The average and local structure of TiVCrNbDx (x = 0, 2.2, 8) from total scattering and neutron spectroscopy

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Acta Materialia

journalhomepage:www.elsevier.com/locate/actamat

The average and local structure of TiVCrNbD _x ( x = 0 , 2 . 2 , 8 ) from total scattering and neutron spectroscopy

Magnus M. Nygård

^a

, Øystein S. Fjellvåg

^a

, Magnus H. Sørby

^a,∗

, Kouji Sakaki

^b

, Kazutaka Ikeda

^c

, Jeff Armstrong

^d

, Ponniah Vajeeston

^e

, Wojciech A. Sławi ´nski

^f

, Hyunjeong Kim

^b

, Akihiko Machida

^g

, Yumiko Nakamura

^b

, Bjørn C. Hauback

^a

aInstitute for Energy Technology, Department for Neutron Materials Characterization, P.O. Box 40, NO-2027 Kjeller, Norway

bNational Institute of Advanced Industrial Science and Technology, AIST West, 16-1 Onogawa, Tsukuba, Ibaraki, 305-8569, Japan

cInstitute of Materials Structure Science, High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan

dISIS Facility, Rutherford Appleton Laboratory, Harwell Campus, Didcot, Oxfordshire OX11 0QX, United Kingdom

eCentre for Materials Science and Nanotechnology, Department of Chemistry, University of Oslo, P.O. Box 1033, Oslo NO-0315, Norway

fFaculty of Chemistry, University of Warsaw, Pasteura 1, Warsaw PL-02-093, Poland

gNational Institutes for Quantum and Radiological Science and Technology, 1-1-1, Kouto, Sayo-cho, Sayo-gun, Hy ¯ogo, 679-5148, Japan

a rt i c l e i nf o

Article history:

Received 15 September 2020 Revised 11 November 2020 Accepted 14 November 2020 Available online 23 November 2020 Keywords:

Metal hydrides Hydrogen storage High-entropy alloys HEAs

Total scattering Reverse Monte Carlo RMC

Inelastic neutron scattering INS

a b s t r a c t

Thevolumetrichydrogendensityof160kgH/m³inTiVCrNbH8 isamongthehighestforinterstitialhy- drides, butthe reportedreversible capacityis onlyabout 2/3of thefull theoretical capacity atroom temperature. Inthepresent workwehave investigatedthelocal structureinTiVCrNbDx,x=0,2.2, 8 withtheaimtounravelhowtheremainingsitescanbedestabilizedwithrespecttohydrogen/deuterium occupationusingtotalscatteringmeasurementsandReverseMonteCarlo(RMC)structuremodelling.Our analysisindicatesthatthepartiallydesorbeddeuteride(x=2.2)adoptsabody-centredtetragonalstruc- ture(I4/mmm)wherethedeuteriumatomsoccupybothtetrahedralandoctahedralintersticeswithlow occupancies.Thereisasignificantlyhigherportionofoccupiedsiteswithnearest-neighbourmetalswith lowvalence-electronconcentrationVEC.Thisobservationisusedtomotivatestrategiesforfurtherdesta- bilizationofthehydride.Inelastic neutronscattering(INS)and densityfunctionaltheory(DFT)calcula- tionsindicatethatthevibrationaldensityofstatesisverydiverseinTiVCrNbH2.4,anditissuggestedthat thehydrogenatomsmightbemobilebetweennearbyinterstices.

© 2020 Acta Materialia Inc. Published by Elsevier Ltd.

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1. Introduction

An environmentally benign energyvector becomes imperative with an increasing share of the global energy distribution from renewable energytechnologies. Hydrogen hasthepotential to fill this need, butsafe and efficientstorage remains a challenge [1]. This is due to the very low density ofgaseous hydrogen atam- bient conditions. One promising solution is to store hydrogen in thesolid-stateusingmetalhydrides.Withthisapproachitispos- sible to achieve much highervolumetric hydrogendensities than in commercial gas tanks where the hydrogen is compressed to 700barH₂.Manydifferentmetalhydrideshavebeenproposed in the literature, but none of these are currently able to fulfill all the requirements ofan idealhydrogen storagematerial. Complex hydrides excel in terms of gravimetric hydrogen densities reach-

∗Corresponding author.

E-mail address: magnus.sorby@ife.no (M.H. Sørby).

ing values as high as18.4wt.% in LiBH₄. Unfortunately, they are oftensubjectto non-reversibility duringhydrogensorption [2–4]. Mg-basedmetal hydridescan also reach high gravimetric hydro- gen densities, e.g. 7.6wt.% in MgH₂. As Mg is an abundant ele- mentthese materials areoftencheap, butthey sufferfromunfa- vorable kinetics and thermodynamics at ambient conditions [5]. Intermetallic hydrides formed fromalloys of type AB, AB₂, AB₅, etc.,havemodestgravimetrichydrogendensities,suchas1.37wt.%

in LaNi₅H₆ or1.89wt.% inTiFeH₂.Their main drawbacksinclude degradationafterrepeatedhydrogenabsorption/desorptioncycling, surface passivation and slow hydrogen sorption kinetics [1,6–9]. Some oftheseissuescanbe mitigated ifsmall amountsofeither A,B,orbothissubstitutedwithcarefullychosenelements[9–12]. Recently, this alloying strategy has been taken to its ex- treme in a novel materials class known as high-entropy alloys (HEAs).Thisisamulti-principalelementapproachwherethealloy containsfour or more elementsmixedtogether in nearequimo- larcompositions.Thesematerials tend toformsingle-phasesolid

https://doi.org/10.1016/j.actamat.2020.116496

1359-6454/© 2020 Acta Materialia Inc. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )

