structure of naturally hydrated ferrihydrite revealed ...b. x-ray diffraction x-ray diffraction data...
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This is an author produced version of Structure of naturally hydrated ferrihydrite revealed through neutron diffraction and first-principles modeling.
White Rose Research Online URL for this paper:http://eprints.whiterose.ac.uk/121080/
Article:
Chappell, HF, Thom, W, Bowron, DT et al. (3 more authors) (2017) Structure of naturally hydrated ferrihydrite revealed through neutron diffraction and first-principles modeling. Physical Review Materials, 1 (3). 036002. ISSN 2475-9953
https://doi.org/10.1103/PhysRevMaterials.1.036002
(c) 2017, American Physical Society. This is an author produced version of a paper published in Physical Review Materials. Uploaded in accordance with the publisher's self-archiving policy.
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Structure of naturally hydrated ferrihydrite revealed through neutron diffraction
and first-principles modeling
Helen F. Chappell1, 2*, William Thom2,3, Daniel T. Bowron4, Nuno Faria2,3, Philip J. Hasnip5 & Jonathan J. Powell2,3
1SchoolofEarthandEnvironment,UniversityofLeeds,Leeds,LS29JT
2MRC,ElsieWiddowsonLaboratory,120FulbournRoad,Cambridge,CB19NL,UnitedKingdom.
3DepartmentofVeterinaryMedicine,UniversityofCambridge,Cambridge,CB30ES,UnitedKingdom
4ISISPulsedNeutronandMuonSource,STFC-RutherfordAppletonLaboratory,Harwell-Oxford,Didcot,OX110QX,UnitedKingdom
5UniversityofYork,DepartmentofPhysics,Heslington,York,YO105DD,UnitedKingdom
(Received8thJune2017;published14thAugust2017)
Abstract
Ferrihydrite,witha‘twoline’X-raydiffractionpattern(2L-Fh),isthemostamorphous
oftheironoxidesandisubiquitousinbothterrestrialandaquaticenvironments.Italso
playsacentralrole in theregulationandmetabolismof iron inbacteria,algae,higher
plants, andanimals, includinghumans. In this studywepresenta single-phasemodel
for ferrihydrite that unifies existing analytical data whilst adhering to fundamental
chemical principles. The primary particle is small (20-50 Å) and has a dynamic and
variablyhydratedsurface,whichnegates long-rangeorder;collectively, these features
have hampered complete characterization and frustrated our understanding of the
mineral’s reactivity and chemical/biochemical function. Near and intermediate range
neutrondiffraction(NIMROD)andfirstprinciplesdensityfunctionaltheory(DFT)were
employed in this study to generate and interpret high resolution data of naturally
hydrated, synthetic 2L-Fh at standard temperature. The structural optimization
overcomes transgressions of coordination chemistry inherent within previously
proposedstructures,toproducearobustandunambiguoussingle-phasemodel.
DOI:10.1103/PhysRevMaterials.1.036002
I.INTRODUCTION
Ferrihydrite(Fh) isahydrated ironoxidemineral,ubiquitous ingeochemicalsystems
andinbiologydespiteahighsolubilityproduct(log10*KSO,~3.96)andtendencytowards
phaseconversion;thesefactorsbeingoutweighedbyitsrapidformationkinetics.Asa
consequenceofthelatter,Fhprecipitatesreadilyfromaqueoussystemsacrossawide
rangeofpHs(≥2)inpreferencetoslowerformingstablemineralssuchasgoethiteand
hematite. The large specific surface area (>600m2/g) of its typical nanocrystalline
agglomerates, and associated structural disorder, engender much of Fh’s unique
chemistrybutalsohampercharacterization.Thus,despitecrucialrolesinnature[1,2,
3], biology [4], technology [5] and medicine [6], the mineral structure of Fh remains
contentious.
Two-line ferrihydrite (2L-Fh), so termed because of the two broad Bragg peaks
observed with X-ray diffraction, is the primary natural form of the mineral and has
recentlybeenshowntonucleatefromaFe13Kegginionprecursor[7].Withaprimary
particle size of only 2-5 nm [8] the structural features of 2L-Fh are dominated by
surfaceatoms.Thislargesurface:volumeratiocoupledwiththeconsequentlossoflong-
range order has foiled multiple techniques in the absolute characterization of 2L-Fh
particles.Moreover, themineral surface isdynamicandhydrated, andall attempts to
stabilize the core mineral phase through high temperature treatment have led to
surface water loss and inevitable structural changes. For example, Harrington et al
heated their 2L-Fh samples to 300 °C for 30 minutes under vacuum to increase the
crystallinityofthemineralcoreandremovenoiseintheneutrondiffractionanalysis[9].
