, Hongbin Bei, Yanfei Gao, Minru Wen, Jixue Li, Ze Zhang, Ting Zhu, Robert O. Ritchie, and\nQian Yu. \"Tuning Element Distribution, Structure and Properties by Composition in High-Entropy\nAlloys.\" Nature 574, no. 7777 (2019): 223-27. https://dx.doi.org/10.1038/s41586-019-1617-1.\n[2] Moniri, Saman, Yao Yang, Jun Ding, Yakun Yuan, Jihan Zhou, Long Yang, Fan Zhu, Yuxuan\nLiao, Yonggang Yao, Liangbing Hu, Peter Ercius, and Jianwei Miao. \"Three-Dimensional Atomic\nStructure and Local Chemical Order of Medium- and High-Entropy Nanoalloys.\" Nature 624, no.\n7992 (2023): 564-69. https://dx.doi.org/10.1038/s41586-023-06785-z.\n[3] Li, J., Y. Chen, Q. He, X. Xu, H. Wang, C. Jiang, B. Liu, Q. Fang, Y. Liu, Y. Yang, P. K. Liaw,\nand C. T. Liu. \"Heterogeneous Lattice Strain Strengthening in Severely Distorted Crystalline\nSolids.\" Proceedings of the National Academy of Sciences of the United States of America 119, no.\n25 (Jun 21 2022): e2200607119. https://dx.doi.org/10.1073/pnas.2200607119.\n[4] Chen, X., Q. Wang, Z. Cheng, M. Zhu, H. Zhou, P. Jiang, L. Zhou, Q. Xue, F. Yuan, J. Zhu, X.\nWu, and E. Ma. \"Direct Observation of Chemical Short-Range Order in a Medium-Entropy Alloy.\"\nNature 592, no. 7856 (Apr 2021): 712-16. https://dx.doi.org/10.1038/s41586-021-03428-z.\n[5] Li, Q. J., H. Sheng, and E. Ma. \"Strengthening in Multi-Principal Element Alloys with Local-\nChemical-Order Roughened Dislocation Pathways.\" Nat Commun 10, no. 1 (Aug 8 2019): 3563.\nhttps://dx.doi.org/10.1038/s41467-019-11464-7.\n[6] He, Q. F., J. G. Wang, H. A. Chen, Z. Y. Ding, Z. Q. Zhou, L. H. Xiong, J. H. Luan, J. M. Pelletier,\nJ. C. Qiao, Q. Wang, L. L. Fan, Y. Ren, Q. S. Zeng, C. T. Liu, C. W. Pao, D. J. Srolovitz, and Y.\nYang. \"A Highly Distorted Ultraelastic Chemically Complex Elinvar Alloy.\" Nature 602, no. 7896\n(Feb 2022): 251-57. https://dx.doi.org/10.1038/s41586-021-04309-1.\n10\n5. Assess the reversibility. Reversibility and stability are of great importance for the applications of\nsuperelastic materials. Because the fatigue life is closely related to stress hysteresis and the\n(TiZrHf) Ni Co high-entropy alloy has quite a large stress hysteresis (depending on the\n50 50-x x\ntemperature), the audience may wonder what the reversibility and stability of the high-entropy\nsuperelastic alloy would look like. If possible, the authors are advised to add relevant experiments\nor discussions.\nResponse: We thank the reviewer for raising this important point. To address this comment, we\nconducted additional cyclic micropillar compression experiments on the Co22 alloy. Each test\nconsisted of 20 loading unloading cycles to minimize thermal drift of the nanoindenter, and the test\nwas repeated three times on the same specimen, yielding a total of 60 cycles. The representative\ncyclic curves are shown in Fig. R3. The results reveal that during the initial cycles, the Co22\nmicropillar exhibits nearly full strain recovery with a pronounced hysteresis loop characteristic of\nstress-induced transformation. With increasing cycle number, the hysteresis loops gradually\ndecreases and the recoverable strain slightly diminishes. After approximately 15 cycles, the cyclic\nresponse stabilizes, showing minimal changes in the loading–unloading loops. Similar phenomena\nhave been widely reported in conventional NiTi SMAs and SMA-reinforced composites [1–4]. With\nincreasing cyclic number, the residual plastic strains gradually increase while the recoverable\ndeformation strains slight decrease [1-4]. The evolution of residual plastic strain is closely related\nto transformation-induced plasticity and structural relaxation events [1-2]. However, a systematic\ninvestigation of this phenomenon is part of our ongoing work. A detailed study of fatigue and\nstructure relaxation behaviors of this alloys extends beyond the scope of the present manuscript, and\nwe will explore these physical insights more comprehensively in our future work.\nReference:\n[1] Hua, P., M. Xia, Y. Onuki, and Q. Sun. \"Nanocomposite Niti Shape Memory Alloy with High\nStrength and Fatigue Resistance.