M.M. Nygård, Ø.S. Fjellvåg, M.H. Sørby et al. Acta Materialia 205 (2021) 116496

solutions withsimplestructuressuch asbody-centredcubic(bcc) andcubicclose-packed(ccp)[13].Asaconsequence,thedifferent elements are randomly distributed over a single crystallographic site causing a wide diversity of local atomic arrangements. Sev- eral HEAs have been reported to form metal hydrides in which the hydrogenatoms occupythe tetrahedral and/or octahedral in- terstices ina body-centred tetragonal (bct) orface-centred cubic (fcc) lattice [14–20]. Usuallythe thermodynamicsareunfavorable forapplicationsatambientconditions[16–18],butithasrecently been demonstratedthat the metal hydridesare destabilized with increasing valence-electron concentration (VEC) in the HEA [21]. Based upon thisinsight,reversibleroom temperature(RT)hydro- genstoragehavebeenrealizedintheHEATiVCrNbH8(VEC=5.0) andtheC14Laves-phaseTiCrMnFeNiZrH₆ (VEC=6.4)[21,22].The volumetric hydrogen density achievedin TiVCrNbH₈ is the high- estreportedforanyinterstitialhydride,namely160kgH/m³.Inter- estingly,thereversiblehydrogenstoragecapacityof1.96wt.%Hin TiVCrNbH₈is just61.3% of the theoretical fullcapacity of 3.20wt.%.

Thisisindicativeofcertainmorestablesiteswheretheremaining hydrogenatomsaretrapped.Thesesitesmustbedestabilizedifthe full hydrogenstoragecapacityinTiVCrNbH₈ shouldbecomeavail- ableatRT.Itispossiblethatthiscanbeachievedbyfinelytuning the chemicalcomposition oftheHEA.Inthiscontextitwouldbe beneficial toknowwhetherthereare anypreferredmetallicenvi- ronmentssurroundingthehydrogenatomsthataretrappedinside thestructureatRT.

Thispaperpresentsa detailedinvestigationofthe localshort- rangeorder(SRO)forTiVCrNbDx,x=0,2.2,8usingReverseMonte Carlo (RMC) structure modelling from total scattering measure- ments[23].Totalscatteringextendsregulardiffractionandinvolve extra rigorousmeasurementsto obtainan accurateassessment of both the Bragg and diffuse scattering from the sample. Previous total scatteringinvestigations indicatedthat deuteriumhasapre- ferrence foroccupyingsitessurrounded bymuchTi indeuterides formed fromTi_0.45Cr_0.35Mo_0.20 [24].However, this resultwasob- tainedbypeakfittingratherthanRMCmodelling,andthus,amore accurateassessmentofthelocalstructureisobtainedinthiswork.

The hydrogen vibrations and local bonding mechanism are also elucidated fromhigh-resolution inelasticneutron scattering (INS) measurements. These are discussed and compared with density functionaltheory(DFT)calculationsandtheRMCstructuremodels.

2. Experimental 2.1. Synthesis.

Alloys with the composition TiVCrNb were synthesised from lumpsofTi,Cr,Nb(Goodfellow,99.99%metalsbasis)andV(Good- fellow, 99.6% metals basis) by arc meltingunder Ar atmosphere.

Thealloysweremeltedinbatchesof1.86(1)g.Thesewereturned andremeltedsixtimestoenhance homogeneity.Themass losses during arc melting were in all cases measured below 0.6wt.%.

Thus,thefinalcompositionscanbeconsideredasveryclosetothe nominal.

Aboutonethirdoftheascastalloywascrushedtoafinepow- der usingahammerandanvil.Anotherthirdofthe materialwas sealedunderArinastainlesssteelautoclaveandconnectedtoan in-housebuiltSievertsapparatus[25]equippedwithaVacuubrand diaphragm vacuumpump. A partially hydrogenated material was obtained by the following synthesis. The material was heatedto 352(2) ^◦C underdynamicvacuumfor2hforactivation.The sam- ple was subsequently cooled to RT where hydrogen loading was performed in a direct gas-solid-statereaction. The final pressure wasstableat33.9(3) barH2,andthecomposition wasmeasured to TiVCrNbH_7.68(2) by manometric means. The sample was then heatedto99.0(⁴)^{◦Candexposedtodynamicvacuumfor3huntil}

thevacuumwasat∼2×10⁻⁶ mbar.Thisindicates thathydrogen desorption hasfinished. Hydrogengasloading wasthenrepeated atRT andthe reversiblecapacity determined to H/M=1.214(⁷)^. Theloadingcyclewasrepeatedonemoretimewithnosignificant changein thereversible capacity.A partially hydrogenatedmate- rial wasfinally obtainedby repeating theheatingandevacuation proceduredescribedabove.Theremainingonethirdoftheascast alloywasexposed to an identicaltreatment withdeuterium (²H, purity99.6%)insteadofnaturalhydrogen.The compositionofthe fully deuterated material and the reversible capacity was deter- mined manometricallyto TiVCrNbD_7.65(7) andD/M=1.26(³),re- spectively.All samplehandlingwasfromthispoint performedin anMBraunUnilabgloveboxwithpurifiedAratmosphere(<1ppm O₂ andH₂O).

A deactivated dideuteride was also obtained by the follow- ing synthesis. Part of the partially deuterated material obtained above was sealed in a stainless steel autoclave and reconnected to the Sieverts apparatus. Deuterium gas loading wasperformed as described above and the final composition was measured to TiVCrNbD_7.82(1). To prevent outgassing of deuterium the sample wascooledto−196^◦Cbysubmergingthestainlesssteelautoclave inaliquidN₂bath.Duringcoolingthesamplewaskeptunderdeu- terium gaspressure. The samplewasthen quicklyremovedfrom the autoclaveandplaced in acetonewhere itwasgrounded to a finepowder.Thelatterstepservedtopassivatethesurfacesofthe dideuterideparticles,andtherebypreventingDdesorption.