As a result, structures for 2L-Fh have been proposed from a suite of techniques that
haveusedferrihydriteinamultitudeofdifferentphysiochemicalforms(TableI).
Notwithstanding,twostructureshavecometodominatethelandscape.Thefirstisthe
3-componentmodeloriginallyproposedbyDritsetal[10].Themodeliscomposedofa
defective,randomlyoccupiedphase,adefect-freeclosepackingphaseandlowlevelsof
ultra-dispersedhematite[10].Apartfrombeingthefirststudytoproposeamulti-phase
model, it was also unusual in suggesting that all the Fe would be octahedrally
coordinated.InsupportofthismodelistheEXAFSandXANESstudyofManceauetal,
who, in examining the surface structureofFh, show that theoctahedral-only3-phase
modelprovidesamatchfortheirexperimentaldata11.Incontrast,therearenumerous
studies,fromtheearlyEXAFSandX-rayabsorptionedgespectroscopyofHeald[12]and
Eggleton[13]totheelectronenergy lossspectroscopystudyofVaughanetalin2012
[14],whichshowthat themineralcontainsbothoctahedralandtetrahedral ironsites,
althoughthereisdisagreementovertheactualpercentageoftetrahedralFe.Thesecond
predominantstructureisasingle-phasemodel,proposedbyMicheletal [15,16]. It is
baseduponisostructuralakdalaiteandhasalotincommonwiththeearlieststructures,
with its mix of octahedral and tetrahedral Fe sites [12, 13, 15], and was determined
from XRD generated Pair Distribution Functions (PDFs) [9, 15]. In support of this
model are the many studies that conclude the mineral phase must include both
tetrahedrallyandoctahedrallycoordinatedFe[TableI;12,13,14,15,17,18].However,
thissingle-phasemodeldemonstratescertainstructuralanomalies,e.g.[19,20,21,22],
namely tetrahedral Fe-O bonds which are effectively too long, giving tetrahedral and
octahedralvolumesthatareequal,andanunrealisticallyshortbondwithinthatsame
tetrahedral environment, which gives each tetrahedra a large degree of eccentricity,
suggestingthermodynamicinstability[20].
Onerecurringissuewithallthesestudies,particularlywiththemoremoderndiffraction
data, isthelackofanalysisonsampleswithoutheat-treatment,asonlythenissurface
hydrationmaintainedandtheriskofstructuralchangesavoided.HereweusedtheNear
andIntermediateRangeNeutronDiffractometer(NIMROD)togeneratehigh-resolution
neutrondiffractiondataof2L-Fh.Theinstrument,whichisoptimizedformeasuringthe
diffuse scattering signals of light-element containing systems, is ideal for the 2L-Fh
nanoparticulate system where there is not well-defined Bragg scattering in the F(Q).
Thishasallowedustouseferrihydritedriedatjust40°C,butwithnosubsequenthigh-
temperature treatment thatwould risk significantdehydrationor evenphase-change.
We have revisited the previous single-phasemodel ofMichel etaland optimized the
structure from first principles. Importantly, we have shown that an improved single-
phasemodel,whichhasallthechemicalambiguitiesremoved,isanexcellentmatchfor
the experimental data without the need for resorting to over-fitted multi-phase
structures.
StudyTechniquesSampleImplicationsToweetal,1967
[23]IR;XRD;differential
thermalanalysisFerritin;2L-Fh,
preparedat85°C.Samplesdriedat50
°C&110°C.
Hematite-likestructure;Oct&Tet
Fesites.
Harrisonetal,1967[4]
X-ray&electrondiffraction
Ferritin Oct&TetFesites
Healdetal,1979[12]
EXAFS Ferritin Oct&TetFesites
Eggletonetal,1988[13]
X-rayAbsorptionEdgeSpectroscopy;
electronmicroscopy;X-raypowderdiffraction;
thermalanalysis
2L-Fh&6L-Fh.Preparedat60°C&75°Crespectively.
Oct&Tet(36%)Fesites;
developmentofmaghemiteafter
300°C
Dritsetal,1993[10]
XRD 2L-Fh&6L-Fh 3-componentmodel;defective,defect-freeandultra-dispersed
hematite(10%).OctFeonlysites.