\" Nat Nanotechnol 16, no. 4 (Apr 2021): 409-13.\nhttps://dx.doi.org/10.1038/s41565-020-00837-5.\n[2] Yahui Zhang. Low cycle fatigue of shape memory alloys. Material chemistry. Université Paris\nSaclay (COmUE), 2018. English. NNT : 2018SACLY004 . tel-01880307\n[3] Dornelas, Vanderson M., Sergio A. Oliveira, Marcelo A. Savi, Pedro Manuel Calas Lopes\nPacheco, and Luis Felipe G. de Souza. \"Fatigue on Shape Memory Alloys: Experimental\nObservations and Constitutive Modeling.\" International Journal of Solids and Structures 213 (2021):\n1-24. https://dx.doi.org/10.1016/j.ijsolstr.2020.11.023.\n[4] Daghash, Sherif M. and Osman E. Ozbulut. \"Characterization of Superelastic Shape Memory\nAlloy Fiber-Reinforced Polymer Composites under Tensile Cyclic Loading.\" Materials & Design\n111 (2016): 504-12. https://dx.doi.org/10.1016/j.matdes.2016.09.034.\nof 20 cycle at one test. The stress-strain response at (b) 1st-20th cycle, (c) 21st-40th cycle and 41st-\n60th cycle.\n6. Minors. (1) In the Abstract, the mechanism should be expounded in an information-rich manner.\n(2) Please ensure the fonts in Figures are legible and consistent in size.\nResponse:Thank you for the suggestions. We have revised the abstract and checked the figure fonts\naccordingly.\nIn the revised abstract:\n“…By combining atomic-scale strain mapping and extensive first-principles calculations, we\nreveal that this tunability is governed by a hidden strain order, arising from frustrated\ncrystallization of two competing phases. As a result, local lattice distortion arises, producing a\nheterogeneous strain landscape that modulates phase stability, phase transformation propensity,\nand elastic response. Our findings establish a materials design strategy for programming\nHookean and non-Hookean elasticity behavior on demand, with promising applications in\nmicroelectromechanical systems, high-precision actuators, and adaptive damping devices.”\nReviewer #3 (Remarks to the Author):\nThis paper presents an interesting study of the mechanical properties of a class of B2-B19' high\nentropy alloys. The authors find that by tuning the composition, they can tune the properties of the\n12\nmartensitic transformation. The ability to tune the MT is attributed to changes in the stress\nfluctuations associated with the composition fluctuations inherent in an HEA.\nOverall, I find the paper interesting and worthy of publication. I do, however, have a few\nquestions/observations that I would like the authors to address before publication.\nResponse: We appreciate the reviewer’s positive comments. We addressed the raised concerns and\nprovide the following responses.\n(1) Figure 2. I think I understand the origin of the plot symbols and most of the lines. I think I even\nunderstand why the blue line is dashed above 22% Co. Nevertheless, the figure would be more useful\nif the origin of the various features within it were described in the caption.\nResponse: Thank you for the suggestions. We have revised the caption of Figure 2 to provide more\ndetailed explanations of the symbols and lines.\nIn the revised manuscript:\n“The solid black squares and open blue circles are experimental data set. The black solid line\ndenotes the martensite start temperature M, while the solid and dashed blue lines indicate the strain\ns\nglass transition temperature T .”\ng\n(2) With respect to fig. 3, I presume the stress vs. strain curves were obtained at room temperature.\nIf so, this should be stated in the manuscript.\nResponse: Yes, both the macroscopic and micropillar tests shown in Figure 3 were conducted at\nroom temperature. To avoid any misunderstanding, we have emphasized this point in the revised\nmanuscript.\nIn the revised manuscript:\n“Figure 3. Multi-scale mechanical characterization of (TiZrHf) Ni Co alloys at room\n50 50-x x\ntemperature…”\n(3) For the geometric phase analysis, I presume the authors need to choose a reference state from\nwhich to measure the strain. How was this chosen? Does this choice affect the computed von Mises\nstrains?