2.2. Thermalanalysis.

Thermogravimetric differential scanning calorimitry (TG/DSC) wasmeasured with a heat flux type Netzsch STA 449 F3 Jupiter apparatus. The samples were confined inside Al₂O₃ crucibles equippedwithpiercedlidsandheatedto600^◦Cat10^◦C/min.The measurementswereconductedunderflowingArat50mL/min.

2.3. Sievertsmeasurements.

Thepowderedalloyswereplaced insidea stainless-steelauto- clavefor the pressure-composition isotherm (PCI) measurements.

The autoclave was heated to 150 ^◦C and evacuated by rotary pumpformorethan2h.PCIswerethenmeasuredduringabsorp- tion/desorptionatthreedifferenttemperaturessothattheabsorp- tion/desorptionenthalpyandentropycouldbeevaluated.Separate measurementswereconductedwithhydrogenanddeuteriumgas.

2.4. X-rayandneutrontotalscatteringmeasurements.

Powderneutrondiffraction(PND)wasmeasuredwiththeNOVA instrumentatJapanProtonAcceleratorResearchComplex(J-PARC) inIbaraki Prefecture,Japan. The sampleswere loaded into6 mm diametercylindricalV₉₆Ni₄alloycontainersunderHeatmosphere.

Each sample was measured for 3.5h under ambient conditions.

Measurements were also made of an empty sample container, a Vrodandtheemptyinstrument.Thisallowedustoperformback- groundsubtractionanddatacorrectionbystandardmeans[26]to obtain the total scattering structure factor F(^Q) ^{and its Fourier} transform,thepairdistributionfunction(PDF),G(^r)^definedas:

G

(

^r

)

= N

i=1

N

j=1

c_ic_jb_ib_j

g_{i j}

(

^r

)

−1

(1)

where

{

^ci

}

^Ni=1 and

b_i

N

i=1 are the concentrations and coherent boundscatteringlengthsoftheN chemicalspeciespresentinthe system,respectively[27].g_{i j}(^r)^{arethepartialPDFsdefinedas:}

g_{i j}

(

^r

)

= 1

ρ

j

ni j

(

^r

)

4

π

^{r2dr (2)}

where

ρ

j=c_j

ρ

0,

ρ

0 isthe average numberdensityof the mate- rial andn_{i j}(^r) ^{is the number of atomsof type j between r and} r+dr from an atom of type i. Thus, g_{i j}(^r) ^{shows the distribu-} tion ofinteratomic distancesbetweenatoms oftype i and j. Ad- ditionally,the differentialcorrelation function D(^r) ^isobtainedas D(^r)=4

π

^r

ρ

0G(^r)^.

Synchrotron radiation powder X-ray diffraction (SR-PXD) was measured at the BL22-XUbeamline ofSPring-8 in Hy¯ogo Prefec- ture,Japan[28].ThebeamlineisequippedwithaRigakuR-AXISV detectorandthewavelengthwas

λ

=0.1778 ˚A.Thesampleswere placed inside1.0mm diameterkaptoncapillaries withwall thick- ness0.05mm.Theexposuretimeswereinallcases30s.Anempty capillary was also measured so that background subtraction and data correction could be performed using the program GudrunX [29].Thus, X-ray equivalentsof the totalscattering functionsde- scribedabovewereobtained.

CrystallographicanalysiswasperformedwithbothSR-PXDand PNDdatasimultaneouslyusingtheRietveldmethodintheGeneral StructureAnalysisSystem(GSAS)[30,31].The backgroundwasfit- tedbya12thordershifted-Chebyshevpolynomial,andtheSR-PXD peaks were modelledby aThompson–Cox–Hastings pseudo-Voigt function [32]. The PND peaks were modelled by a pseudo-Voigt function convoluted with the Ikeda–Carpenter function [33]. The Debye–Waller factors were also refined, but for the metals they wereconstrainedtobeequal.

2.5. ReverseMonteCarlo(RMC)modelling.

In the RMC techniquea three dimensional structure modelis constructed fromexperimentally observed data. In the case of a crystalline material, the initial model is a supercell of the crys- tallographic unit obtainedfrom a Rietveld refinement. The theo- retical function, e.g.G(^r)^{, fromthis}configuration ofatomsiscal- culatedandcomparedwiththeexperimentallyobtainedfunction.

The atoms within the configuration is then allowed to translate andswapplaces.Foreachmovethenewagreementwiththeex- perimentaldata

χ

²j iscalculatedas:

χ

²j = M

i=1

(

^fmeas

(

^xi

)

−fcalc,j

(

^xi

))

²

A·

σ (

^xi

)

⁽³⁾

where fmeas(^xi) ^{is the} experimental function with uncertainty

σ

(^xi) ^{at point x}i and f_calc,j(^xi) the corresponding function cal- culated from the model after move j has been implemented.

A is a user defined constant that is used to change the rela- tive weighting of the different functions. If

χ

²_j ≤

χ

²_j−1 ^{the move}

is always accepted. If

χ

²_j >

χ

²_j−1 it is accepted with probability exp(−0.5·(

χ

²j −

χ

²_j−1))^{. In principle, any technique for which a} theoretical pattern can be calculated from the structure model could be included into the RMC process. In the present work, a combination of neutronand X-raytotal scattering measurements isused.ThisisnecessaryduetothelowX-rayscatteringintensity from Datomswithrespect tothe metalsandviceversa forneu- trons.Thisalsoensuresgoodcontrastbetweenallthemetals.

TheRMCmodellingwasinthepresentworkdonewiththede- velopment version ofRMCProfile v7 which will succeedthe cur- rent version RMCProfile v6 [34]. A total of eight different func- tions, fourfor each probe, were included in the RMCprocedure.