Zhaoetal,1994[17]
XAFS 2L-Fh&6L-Fh.Preparedatvarious
temperaturesbetween50–500°C
Oct&Tet(10%)Fesites.Tetsitesat
thesurface.
Manceauetal,1997[11]
XANES 2L-Fh&6L-Fhpreparedat92°Candair-driedat25
°C.
OctFesites.OverestimationofTetFesites,fromprevious
study(Zhaoetal,[17]).
Jansenetal,2002[24]
XRD,NeutronDiffraction
6L-FhPreparedat75°C.
Nohematite.50%defective,50%
defect-freephases.
Micheletal,2007[15]
XRD,PDFs 2L-Fhpreparedat23°C,3L-Fh,6L-Fhpreparedat75°C.
Single-phasemodelwithbothOct&Tet
(20%)Fesites.
Rancourtetal,2008[19]
XRD 2L-Fhpreparedat60°Canddriedat
110°C.6L-Fhpreparedat75°C.
Single-phasestructureincorrect.
Malliotetal,2011[18]
EXAFS 2L-Fhpreparedat75°C,air-dried.4L-Fh,5L-Fh&6L-Fh.
Oct&Tet(15-35%)Fesites.
Vaughanetal,2012[14]
ElectronEnergyLossSpectroscopy
2L-Fh&6L-Fh.Preparedat70°C.
Oct&Tet(10%)Fesites.
ThisStudy NeutronDiffraction,PDFs,XRD,
Elementalanalysis
2L-Fh,preparedat20°C,driedat40°C.
Single-phasemodelresolved
TABLEI.Landmarkstudiesinthestructuralanalysisofferrihydrite,illustratingthe
differenttypesofsamplesandtechniquesemployed.
II.METHODS
A.SynthesisofFerrihydrite
2-line ferrihydrite(Fh)waspreparedbyprecipitation-titration;40mMferricchloride
solutionwasneutralisedviadrop-wiseadditionof5MNaOH(atSTP)underconstant
agitation.PrecipitateswerefilteredandwashedtwicewithUHPH2O,yielding3.89gof
solidproduct.Dryingtoconstantmassat40°Cyielded2.16goffinalproduct.
B.X-RayDiffraction
X-RaydiffractiondatawerecollectedwithaBrukerD8PowerDiffractometerusingCuK
α1 radiation, a Ge primary monochromator and a Lynx Eye Detector. The scanning
rangewas5-70degrees2thetaataspeedof7.5s/stepandastepsizeof0.01degrees.
Bruker Eva software was used to process the data with calibration peaks fitted to
referencesintheICDD(internationalcentrefordiffractiondata)database.
C.ElementalAnalysis
Totalironcontentwasdeterminedafteraciddissolutionbyinductivelycoupledplasma
opticalemissionspectrometry(ICP-OESJY2000,HoribaJobinYvonLtd.,Stanmore,UK).
CHN and O analysis were carried out by Elemental Microanalysis Ltd (Okehampton,
Devon).CHNquantificationwasachievedviaDumasCombustionandGC-TC(EA1110,
CE Instruments,Wigan,UK),whilstoxygen contentwasdeterminedviaUnterzaucher
PyrolysisandGC-TC(NA2000,Fisons).Chlorinequantificationwascarriedoutviathe
oxygen flask method with a mercuric nitrate titrant solution and diphenylcarbazone
indicator.TableIIprovidesdetails.
Element Relative
Abundance
Fe 1(±0.012)
O 2.4(±0.056)
H 1.59(±0.022)
Cl 0.03(±0.001)
C 0.04(±0.001)
TABLEII.Relative(toFe)elementalabundancesofsynthesized2-lineferrihydrite.The
mineral is principally composed of iron, oxygen and hydrogen – quantified by
inductively coupled plasma optical emission spectrometry (ICP-OES), Unterzaucher
Pyrolysis and Dumas Combustion respectively. Trace levels of carbon and chlorine
arising from the mineral synthesis were detected via Dumas Combustion and the
oxygen flask method but play no fundamental role in the mineral structure. Around
23%ofthesamplecomposition(63%oftheoxygen)was inferredfromthe inevitable
formationofironoxidesduringpyrolysis.