\nResponse: We thank the reviewer for this question. In the geometric phase analysis (GPA), the\nreference lattice is mathematically defined following the standard procedure established by Hÿtch\net al. [1] and implemented in the Strain++ algorithm [2]. Specifically, the reference state is defined\nin reciprocal space by selecting two non-collinear reciprocal lattice vectors (g1 and g2) from the\nFourier transform of the high-resolution STEM image. These two g vectors establish the basis of\nthe reference lattice in real space. Following the standard method as detailed in Ref. [1], a small\nregion of undistorted lattice within the same high-resolution STEM image, identified as an area of\nuniform phase contrast, is selected in the phase image as the reference area. The reference region\nwas repeatedly refined until the computed strain fields, including the von Mises strain, converged\nto a stable value. This approach ensures that the choice of reference does not introduce artificial\ndistortions or affect the reliability of the measured local strains. This analysis procedure is widely\nadopted in the literatures for atomic strain analysis in HEAs [3-5], providing a robust way to\n13\nquantify strain heterogeneity at the atomic level.\nReference:\n[1] Hÿtch, M. J., E. Snoeck, and R. Kilaas. \"Quantitative Measurement of Displacement and Strain\nFields from Hrem Micrographs.\" Ultramicroscopy 74, no. 3 (1998/08/01/ 1998): 131-46.\nhttps://dx.doi.org/https://doi.org/10.1016/S0304-3991(98)00035-7.\n[2] https://jjppeters.github.io/Strainpp/\n[3] Chen, X., Q. Wang, Z. Cheng, M. Zhu, H. Zhou, P. Jiang, L. Zhou, Q. Xue, F. Yuan, J. Zhu, X.\nWu, and E. Ma. \"Direct Observation of Chemical Short-Range Order in a Medium-Entropy Alloy.\"\nNature 592, no. 7856 (Apr 2021): 712-16. https://dx.doi.org/10.1038/s41586-021-03428-z.\n[4] Ding, Qingqing, Yin Zhang, Xiao Chen, Xiaoqian Fu, Dengke Chen, Sijing Chen, Lin Gu, Fei\nWei, Hongbin Bei, Yanfei Gao, Minru Wen, Jixue Li, Ze Zhang, Ting Zhu, Robert O. Ritchie, and\nQian Yu. \"Tuning Element Distribution, Structure and Properties by Composition in High-Entropy\nAlloys.\" Nature 574, no. 7777 (2019): 223-27. https://dx.doi.org/10.1038/s41586-019-1617-1.\n[5] Wang, L., J. Ding, S. Chen, K. Jin, Q. Zhang, J. Cui, B. Wang, B. Chen, T. Li, Y. Ren, S. Zheng,\nK. Ming, W. Lu, J. Hou, G. Sha, J. Liang, L. Wang, Y. Xue, and E. Ma. \"Tailoring Planar Slip to\nAchieve Pure Metal-Like Ductility in Body-Centred-Cubic Multi-Principal Element Alloys.\" Nat\nMater 22, no. 8 (Aug 2023): 950-57. https://dx.doi.org/10.1038/s41563-023-01517-0.\n(4) The DFT calculations use cells that are quite anisotropic in shape. For example, the B2 unit\ncells extend much more in the x and y directions than they do in the z directions. It seems that these\nwill ensure that one direction is different than the other two directions (at least for the B2 phase).\nWhy was this choice made?\nResponse: We thank the reviewer for this meticulous observation. To accurately model the\ncompositions of the considered intermetallics, which are highly sensitive to the Ni/Co ratio, we\nemployed the SQS method with a supercell size constrained to 100 atoms. This constraint led to a\n5×5×2 supercell for the B2 phase (2 atoms/unit cell) and a 5×1×5 supercell for the B19’ phase (4\natoms/unit cell).\nTo confirm that our results are not biased by the supercell selection, we repeated the volume-\nenergy fitting for the Ni:Co=1:1 composition using more isotropic supercells, a 2×2×2 supercell for\nB2 and a 3×2×2 supercell for B19’. As shown in the table below, the resulting lattice constants,\nwhen normalized to their conventional unit cells, deviated by less than 0.3%. This excellent\nagreement confirms that the systematic bias from the anisotropic 100-atom supercells is negligible,\nvalidating the reliability of our chosen simulation cells.