TheseareF(^Q),G(^r),D(^r)^{andtheBraggpeak}intensities.Thedi- mension of the startingconfigurations were chosen so that G(^r) and D(^r) ^{could be calculated up to 30 ˚A. Thus, the models of} the alloy,partiallydeuterated andfully deuteratedmaterials con- tain 20×20×20(16,000atoms),19×19×19(21,310atoms)and 14×14×14(32,928atoms)unitcells,respectively.Translationand swap moves were attempted with equal probability during the simulations. The maximum translationdistance wasrestricted to

0.10 ˚A. The atomswere constrainedto not move closertogether thanthe predefinedcut-off distance of 2.28 ˚A in TiVCrNb,1.32 ˚A inTiVCrNbD_2.2,and1.38 ˚AinTiVCrNbD₈.Thesevaluesweretaken foreach simulationasther-valuewherethefirstinteratomicdis- tancepeak isseen intheexperimental G(^r)^{.No further chemical} knowledgeorconstrainswereimposedonthemodels.Therelative weightingofthedifferentdatasetsweredecidedbytrialanderror sothat agood fitwasobtainedforall includedfunctions. Atotal of10simulations withdifferentstartingconfigurationsweredone foralltheconsideredsystems.

2.6. Inelasticneutronscattering(INS).

High-resolution INS measurements were conducted at the indirect-geometry spectrometerTOSCA atISIS NeutronandMuon Source, Rutherford Appleton Laboratory in the United Kingdom [35,36]. 5 g samples of the alloyand the partially desorbed hy- dride were placed inside flat Al cells with cross-sectional area 4.0×4.8cm²andthickness0.5mm.Thecross-sectionofthebeam was4.0×4.0cm².TheINSspectrawere collectedbelow−258^◦C using a closed-cycle He refrigerator. This was done to minimize the contribution ofthe Debye–Waller factor. 10g of the partially desorbedhydride wasalso placedinsidea stainlesssteelcylinder withdiameter 12.5mm and height 6.0cm.Hydrogen gas loading wasperformedbyexposingthesampleto35barH₂at127^◦Cun- tilnochangecouldbe observedintheINSspectrum.Thesample wasthen cooledtoRT wheretheINSspectrumwasrecordedun- derhydrogengaspressure.

2.7. Densityfunctionaltheory(DFT)calculations.

Phonon spectra were calculated by DFT to generate in silico spectraforcomparisonwithexperimental INSequivalents.Forthe fullyhydrogenatedcompound,thebinaryhydrideswithCaF₂-type structures were investigated. For TiVCrNbH_2.4, a 2×2×2 super- cell with nominal composition TiVCrNbH_2.25 with random struc- ture approximation wasutilized. In thissimulation, the Ti, V, Cr andNbatomsareswappedrandomlytofindtheminimumenergy configuration.Thephononcalculationwascarriedoutonlyforthe final,lowenergyconfiguration.

Total energies were calculated by the projected-augmented plane-wave(PAW)implementationoftheViennaabinitiosimula- tionpackage(VASP)[37,38].Allthesecalculationsweremadewith thePerdew–Burke–Ernzerhof(PBE)[39]exchangecorrelationfunc- tionalwith theHubbard parametercorrection (LDA+U), following therotationallyinvariantform[40,41].EffectiveUvaluesof3.25eV and3.7eVwereusedfortheV-dandCr-dstates,respectively.

Ground-state geometries were determined by minimizing stressesandHellman–Feynmanforcesusingtheconjugate-gradient algorithm with force convergence less than 10⁻³eV/˚A. Brillouin zone integration was performed with a Gaussian broadening of 0.1eV during all relaxations. From various sets of calculations it wasfound that 512 k-points in the whole Brillouinzone forthe structure with a 600eV plane-wave cutoff were sufficient to en- sureoptimumaccuracyinthecomputedresults.Thek-pointswere generated usingthe Monkhorst–Pack methodwith a grid size of 8×8×8forstructuraloptimization.Asimilardensityofk-points andenergycutoff wereusedtoestimatetotalenergyasafunction ofvolumeforallthestructuresconsideredinthepresentwork.

Afrozenphononcalculationwasappliedtothesupercellsusing thephonopyprogram toobtain thephonon dispersioncurve and phonondensityofstates[42].Anatomicdisplacementof0.0075˚A wasusedwithasymmetryconsideration toobtaintheforcecon- stantsforthephonon calculations.The displacementsinopposite directionsalong all possibleaxes wereincorporated inthe calcu- lationstoimprovetheprecision.Theforcecalculationsweremade

M.M. Nygård, Ø.S. Fjellvåg, M.H. Sørby et al. Acta Materialia 205 (2021) 116496

Fig. 1. PCIs (left) and corresponding van ’t Hoff diagrams (right) for absorption and desorption of hydrogen (a) and deuterium (b) in TiVCrNb.

using the VASPcode withthe supercellapproach (with LDA +U correction)andtheresultingdatawereimportedintothePhonopy program. The dynamical matrices were calculated fromthe force constants,andphonondensityofstates(PhDOS)curveswerecom- puted usingtheMonkhorst–Pack scheme[43].Phononcalculation wasweightedwiththe neutronscatteringcrosssectionsincluded with AbINSinthe Mantid softwareto obtain in silicospectra for comparisonwiththeexperimentalINSspectra.[44,45].

3. Resultsanddiscussion

TheHandDcontentsofthepartiallyhydrogenated/deuterated materialscanbedeterminedfromthedifferencebetweenthemax- imumandreversiblehydrogencontentsmeasuredmanometrically.

This calculation suggests that the synthesized compounds have compositions TiVCrNbH_2.82(3) and TiVCrNbD_2.60(16), respectively.

TG/DSC data were also measured to verify these results. It was found that the compositions are lower than what wassuggested fromthemanometric measurements,namelyTiVCrNbH_2.44(3) and TiVCrNbD_2.20(4). A possible explanation to these discrepancies is that the maximum H and Dcontents are reducedfrom the first tothesecondloadingcycle.