FIG.1.(a)FerrihydriteX-raypowderdiffractionpattern,overlaidwithreflectionsfor2-
lineFh. (b)Fittingof theNIMRODexperimentaldata toa simple sphericalmodel. (c)
Distributionofnanoparticle sizeswithin the sample asdeterminedbyNIMROD:peak
radiusis17Å.(Wideformat–doublecolumn)
D.Neutrondiffraction
Neutron diffraction experiments were carried out with the Near and InterMediate
Range Order Diffractometer (NIMROD) instrument at the UK’s pulsed neutron and
muon source, ISIS (Harwell-Oxford). This instrument is able to simultaneously access
lengthscalesfrom<1Åto>300Å,thusprovidingrobustbond-lengthinformationatthe
required length scales. Moreover, as noted above, the study was undertaken with
material dried at just 40 °C thereby maintaining its natural 2L-Fh structure. A null
scattering vacuum-sealed Ti0.676Zr0.324 alloy sample holder, sealed against the
instrumentvacuumusingPTFEo-rings,wasusedtocollectscatteringdataat293Kfor
123 minutes. Collected data were corrected for background, multiple scattering and
absorption, and normalized to a vanadium calibration standard using GudrunN [25].
Neutronwavelengthsfrom0.05Åto14Åoveramomentumtransferrangeof0.02Å-1≤
Q≤50Å-1wereusedtogeneratethe interferencedifferentialscatteringcrosssection,
whichwasFouriertransformedtothePairDistributionFunction(PDF)[26].
Full and partial Pair Distribution Functions (PDFs) were calculated for modelled
structures and previously published models, using PDFgui [27]. For the purposes of
generating the PDFs, the models were constructed as laid out in the appropriate,
previouslypublishedwork[10,15].Forthe3-phasemodelthisrequiredtheproduction
of a compositePDF, created from theappropriateproportionsof the three structures
proposedinthemodel:namely,defective,defect-freeandhematite.
E.Computationalmodelling
FirstprinciplesDensityFunctionalTheory(DFT)calculationswerecarriedoutusingthe
plane-wavesimulationcode,CASTEP[28].Akineticenergycut-off,determinedthrough
convergence testing, of 700 eVwas employed alongwith aMonkhorst Pack3x3x3k-
pointgridforsamplingoftheBrillouinzone[29],givingamaximumk-pointseparation
of 0.05 2π/A. Convergence tolerances for energy change, maximum displacement,
maximumforceandmaximumstressweresetat1×10-5eVatom-1,0.001Å,0.03eVÅ-1
and0.05GParespectively.Ultrasoftpseudopotentials(BIOVIAlibrary)wereemployed
[30] along with the local spin-density approximation (LSDA) exchange-correlation
functional [31]. The strongly correlated 3d iron electrons were corrected with the
HubbardU formulationat4eV [32].Theelectronicgroundstatewas foundusing the
spin-polarized Ensemble Density Functional Theory method [33]. The spin states,
corresponding to the ferromagnetic ground state, were the same as those previously
calculatedbyPinneyetal[34].
Thestartingstructureforthesingle-phasemodel,whichisisostructuralwithakdalaite,
has a P63mc space group and lattice parameters of a=b=5.95 Å and c=9.06Å [15].
However,thespacegroupwasalteredtoP1fortheDFTsimulation,toallowcomplete
freedom of all parameters, thus removing the a=b constraint. It should be noted
however,thatnotwithstandingthisrelaxationinthecrystalsymmetry,thestructuredid
retaina=blatticeparametersatthecompletionofthegeometryoptimization.
III.RESULTS&DISCUSSION
A.Ferrihydritesampleanalysis
XRD analysis of synthetic ferrihydrite was undertaken to provide mineral phase
confirmation.Thisyieldedtwodiffusemaxima,whichwasbothtypicalofandconsistent
withreferencepeaksfor2-LFh(Fig.1(a)).
Further to this phase confirmation, we used the NIMROD neutron diffraction data to
interrogatebothparticlesizeandshape.Fittingatwo-spherecorrelationmodeltothe
low-Qregionof theNIMRODdata(0.02<Q<1.0) (Fig.1(b))yieldedpositiveresults,
suggestingagoodfitwithasphericalparticleshape.Ananocrystallitesizedistribution
wasalsoproducedwithameanparticlediameterof3.4nm±0.5Å(Fig.1(c)),which
falls within the expected size range (2-5 nm diameter) of 2-line Fh, as previously
determinedfromHigh-ResolutionTEM[8].