\nWe have added the following explanations in the Method part of the revised manuscript:\n“To accurately model these compositions, which are highly sensitive to the Ni/Co ratio, we\nconstrained the SQS supercell to 100 atoms.”\n“Taking the Ni:Co = 1:1 composition as a representative case, we performed volume-energy fitting\nusing more isotropic supercells, a 2×2×2 supercell for B2 and a 3×2×2 supercell for B19'. As shown\nin the Table S2, the resulting lattice constants, when normalized to their conventional unit cells,\n14\ndeviated by less than 0.3%. This excellent agreement confirms that the systematic bias from the\nanisotropic 100-atom supercells is negligible.”\nTable S2 has also been included in the supplementary materials.\nTable S2. Lattice parameters and their deviations for the B2 and B19’ phases across different\nsupercells.\nB2-5×5×2 B2-2×2×2 δ B19'-5×1×5 B19'-3×2×2 δ\nB2 B19'\na 15.5994 6.2298 0.16% 15.0163 9.0081 0.02%\nb 15.5994 6.2298 0.16% 4.2473 8.4931 0.02%\nc 6.2397 6.2298 0.20% 24.0395 9.6140 0.02%\nAlso, the description of the minimization procedure makes sense for the B2 alloys, but for the B19'\nstructure, one needs to vary the lattice parameters independently. Is this what was done? If so, for\nthe B19' structure, I would expect an unusually large number of structures (over 1700 for a\nsingle composition) would be necessary. The authors should explain this procedure more carefully with\nrespect to the B19' structure.\nResponse: We acknowledge the reviewer’s insightful question regarding the lattice parameter scan.\nWhile a fully independent scan of the lattice parameters for the B19’ phase is valid, it would require\nsampling over 1700 structures. This highly demanding computation-scale also risks introducing\nsignificant noise into the data, complicating the fitting procedure and potentially compromising the\nrobustness of the results.\nTherefore, our optimization approach starts with independent lattice parameter perturbations\nfrom -1% to +1% to identify the energy-lowering pathway. As shown in Fig. S17(a), the most\nsignificant energy reduction occurred when all three axes were scaled uniformly by +1%.\nAccordingly, for the B19' phase, we employed a uniform scaling approach to determine the\nequilibrium volume. This method is efficient and well-suited to our primary objective of\ninvestigating systematic compositional trends within a consistent supercell framework, thereby\nensuring meaningful cross-compositional comparisons.\nAfter the optimized structure was obtained, we performed a more detailed analysis to determine\nwhether any lower-energy configurations could exist by applying uniaxial perturbations from -2%\nto +2% strain (in 1% steps) independently along the lattice axes of the optimized structure. The\nresults, plotted in Fig. S17(b), demonstrate that the central point (0, 0, 0), corresponding to our\noptimized structure, is unequivocally the minimum energy state. This validation confirms that our\nuniform scaling method was both reasonable and sufficiently accurate for the purposes of this study.\nWe have added the following explanations to the Method part of the revised manuscript:\n“To determine the equilibrium lattice parameters, the uniform scaling factor of each structure was\nsystematically varied from 0.94 to 1.05 in increments of 0.01, and single-point total energies were\ncomputed for each of the resulting 12 configurations.”\n15\n“For the lower-symmetry B19' supercells, using the Ni:Co = 1:1 composition as a representative\nexample, we first applied independent -1% to +1% perturbations to the three lattice parameters of\nthe initial structure. This process confirmed that using a uniform scaling factor provides the pathway\nof steepest energy descent (Fig. S19(a)). With the optimized lattice, we further applied another set\nof independent -2% to +2% perturbations to the three lattice constants. This step confirmed that the\noptimized structure is located at the bottom of the potential energy surface, thereby validating the\nuniform scaling approach (Fig. S19(b)).”