Fig. 1 shows hydrogen and deuterium pressure composition isotherms (PCIs) and the corresponding van ’t Hoff diagrams for TiVCrNbHxandTiVCrNbDx.Themeasuredcurvesarecharacterized by two plateaus. The pressure at the first plateau is below the rangeofthepressuretransducerintheSievertsapparatus.Thesec- ondischaracterizedbyasignificantlevelofhysteresisandaslope

Fig. 2. Rietveld refinements of PND and SR-PXD patterns for TiVCrNbD x, x = 0 , 2 . 2 , 8 at RT . Visible peaks corresponding to Fe are indicated by black arrows. The inset of the upper middle panel shows an enlargement of the PND fit for TiVCrNbD 2.2.

in the plateaupressure. Attempts were madeto measure PCIs at RT,butthiswasnotpossible.Extrapolationsuggeststhatthedes- orption plateaupressures are0.01barand0.002barfor hydrogen anddeuterium,respectively.Thesevaluesarebelowthelowerlimit of0.03barofthepressuretransducerwhichexplainswhywewere unabletomeasurethePCIsatRT.Itisclearthattheplateaupres- sures arehigherforhydrogenincomparisonwithdeuterium,but the shape ofthecurves aresimilar. Moreover, the final hydrogen contents of the full and partially desorbed materials are compa- rable.Thissuggeststhat thestructures ofdeuterides mustbethe sameasthoseofthehydrides.Thus,thehydrogenation/deuteration processcanbedescribedas

α β γ

⁽⁴⁾

where

α

^{denotesthedeuteriumfree alloy,}

β

^{thepartiallydeuter-}

atedsystemand

γ

^thedideuteride.

Fig. 2 presents Rietveld refinements of PND and SR-PXD pat- terns of TiVCrNbDx, x=0,2.2,8.0. The corresponding crystallo- graphicinformationisgiveninTable1.Theascastalloy(

α

^)isbcc

(Im3m),thepartiallydeuteratedmaterial(

β

^)isbct(I4/mmm)and thedideuteride(

γ

^)hasaCaF2-typestructure(Fm3m).Extrapeaks correspondingtoFecomingfromtheanvilwheretheascastalloys were crushed can be seen in the PND patterns of both TiVCrNb andTiVCrNbD_2.2.ThestrongestpeakforFeisindicatedby arrows in thefigure.These peaksarenot visibleinthe SR-PXD patterns, andourRietveldrefinementindicatesthattheamountofFeisless than0.3wt.%.Thus,thecontributionofthisimpuritytothePDFis insignificant.Noticethemuchlowerscatteringintensitywithboth X-raysandneutrons fromTiVCrNbD_2.2 incomparisonto thealloy anddideuteride.Atthesametimethereissubstantialdiffusescat- tering in the Q-range from2.0 ˚A⁻¹ to 4.5 ˚A⁻¹ of the PND pat- tern.This isindicative ofSROin thedeviations fromtheaverage long-range atomicstructure. All octahedral and tetrahedral inter- stices are occupied by D with low occupancies forthis material (see Table1). The distances betweenthese sites are summarized

Table 1

Crystallographic data for TiVCrNbD x, x = 0 , 2 . 2 , 8 at RT . Note that Ti, V, Cr and Nb occupy the M-site with equal probability. Estimated standard deviations are given in parentheses.

Compound: TiVCrNb

Space group: Im 3 m

Lattice parameter, a : 3.13228(7) ˚A Unit cell volume, V 0: 30.731(12) ˚A ³

Mass density, ρ: 6.585 g/cm ³

Number density, ρ0: 0.0651 atoms/ ˚A ³

Atom Site x y z U iso Occupancy

M 2 a 0 0 0 0.00932(5) 1.0

Compound: TiVCrNbD 2.2

Space group: I4 /mmm

Lattice parameter, a : 3.2048(2) ˚A Lattice parameter, c: 3.2747(3) ˚A Unit cell volume, V 0: 33.635(6) ˚A ³

Mass density, ρ: 6.127 g/cm ³

Number density, ρ0: 0.0924 atoms/ ˚A ³

Atom Site x y z U iso Occupancy

M 2 a 0 0 0 0.022(2) 1.0

D 2 b 0 0 1 / 2 0.0368(9) 0.105(1)

D 4 c 1 / 2 0 0 0.1198(11) 0.081(4)

D 4 d 1 / 2 0 1 / 4 0.0561(16) 0.042(4) D 8 j 0.2118(7) 0 1 / 2 0.0216(7) 0.051(8)

Compound: TiVCrNbD 8

Space group: F m 3 m

Lattice parameter, a : 4.37800(3) ˚A Unit cell volume, V 0: 83.912(2) ˚A ³

Mass density, ρ: 5.142 g/cm ³

Number density, ρ0: 0.1430 atoms/ ˚A ³

Atom Site x y z U iso Occupancy

M 4 a 0 0 0 0.00471(7) 1.0

D 8 c 1 / 4 1 / 4 1 / 4 0.1456(6) 1.006(3)

M.M. Nygård, Ø.S. Fjellvåg, M.H. Sørby et al. Acta Materialia 205 (2021) 116496

Fig. 3. RMC fits to the X-ray and neutron total scattering functions (a) G (^r), (b) D (^r), (c) F(^Q), and (d) Bragg scattering of TiVCrNb.

Fig. 4. RMC fits to the X-ray and neutron total scattering functions (a) G (r), (b) D (r), (c) F (Q), and (d) Bragg scattering of TiVCrNbD 2.2.

M.M. Nygård, Ø.S. Fjellvåg, M.H. Sørby et al. Acta Materialia 205 (2021) 116496

Fig. 5. RMC fits to the X-ray and neutron total scattering functions (a) G (r), (b) D (r), (c) F (Q), and (d) Bragg scattering of TiVCrNbD 8.