Elemental analysis (Table II) suggests a formula of 5Fe2O3.8H2O, in linewith bulk Fh
[24] or a heavily hydrated form of Fh as proposed by Michel et al [15], namely
Fe10O14(OH)2.7H2O. Hiemstra et al determined that Fh particle hydration inversely
correlateswithparticlediameter,decreasingfromawatercontentof~19%for2nm
particles,to~14%for3nmparticlesandbelow10%for8nmdiameterparticles[35,
36].OuranalysisindicatesthatthewatercontentofthissyntheticFh(15.3%)isslightly
higher than thereportedvalues for3nmFhparticles,attributable to theretentionof
physisorbedsurfacewater,aconsequenceofthelowdryingtemperature(40°C)used
topreservelocalFhstructure[18].Itisworthnotingthataccordingtothecalculations
ofHiemstraetal,a2.5nmparticlecouldbeclassedalmostentirelyas‘surface’withat
least67%ofthetetrahedralFebeingdirectlyboundtoasurfacemoietyandthesurface
‘felt’bymostof theother ions [35].This is indicativeof theamorphousnatureof the
mineral,andhenceitslackoflong-rangeorder.Indeed,arecentstudyusingMössbauer
spectroscopyshowedthatatomicvacanciesandstructuraldisorderaremostprevalent
attheparticlesurface,whichmaybeareasonwhysmallerparticlesappeartohavethe
greatestamountofdisorder[37].
B.Pairdistributionfunctionanalysis
To investigate the structural detail further, we employed Pair Distribution Function
(PDF)analysistocalculatethedistancesbetweenion-ionpairs.Thenormalizedall-ion
PDFwasconstructeddirectlyfromtheneutrondiffractiondata(Fig.2).
FIG.2.Neutron-diffractiongeneratedall-ionPDF for fully-hydratedsynthesized2-line
ferrihydrite.Thelargenegativetroughat0.95ÅisaccountedforbyanO-Hcorrelation.
Despite drying, the large trough at 0.95 Å indicates that a substantial amount of
hydrogen remains in the material. Due to hydrogen’s negative scattering length,
hydrogenassociatedpeaks,suchasO-H,havenegativeintensitiesordampenedpositive
signals.Thisdistance(0.95Å)isslightlyshorterthantheO-Hdistanceinwater(0.98Å),
which points towards the hydrogen being found in OH groups, principally on the
surface, rather than as structural water. In a previous neutron diffraction study on a
heated deuterated ferrihydrite sample, this trough can be seen as a positive peak at
approximatelythesamer-value[9].
Figure3showsthesameall-ionPDFofFig.2,togetherwiththePDFsfromthetwomost
acceptedferrihydritestructurespublishedinthe literature:theoriginal(2007)single-
phase [15] and 3-phase models [10]. The latter model was constructed in the 6:3:1
proportions stated in theoriginalpaper, composedof adefect-freephase, adefective
phaseandnano-hematite respectively [10].The inset inFig.3shows thedetailof the
firstpositivepeak(A),whichisindicativeoftheFe-Odistance(Fig.3).Clearly,thispeak
ismodelledmoreaccuratelybythesingle-phasemodel.
FIG.3.Neutron-diffractiongeneratedall-ionPDFforsynthetic2-lineferrihydrite(black)
comparedwith,inred,(a)theall-ionPDFoftheoriginalsingle-phase2-linemodel[15]
and(b)the3-phasemodel[10].ThefullycrystallinemodelPDFshavebeenattenuated
usinganexponential function,G(r)=G(r)0*e-0.234r, tomimic thedecay signal at larger
distances(r-values)thatwouldbefoundinananoparticulatesample.Thisexponential
wasintendednotasafittotheexperimentaldata,butsimplytoremovethelong-range
crystallinityinherentinthemodelledPDFs.TheinsetsshowPeakA,whichrepresents
thefirstFe-Obondlength,indetail.
WithreferencetotheexperimentalPDFinFig.3,itisworthnotingthelargeimpactof
thesurface-boundhydrogen,which,duetoitsnegativescatteringintensity,reducesthe
peakheights,dampeningthepositivesignal.Thisaccountsforthesmallerpeakheights
in the experimental data. As already explained above this surface bound hydrogen,
whichwasnotremovedfromtheparticles’surfacesinahigh-temperaturedryingstep,
marksoneof themost importantdifferencesbetween thehydratedsyntheticmineral
andthestructuralmodels.Equally,thelargenegativepeakintheexperimentalPDFat
0.95Å,whichrepresentssurfaceboundOH,isnotobservedinthemodelPDFasthisis
calculatedfromabulkratherthansurfacestructure.