\nFigure S19. (a) Energy landscape of the initial B19' (Ni:Co=1:1) supercell under independent ±1%\nlattice perturbations. The minimum energy located at the (+1%, +1%, +1%) point confirms that\nuniform scaling provides the pathway of steepest energy descent. (b) Energy landscape of the\noptimized B19' supercell (obtained via uniform scaling) under independent ±2% lattice\nperturbations. The energy minimum is clearly located at the (0, 0, 0) origin, confirming that the\noptimized structure lies at the bottom of the potential energy surface.\n(5) Supplementary figure S3 shows the orientation of the grains for four samples. The figure also\nshows that the grain size is dependent upon Co composition. In particular, the Co22 structure\nappears to have a much larger grains size, on average, than the higher Co concentration alloys.\nThe author should comment on this, and assess to what extent the larger grain size might impact\ntheir conclusions.\nResponse: We thank the reviewer for this insightful comment. Please note that the samples in this\nwork were arc-melting cast and subsequently homogenized at 1000 °C. Since no additional rolling\nand recrystallization was performed after homogenization, the resulting microstructures are not\nequiaxed, and the grain sizes are heterogeneous. Therefore, the apparent differences in grain size\nshown in Supplementary Figure S3 do not directly reflect the influence of Co content. The local\nvariations and the choice of the observed regions also contribute to the measured grain sizes\ndifference. Regarding the effect of grain size on mechanical behavior, our previous studies on the\nCo Ni (TiZrHf) alloy system indicate that macroscopic properties such as strength and elastic\n25 25 50\nlimit show little dependence on grain size due to the high lattice distortion and lattice friction stress\n[1]. Moreover, in the present study, extensive single-crystal micropillar compression experiments\nwere conducted. These measurements isolate the intrinsic behavior of the crystal lattice and exclude\nthe influence of grain boundaries, confirming that the composition-dependent transition between\nHookean and non-Hookean superelasticity arises from atomic-scale mechanisms rather than grain\n16\nsize effects. We have added a clarifying discussion in the revised manuscript to emphasize this point.\nIn the revised manuscript:\n“The single-crystal micropillar experiments confirm that the observed Hookean to non-Hookean\ntransition is governed by intrinsic atomic-scale mechanisms, independent of grain boundary effects.”\nReference:\n[1] He, Q. F., J. G. Wang, H. A. Chen, Z. Y. Ding, Z. Q. Zhou, L. H. Xiong, J. H. Luan, J. M. Pelletier,\nJ. C. Qiao, Q. Wang, L. L. Fan, Y. Ren, Q. S. Zeng, C. T. Liu, C. W. Pao, D. J. Srolovitz, and Y.\nYang. \"A Highly Distorted Ultraelastic Chemically Complex Elinvar Alloy.\" Nature 602, no. 7896\n(Feb 2022): 251-57. https://dx.doi.org/10.1038/s41586-021-04309-1.\n(6) Figure S10 does not have a key telling the reader which atoms are which. This should be fixed.\nResponse: We thank the reviewer for pointing out this issue. We have revised Fig. S13 and Fig. S15\n(originally Fig. S11 and Fig. S12) and added legend to clarify the atomic species.\nRevised Fig. S13 and Fig. S15:\nFigure S13. Structural snapshots of B2 alloys with different Ni:Co ratios after relaxation.\nwith dotted boxes highlighting the B2-like atomic order that forms after relaxation. (b) Structural\nsnapshots of B19′ alloy with Ni:Co=50:0 before and after relaxation. (c) The displacement of each\nelement in B19′ alloys with different Ni:Co ratios and (d) the content of B2-like atomic order present\nin these alloys after relaxation.\n18"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have addressed my concerns.", "reviewer_2": "The authors have responded to the reviewers’ concerns and revised the manuscript accordingly.", "reviewer_3": "The reviewers have addressed all of my comments, as well as those of the other reviewers. I believe the that the paper\nshould be published."}, "author_response": ""}]

Decision letter