Fig. 6. Pairwise multicomponent short-range order parameters (PM-SRO) for the considered compositions extracted from the RMC large box models. The limiting values discussed in the text are indicated by dashed lines. The coordination shells where SRO is observed in TiVCrNbD 8are marked with numbers.

Table 2

Nearest-neighbour distances measured in ˚A for the different atoms in TiVCrNbD 2.2.

Octahedral Tetrahedral M 2a D 2b D 4c D 4d D 8j

M 2a 2.80 1.64 1.60 1.80 1.77 Octahedral D 2b – 2.80 1.60 1.80 0.68

D 4c – – 1.64 0.82 0.92

Tetrahedral D 4d – – – 1.64 1.23

D 8j – – – – 0.96

inTable2.Weexpectthatneighbouringsitesareunoccupiedfrom the Switendick criterion [46], otherwise the D atoms would have been closer than 2 ˚A apart, andthe criterion would be violated.

Thus, itisensured thatallDatomswerefurtherapartthan2.0 ˚A intheinitialconfigurationsoftheRMCmodelling.

Figs.3–5presentstheobtainedRMCfitstoG(^r),D(^r),F(^Q)^and theBraggpeakintensitiesfortheascastalloy,partiallydeuterated and fully deuterated compounds, respectively. The figures show that the obtained fits are in excellent agreement with the ex- perimental data.The quality of the fits andthe obtainedmodels were comparableoverthe10RMCrunsthatwereperformed.The amount ofdisorder inthe systemcan be characterized by calcu- latingthepairwise multicomponentshort-range orderparameters (PM-SRO)fromtheRMCmodels[47].Thesearedefinedas

α

^{i j}

(

^m

)

= p_{i j}

(

^m

)

^−cj

δ

^{i j−cj (5)}

where c_j is the fraction of element j in the alloyand

δ

i j=1 if i= jand

δ

i j=0otherwise.ForanequiatomicHEAwithN=4dis- tinct chemical speciesc_j=c=1/4. p_{i j}(^m) ^isthe probability that anatomisoftype jinthemthcoordinationshellaroundacentral atom oftypei.Itfollowsfromthedefinitionthat 4

j=1p_{i j}(^m)=1 for all elementsi. The PM-SROparameters can be understood as

Fig. 7. A supercell made of 4 ×4 ×4 face-centred cubic unit cells. The coordination numbers relative to the atom marked “0” in the bottom left corner are displayed on the cyan atoms. These atoms are located in coordination shells where there is increased probability of finding Ti around a Ti atom or Nb around a Nb atom in the RMC structure model of TiVCrNbD 8, i.e., coordination shell 4, 8, 12, 15, 19, 23, 27, 30 and 34. It can be seen that these sites form a 2 ×2 ×2 supercell. One such supercell is outlined with thicker, cyan lines.

therelativedeviationfromacompletelyrandomizedsolidsolution.

Inthe limitingscenarios,

α

ii(^m)=1is obtainedifthere are only atomsoftypei and

α

ii(^m)=−1/3iftherearenoatomsoftype i inthemthcoordination shell.Acompletelyrandomized solid so- lution without anySRO is characterized by

α

i j(^m)=0. For i=j,

M.M. Nygård, Ø.S. Fjellvåg, M.H. Sørby et al. Acta Materialia 205 (2021) 116496

Fig. 8. Gaussian peaks fitted to the metal-only strain-PDF G strain(^r) of TiVCrNb (a) and TiVCrNbD 8(b). The peaks full-widths at half maximum (FWHM) are compared to values from a similar analysis for TiVNb, TiVZrNb and TiVZrNbHf (c) and the corresponding dideuterides (d). Values for these other systems are adopted from Ref. [48] . In (c) and (d), the dashed black lines indicates the typical magnitude of the FWHM corresponding to thermal vibrations. Assuming a normal distribution of oscillations and a typical mean-square displacement ( msdor U iso) of 0.01 ˚A, a value of around 0.24 ˚A is obtained using the relation FWHM = 2

2 ln (2)·msd .

α

i j(^m)=−3ifthereareonlyatomsoftype j inthecoordination shelland

α

i j(^m)=1iftherearenoatomsoftype j.ThePM-SRO parameters of the obtained RMCmodels are shown in Fig. 6. In general, the elementsseems to be well dispersed and the metal lattice canbecharacterized asbeingveryclosetoarandomsolid solution.However, therearesome tendenciestowardsorderingin the deuterides. Inparticular, there isan increased probability for Nbtobe coordinatedbyitself inthefirstcoordinationspheres of TiVCrNbD_2.2.TiVCrNbD₈ hasthe same local ordering as reported for TiVNbD_5.7 [48]. In particular, the probability is higher for Ti and Nb to be coordinated by itself in the 4th, 8th, 12th, 15th, 19th,23rd,27thand30thcoordinationsphere.Thesecoordination spherescorresponds toa2×2×2face-centredcubicsupercell,as presentedinFig.7.Nevertheless,thedeviationsfromacompletely randomized solidsolutionarefarfromthelimitingscenariosout- linedabove.

Many exceptional properties reported forHEAs have been at- tributed to severe lattice distortion caused by differently sized

atoms in the alloy[13]. The lattice distortion is often quantified bytherelativevariationinatomsizes

δ

^{rthatisdefinedas}

δ

^{r= N}

i=1

ci

1−r_i r

2

·100% (6)

where r=N

i=1c_ir_i with

{

^ci

}

^Ni=1 and

{

^ri

}

^Ni=1 asthe concentrations andradiioftheNelementsintheHEA,respectively.Thedirectev- idence of thiseffect is limited in theliterature [49].One reason behindthisisthe difficulty toperform suitable measurements. It hasbeensuggestedthattheleveloflocallatticestraincanbe as- sessedfromanalyzingthefull-widthsathalfmaximum(FWHM)of thepeaksinastrain-PDFobtainedfromRMCmodelling[50].Such an analysis has recently been performed for TiVNb (