As shown in Fig. 4(c), peaks a, d and f (as labelled in Fig. 4(a)) are almost entirely
identifiableas thedistancesbetweenFeandO ions.Peak c is stronglyaccounting for
both the Fe-Fe (Fig. 4(b)) and Fe-O (Fig. 4(c)) distances. However, other peaks,
particularlybande,representanumberofdifferention-ionpairs.Thus,withreference
toFig.2,theaverageFe-ObondlengthinthesynthesizedFhis2.04Å,withfurtherFe-O
distancesof4.77Åand6.42Å.Otherpeakswerenotsecurelyassignedtoparticularion
pairs,duetooverlapinsignal.
TheexperimentalFe-Obondlength(2.04Å)isclosertothesingle-phasemodel(2.00Å,
[15])thanthe3-phasemodel(1.90Å,[10]),althoughitshouldbenotedthatthissingle-
phasemodelincludesheavilydistortedFetetrahedrathathaveoneshorterFe-Obond,
indefianceofPauling’ssecondlaw.The3-phasemodelFe-Obondlength,obtainedfrom
thecompositePDF,fitspoorlytothenewdataandtootherreportedFe-Odistancedata
(1.97A)obtainedviaX-rayabsorptionfinestructure(EXAFS)spectroscopy[18].Evenif
theproportionsofthedefectiveanddefect-freephasesarevariedforthislattermodel,
itisonlywhenthemodelreachesitsdefect-freemaximumthattheFe-Opeak,ataround
1.93Å,approachesthelowestpointoftheexperimentaldatapeak.Doingthis,however,
eliminatestheamorphouscharacterofthemineral(whichwaseffectivelymodelledby
thedefectivephase),makingthestructurealtogetherunrealistic.
Wenextsort toaddresswhetherthesingle-phasemodelcouldberefinedtobetter fit
theexperimentaldataandtoaddresssomeoftheinconsistenciespreviouslynotedand
discussedabove.Inparticular,thetetrahedrallybondedFeatomshaveoneshortFe-O
bond(aslowas1.79Åinthe6-linemodel),makingthetetrahedraheavilyasymmetric
[20, 21, 34]. Furthermore, the octahedral and tetrahedral Fe-O bond lengths are
approximatelyequalandhencethespaceoccupiedbythesetwoenvironmentsisalmost
thesame,whichisdubious[21].Notwithstanding,asastartingpoint,wetookthisbest
currentestimateofthe2-linesingle-phasestructure[15]and,usingDFT,performeda
geometry optimization to see if improvements could be made that match the
experimentalNIMRODdata(previousDFToptimizationhasbeenreportedbutusingthe
6-line single-phase structureas the startingposition [34]).The latticeparameters for
theresultingmodelarepresentedinTableIII.Althoughwedidnotconstraintheaandb
parameters, unlike in the work with the refined 6-line model [34], they did,
nevertheless,remainequal.
In the refined structure, the aand bparameters are reduced compared to the prior
state-of-the-art 2L-Fh model (Table III), while the c parameter is increased; an even
greater increase in the c parameter is also observed in the previous 6-line Fh DFT
refinement. This was explained by the authors as an illustration of the inherent
crystallinityof theirmodelascompared to theexperimentallyderivedmodel [15],an
argumentthatisequallywellappliedtoourDFTresults.Indeed,ourc-parameterisjust
0.3%longerthanthatoftheexperimentallyderived6-linevalue,whichcomesfromthe
mostcrystallineofthesamples[15].
FIG. 4. The split all-ion PDF of the single-phase 2-line model [15]. The all-ion PDF is
showninblackineachframeandtheindividualPDFsareshowninred.(a)all-ion,(b)
Fe-Fe,(c)Fe-O,(d)O-O,(e)Fe-H,(f)O-H.TheH-HPDFonlyhasaveryminoreffecton
theall-ionPDFandhas,forclarity,notbeenshown.
Parameter
Optimized2-line
DFT
Single-
phase
2-line(18)
a(Å) 5.84(-1.9%) 5.96
b(Å) 5.84(-1.9%) 5.96
c(Å) 9.15(+2.1%) 8.97
Volume(Å3) 270.66(-1.8%) 275.60
TABLEIII.LatticeparametersofthenewDFT-optimizedferrihydritemodel,compared
tothe2-linesingle-phasemodelofMicheletal[15].The%valuesinbrackets,arethe
differencebetweenthegivenDFTmodelandthatofMicheletal[15].
Furthertotheresultsabove,geometryoptimizationsofallthreesingle-phasestructures
(2, 3&6-line ferrihydrite) and the optimized6-lineDFT structurehavebeen carried
out. All these optimized structures relaxed to the same structure (within 2 decimal
places) as the model described by the parameters in Table III. Complete structural
parametersarepresentedinTableIVandintheciffileincludedinRef.[38].