δ

^r=4.29%), TiVZrNb (

δ

^r=6.87%) and TiVZrNbHf (

δ

^r=6.96%) and the corre- spondingdideuterides[48].Forthesesystemsitwasobservedthat theFWHMof thepeaksin thestrain-PDFof thealloysincreased

Fig. 9. The D-D and M-D partial PDFs for TiVCrNbD 2.2(a) and TiVCrNbD 8(b) averaged over the ten fits obtained from the RMC modelling. The horizontal black lines indicates one standard deviation about the mean M −D nearest-neighbour and second-nearest neighbour distances for the tetrahedral and octahedral interstices in the RMC model of TiVCrNbD 2.2.

significantly from TiVNb to TiVZrNb and TiVZrNbHf. This is ex- pected from the higher

δ

^{r values in the latter HEAs. The strain}

waslowerinthecorrespondingdeuterides,butthetrendwasstill present. The atomicradii of Ti, V, Cr andNb are 1.46 ˚A, 1.32 ˚A, 1.25 ˚Aand1.43 ˚A,respectively[13].Thus,TiVCrNbhas

δ

^r=6.18%, anditshouldbe expectedthat alsothisalloyisseverelystrained.

However, Fig. 8 demonstrates that the strain is comparable with that obtainedforTiVNbforwhichmostoftheFWHMcanbe ex- plained bythermalvibrations.Themaindifferencebetweenthese alloysiswhethertheelementthatcauses

δ

^{rtoincreaseissmaller}

orlargerthantheothers.Thus,ouranalysisindicatesthattheHEA lattice islesspronetowards strainwhensmallerelementsare in- troduced intoa matrix oflarger atoms. Since

δ

^{r is} insensitiveto this, itcanbe amisleadingmeasureofthelocallatticedistortion inaHEA.

Fig. 9presentsthe D-DandM-D partial PDFsforTiVCrNbD_2.2 andTiVCrNbD₈.Thefirst peakin theD-Dpartial isinboth cases just above 2 ˚A in compliance withthe Switendick criterion. This resultcomessolely fromtheexperimental dataandnotfromany imposed constraintorpenalty duringthe modellingprocess. The M-D partials of TiVCrNbD8 are characterized by well-defined co- ordinationshells.However, forTiVCrNbD_2.2 theM-Dpartials have a continuousdistribution. Moreover, for thiscompound it is ob- servedthatDhasasignificantlyhigherprobabilityofbeingcoordi- natedbyTiandVthanCrandNb.Thisresultisincompliancewith resultsreportedfordeuteridesformedfromTi_0.45Cr_0.35Mo_0.20[24]. Moreover,itisalsoclearthatthiseffectisonlypresentinthefirst coordination sphere (r<2.2 ˚A). The first two peaks in the M-D partialsareattributedtotheoctahedralandtetrahedralinterstices, respectively.Inthetetrahedralinterstices,Discoordinatedbyfour

nearest-neighbour metals at r=1.9(³) ^{˚A in the RMC model. In} theoctahedral interstices,the metal octahedronsurroundingDis madeoutoftwonearest-neighbourandfoursecond-nearestneigh- bour metals. The distance from Dto theseare r=1.6(²) ^{˚A and} r=2.6(³) ^˚A,respectively.The meanvaluesofthe octahedraland tetrahedralnearest-nighbourdistancesareinverygoodagreement withthevaluesexpectedfromcrystallography(seeTable2).Analy- sesofthelocalcoordinationenvironmentsindicatesthattheocta- hedralsecond-nearestneighboursarerandomlydistributed.Fig.10 shows the fraction of occupied tetrahedral and octahedral inter- sticesin theRMC structuremodel withdifferentmetals asnear- estneighbours.Itisclearthatalargerfractionofthesitesareoc- cupied if theVEC of the nearest-neighbours are lower. Thus, the destabilization effectpresented inRef. [21]is alsopresent atthe locallevel.This suggeststhatit could bepossible toincrease the reversiblehydrogenstoragecapacityby fine-tuningtheHEAcom- position.InthisendeavoritshouldbekeptinmindthatVEC>5.0 oftenresultsinareductioninthemaximumhydrogenstorageca- pacity[21].Thus,theoverallVECshouldbekeptat5.0.Onepossi- bilitytoachievethisistoreducetheamountofTiandCrequally.

AnotherstrategyistoreducetheamountofTiandaddanappro- priateamountofanotherelementwithhigherVEC,e.g.Mn,Feor Ni.

The analyses presented above indicate that theremaining hy- drogenatomsinthepartiallydesorbedmaterialoccupysiteswith allpossiblecombinationsofnearestneighboursinbothoctahedral andtetrahedral interstices. Thus, the local metallic environments around thehydrogen atomsarevery diverse. Thisshould also be reflectedin thevibrationaldensityofstates(vDOS)ofthehydro- genatomsasmeasuredbyINS.Fig.11presentsthemeasuredINS

M.M. Nygård, Ø.S. Fjellvåg, M.H. Sørby et al. Acta Materialia 205 (2021) 116496

Fig. 10. The fraction of tetrahedral and octahedral interstices with different nearest-neighbour metals that are occupied by D within the RMC structure model of TiVCrNbD 2.2. The insets presents the polyhedra with the D and Mindicated by green and grey balls, respectively. For the octahedron, the second-nearest metals are within the horizontal plane. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

spectraofTiVCrNb,TiVCrNbH_2.4and TiVCrNbH₈ as well as the to- talscatteringcontributionscalculatedfromDFTforthehydrides.In theINSspectrumofTiVCrNbH8 thereisasingle,broadvibrational band inthe range 150–300meV. The energy rangeof the vibra- tion isincompliancewiththat expectedfora regulartetrahedral environment[51].

The INS spectra can be evaluated with respect to the mod- els obtainedfromtheRMCstructure modelling.Fig.9showsthat the M–D bond length distribution is separated into well-defined peaks in the RMC structure model of TiVCrNbD₈. The distribu- tion anddisorderofM–D bondingin TiVCrNbD₈ ismanifested in the widthsofthesepeaks.Duetothedisordered atomicarrange- ment with severaldifferently sized atoms, it should be expected that the INS spectra and vDOS reflect the diversity in different M–Hbond lengths. Indeed,thebroadnessofthe vibrationalband ismuchlargerthanexpectedforabinarymetalhydride.Thus,the INSspectrumofTiVCrNbH₈ representsalargediversityfortheM–

Hbonds and hydrogenvibrations. It shouldbe noted that noin- tensityisobservedintheenergyrangearound128meVwherevi- brationsfromhydrogeninanoctahedral environmentisexpected [51].This indicates that hydrogensolely occupies the tetrahedral intersticesinTiVCrNbH₈.Furthermore,DFT calculationssubstanti- atethesefindings. Fig.11alsodisplaysthe insilico INSspectrum of TiVCrNbH₈ where contributions from all the binarymetal hy- drides have been summed. The in silico INS spectra of the indi- vidualmetalhydridesshowsome splittingofthepeaks.However, when all the binary spectra are combined the broadness of the measured INSspectrumiswell reproduced,once againindicating alargediversityinM–Hbondsandhydrogenvibrations.Theover- all shape oftheexperimental andin silico spectraare incompli- ance,butthevibrationalenergiesareslightlyoverestimatedinthe latter. However, thisis a common trait when calculatingphonon spectra by DFT where the harmonic nature is often exaggerated [52–55].

Fig.11 alsopresentsthe INS spectrumof TiVCrNbH_2.4. Inthis case,theINSspectrumissmearedandwithoutsharpfeatureswith twoverybroadbandscentredat90meVand170meV.Thisisin contrast tothe well-defined peak in the measured INS spectrum ofTiVCrNbH₈.Yet,thespectrumisincontrasttothatmeasuredof thehydrogen-freealloywhichisnoughtabovethemetalphonons at0–70meVconfirmingthepresenceofhydrogeninTiVCrNbH_2.4. Fig.9showsthattheM–DbondlengthdistributioninTiVCrNbD_2.2 iscontinuous.Thisisaverydifferentcharacteristicthanthewell- definedpeaksinthecorrespondingdistributionofTiVCrNbD₈.This observation provides an indication of the severity of the disor- derinthehydrogensublatticeofTiVCrNbH_2.4.Itseemsreasonable thatacontinuousdistributionofM–HbondlengthsinTiVCrNbH_2.4 couldcauseacontinuousvDOSforhydrogenwithacorresponding, continuousINS spectrumlike the one presentedin Fig. 11. Thus, the RMC structure model provides a possible explanation to the smearedINSspectrumofTiVCrNbH_2.4.Theinsilicospectrumpre- sentedinFig.11isgeneratedfroma2×2×2supercellwithnom- inalcompositionTiVCrNbH_2.25 bytherandom structureapproach.

The spectrum displays a wide range of distinct hydrogen modes fromthe differentlocal environments forhydrogen inthe super- cell. However, because of the limited size of the model, only a limitednumberof vibrationalmodesare observed.The modelis, therefore,not able to reproducethe continuousshape of theex- perimentalINSspectrum.Weexpectthatalargersupercellwould provideamorerealisticvDOS,butcalculationsfromsuchamodel would be computationally expensive and is, for this reason, not pursued.Thus,it isconcludedthatthecalculationreproduces the mostimportantaspectsofthespectra,i.e.,thediversityoflocalen- vironmentsforhydrogen.Asmentionedabove,thephononcalcula- tionoverestimatesthevibrationalenergies,andwiththisinmind, alsothe low energyvibrationalmodesforhydrogen isaccounted for.

Fig.12showsthedistribution ofdeuteriumatomsintheRMC structure models of TiVCrNbD_2.2 and TiVCrNbD₈ projected onto the xy-, xz- and yz-plane of the respective unit cells. The fig- ure clearly demonstrates that the probability of finding a deu- terium atom outside the tetrahedral interstices in TiVCrNbD8 is zero. For TiVCrNbD_2.2 the probability of finding the deuterium atomsinthecrystallographicallyexpectedpositionsishigh.How- ever,in thiscasethereis alsoa significantprobability ofobserv- ing thedeuterium atomsbetweenthe octahedral andtetrahedral interstices.Thisindicatethat hydrogenatomsaremobilebetween the available sites. Quasi-elastic neutron scattering (QENS) could reveal if the diffusion is predominately local or long-range, but this is beyond the scope of this work and thus left for future studies.

Fig. 11. Measured INS spectra (top row) and in silico equivalents calculated by DFT (bottom row). The in silico spectrum compared to TiVCrNbH 2.4is generated from a 2 ×2 ×2 supercell with nominal composition TiVCrNbH 2.25. The in silico spectrum compared to TiVCrNbH 8is the sum of those calculated for the binary dihydrides.

Fig. 12. The distribution of D in the RMC structure model of TiVCrNbD 2.2(bct structure) projected onto the xy - (a), xz - (b) and yz -plane of the unit cell. The same is shown for TiVCrNbD 8(CaF 2-type structure) in (d), (e) and (f). The colorbars indicates the percentage of D at any position in the unit cells.

4. Conclusions

The present work has explored the average and local struc- ture of TiVCrNbDx, x=0,2.2,8.0 using total scattering measure- ments and RMCstructure modelling.The metal lattices are close

torandomsolidsolutionsintheobtainedmodels.TiVCrNbisabcc (Im3m) HEA with

δ

^r=6.18%. The prevailing opinion inthe liter- ature of HEAs is that a larger

δ

^{r indicates a more severely dis-}

torted lattice. However, this work demonstrates that the amount of local lattice strain in TiVCrNb as measured by the strain-PDF