LatticeParameters
a(Å) b(Å) c(Å) α(°) β(°) γ(°)
5.843
5.843 9.154 90.000 90.000 120.000
SpaceGroup:P63mc
FractionalCoordinates
Atom x y zH1H2O1O2O3O4O5O6O7O8O9O10O11O12O13O14O15O16Fe1Fe2Fe3Fe4Fe5Fe6Fe7Fe8Fe9Fe10
-0.000003-0.000003-0.000003-0.0000030.3333300.6666630.1663220.1663220.6673460.8336720.8336720.3326470.5145100.5145100.9709690.4854830.4854830.0290240.1663950.1663950.6672000.8335990.8335990.3327930.3333300.6666630.3333300.666663
-0.000003-0.000003-0.000003-0.0000030.6666630.3333300.8336720.3326470.8336720.1663220.6673460.1663220.4854830.0290240.4854830.5145100.9709690.5145100.8335990.3327930.8335990.1663950.6672000.1663950.6666630.3333300.6666630.333330
0.4051470.9051470.0143980.5143980.7545980.2545980.2448810.2448810.2448810.7448810.7448810.7448810.0051460.0051460.0051460.5051460.5051460.5051460.6381630.6381630.6381630.1381630.1381630.1381630.3412550.8412550.9582310.458231
TABLE IV. Complete structural parameters for the new DFT-optimized ferrihydrite
model. The structure was optimized with aP1 space group to allow the structure to
relax with complete freedom. On completion, the space group was recalculated and
foundtobeP63mcwithamaximumdeviationfromsymmetryof0.51e-14Å.
Althoughnotadefiningfeatureoftheferrihydritephasecomparedtootherironoxides
andoxo-hydroxides, it isworthnoting that theFe-Febond lengthsobtained from the
DFToptimization,at2.92Åand3.20-3.54Å,areentirelyinkeepingwithastructureof
thischemicalcomposition.Forcomparison,theneutrondiffractiondatapredictsthese
peaksat2.89Åand3.41-3.58Å,althoughitisrecognizedthatthesepeaksalsocontain
some contributions from other ion pairs (see Fig. 4) and hence do not correspond
preciselytotheFe-Fedistances.Fe-ObondlengthsintheDFTmodelwerealsoanalysed
and bond populations calculated using the Mulliken formalism to define electron
distribution between ions [39]. Octahedral Fe sites were little changed, at 2.00 Å,
compared to those of the original single-phase model, but significant differences
emergedforthetetrahedralFesites.TableVshowstherefinedbondlengthsandbond
populationsfortetrahedralFe.
PreviousSingle-phaseModelDFT-optimizedModel
Fe-OBondPopulation
(|e|)
Fe-OBondLength
(Å)
Fe-OBondPopulation
(|e|)
Fe-OBondLength
(Å)
0.38 1.959 0.42 1.864
0.45 2.019 0.49 1.883
0.45 2.019 0.49 1.883
0.45 2.019 0.49 1.883
TABLEV.ThecalculatedbondpopulationsandbondlengthsoftheFe-Obondsforthe
tetrahedrallycoordinatedFeions.
TheDFTrefinementsledtoincreasedbondpopulationsandshortenedtetrahedralFe-O
bondlengths,resolvingseveralcriticismsoftheprevioussingle-phasemodel.Crucially,
tetrahedral Fe-O bond lengths are contracted to an energetically more favourable
1.88 Å, reflecting the increased electrostatic bond strength associated with lower
coordinationenvironments.WhilstapreviousDFTrefinement[34]partiallyaddressed
thisfailingoftheoriginalmodel,theirtetrahedralFe-Obondlength(1.92Å)remained
outsidetheplausiblerangeforFe3+tetrahedralsites[21,40].Furthermore,tetrahedral
distortion has been virtually eliminated and site volume was reduced by 17 %, as
showninFig.5(a).
FIG. 5. (a) DFT-optimized single-phase 2-L ferrihydrite. The tetrahedral Fe ions are
shown in green and the octahedral Fe ions in orange. In this new structure, the
tetrahedral Fe site is reduced by 17 % compared to the original single-phase model
[15]. The new Fetet-O bond lengths are 1.883 Å (blue-banded) and 1.864 Å (red-
banded).Thedirectlybondedoxygenatomsfortheexampletetrahedralsitesareshown
indarkblue,allotheroxygenionsareshowninredandhydrogeninwhite.Forclarity
some ions have been removed from the illustration to make the example tetrahedral
sites completely visible, and all surfaces have periodic boundary conditions. (b)
SimulatedXRDpatternsfortheprevious(black)andrefined(red)single-phasemodels.
While in the previous single-phase structure both the tetrahedral and octahedral Fe
ionshaveaverageFe-Obondlengthsof2.00Å[15],inournewDFToptimization,Table
IV,theoctahedralFe-Obondsretaina2.00Åaveragebutthetetrahedralaverageisnow
1.88Å.Crucially,plausibletetrahedralFe-Obondlengthswereachievedandthesewere
in line with expectations for such an Fe site based upon published comparisons of
inorganiccrystalstructures[21,41].Thisrefinementthereforeremainsconsistentwith
our experimentaldata (averageFe-Obond lengthof2.04Å)but significantly reduces
the tetrahedral site volume. Furthermore, the eccentricity of this tetrahedral volume
hasbeensignificantlyreducedwithjust1%(ratherthan3%[15])differencebetween
the ‘short’ bond and the other bonds of the tetrahedra. The previous DFT 6-line
refinementalsoreducedthetetrahedralFe-Obondlengthbuttoalesserextent,to1.92
Å[34],andstillabovetherangecitedbyotherauthorsasacceptable[21].
While these refinements resolve the previous chemical inconsistencies, it is clearly
important that the new structure is able to reproduce XRD features of the original
model,beingconsistentwithexperimentalXRDdata.Figure5(b)showssimulatedXRD
patternsforboththeoriginalsingle-phase2-linestructure[15]andthenewrefinement;
it isclearthatthisnewrefinementretainsgoodfitwiththeoriginaldata,andthetwo
major peaks at around 35° and 63° are consistent with those in our own heavily
broadened2L-FhXRDpattern,showninFig.1(a).
IV.CONCLUSIONS
The NIMROD instrument at ISIS was able to produce an accurate diffraction pattern
with2L-Fhmaterialdriedatambienttemperatures,which, forthefirst time,obviated
dehydrationandremovedthepossibilityofphase-transformationthroughheatingsteps
that were necessary for analysis with prior instrumentation. Naturally hydrated
nanoparticulate2-lineferrihydritehasanextremelylargesurface:volumeratioandhas
asurfacethat isheavilypopulatedwithOHgroups,accountingformorethan15%of
theparticleweight.Ourresultsarebestexplainedbyasingle-phasemodelthatallows
for tetrahedrally coordinated iron, in contrast to the octahedral-only 3-phase model,
which is incompatible with the primary Fe-O bond length and amorphous
characteristicsofthemineral.
Crucially, following DFT optimization of the previous state-of-the-art single-phase
model[15],wecannowproposeastructurethathaslatticeparametersfullyconsistent
with experimental data and with tetrahedral Fe sites that do not conflict with basic
principles of coordination chemistry. We present a model that has a refined and yet
simplifiedcrystallographyandisconsistentwithboththeexperimentalXRDdiffraction
patternandtheneutronPDFofnaturally-hydratedferrihydrite.
ACKNOWLEDGEMENTS
ThemodellingworkwasperformedusingtheDarwinSupercomputeroftheUniversity
of Cambridge High Performance Computing Service (http://www.hpc.cam.ac.uk/),
providedbyDell Inc.usingStrategicResearchInfrastructureFundingfromtheHigher
EducationFundingCouncil forEnglandand funding fromtheScienceandTechnology
FacilitiesCouncil.HC,NFandJJPwouldliketothanktheUKMedicalResearchCouncil
(Grant No. MC_U105960399) for their support. Work was carried out on the ISIS
Nimrod instrumentover threedaysunderSTFCexperimentRB1400012.Theauthors
wouldliketothankLesleyNeveattheSchoolofEarthandEnvironment,Universityof
Leeds, for carrying out the XRD measurements, Alan Soper (Rutherford Appleton
Laboratory) for help with analyzing the particle shape and Andy Brown at the
UniversityofLeedsforreviewingthefinaldraft.
H.F.C, W.T., D.T.B. and N.F. all contributed to running the neutron diffraction
experiments at ISIS,Harwell.H.F.C andP.J.H. carriedout themodelling componentof
the project. All authors were involved in discussions as to the objectives and
interpretation of the final results. The manuscript was written by H.F.C. with
contributionsfromallauthors,andeditingfromD.T.BandJ.J.P.
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