Besides,various aspectssuchas systemconfigurations, binding energiesstability,atomicdiffusionbarriers,magnetization,and workfunctionarealsoofconcern.Thosestudiescanberegardedas apremisefo
Trang 1j o ur na l ho me p ag e :w w w e l s e v i e r c o m / l o c a t e / c p l e t t
Department of Materials Science, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam
a r t i c l e i n f o
Article history:
Received 1 August 2014
In final form 18 September 2014
Available online 28 September 2014
a b s t r a c t
Graphenehasbeenahottrendinmaterialresearchforyears
[1,2]becauseofitsexcellentelectronicpropertiesandgreat
ther-mostabilityasproven througha varietyofexperimentalstudies
[3–5].Especially,thespintronic–electronicaspectswiththeaim
tocontroltheelectronicproperties tendtogetmore particular
interests[6,7].Duringthepastfewyears,studiesoftheelectronic
structures and magnetic properties of those two-dimensional
structureshavegained remarkableachievements.Among them,
thestudiesofmetalatomadsorptionsongraphene[8–16]using
densityfunctionaltheory(DFT)calculations[17,18]haveshown
different perspectives in the insights of electronic structures
Besides,various aspectssuchas systemconfigurations, binding
energies(stability),atomicdiffusionbarriers,magnetization,and
workfunctionarealsoofconcern.Thosestudiescanberegardedas
apremisefordevelopingapplicationsinadvancedsemiconductors,
nanomagneticdevices,aswellasgassensors
Theadsorptionsoftransitionmetaldimersongraphenewere
shown to have relatively low binding energies (from 0.16 to
0.27eV), which might result in high mobility of the adatoms
anddimersonthesurface[12].Therefore,itisofimportanceto
sealtheadsorbedmetalatomswithfunctionalgroups(ligands)
Byadopting first-principlescalculations, Avdoshenkoet al [19]
explored the electronic properties of graphene–metal–benzene
complex,andtheligandwascapableofcontrollingtheproperties
∗ Corresponding author.
E-mail addresses: hung.m.le@hotmail.com , lmhung@hcmus.edu.vn (H.M Le).
ofabsorbedmetalatoms,therebyimposedbosonic/fermionic char-acters.Thetheoreticalinteractionsbetweentwographenelayers andCrwerealsoinvestigatedinthegraphene–Cr–graphene inter-calatingnanostructures[20].Fromtheanalysisofbindingenergy andelectronicstructures,itwasshown thathighCr-occupation rategave anunstablestructure, whiletheloosenedoccupations (lowerconcentration)ofCrresultedinmorestablestructures.In anotherstudyreportedbyLeetal.[21],C60wasutilizedasaligand
todecoratethegraphenesurfaceviacoordinationbondswithCr (G–Cr–C60); meanwhile, interesting magnetic properties exhib-itedbyG–Cr–C60 itselfanditscombinationwithametalcluster (Ni4/Pd4/Pt4)werefound
Acknowledging the significance of graphene–metal–ligand structuresinspintronicandelectronicapplications,inthepresent study, we demonstrate a theoretical investigation of three-componentgraphene-basednanostructures,inwhichnaphthalene (C10H8,abbreviatedasNp)isattachedtographenevia coordina-tionbondswithaCr/FeatomorCr2/Fe2 dimer(forconvenience, thestructuresaredenotedasG–M–Np orG–M2–Np).Structural stabilityandmagneticmomentsofthosestructureswillbe delib-eratelydiscussedinthelightofelectronicstructuredatagivenby DFTcalculations
First-principlescalculationsbasedonDFTareperformedwithin localspindensityapproximationinordertoevaluatethedegree
of spin polarization in the bonding schemes between Cr/Fe and graphene/naphthalene All DFT calculations are executed usingQuantumEspresso,anopen-sourcecomputationalpackage
[22] The Perdew–Burke–Ernzerhof (PBE) exchange-correlation
http://dx.doi.org/10.1016/j.cplett.2014.09.047
0009-2614/© 2014 Elsevier B.V All rights reserved.
Trang 2forallatomsinvolved[25,26].Thek-pointsaregeneratedusingthe
Monkhorst–Packmethodwithachosenmeshof(6×6×1),which
issufficienttoensurethereliabilityoftotalenergycalculations.The
kineticenergycut-offisselectedas45Rydberg(612eV)for
plane-waveexpansions.Thetwo-dimensionallattices(atomicpositions
andunitcellparameters)aresimultaneouslyoptimizedusingthe
Broyden–Fletcher–Goldfarb–Shannoalgorithm[27]withanenergy
convergencecriterionof10−5eV/cellandagradientconvergence
criterionof 10−3eV/ ˚A/atom Thetwo-dimensional unitcells are
constructedbyemployinglargeclatticeparameters(30Bohror
15.88 ˚A).Theoptimized structuresandelectronicstructuredata
hereinarereportedwithoutconsideringtheempiricaldispersion
correctionterms.Itwasshowninanearlierstudythatdispersion
interactionscontributedasignificantroleinthebindingbetween
grapheneandaromaticmolecules[28].Therefore,wealsoperform
additionaloptimizationswiththeD2empiricaldispersions
correc-tions[29,30]andupdatethebindingenergies
A (4×4) supercell of graphene containing32 carbon atoms
isemployedtohosttheM–NpandM2–Npcomplexes.The
cho-sengraphenecellis wideenoughtoavoidpossibleinteractions
betweentheattachedcomplexesduetoperiodicboundary
con-ditions.Inthefirstpart,theperiodicgraphenesheetisdecorated
withtheC10H8ligandusingonlyonetransitionmetalatom(either
CrorFe)asthebridgingatom.IntheG–Cr–Npstructure(Figure1a),
theCr atomclings tothe hollowsite of two honeycomb units
ingrapheneand C10H8.Thisbindingbehavior issimilartothat
observedintwopreviousstudies[19,21].InthecaseofG–Fe–Np,
twodifferentconfigurationsarefound.AsshowninFigure1 and
c,theFeatomcansettleeitheronthehollowsiteorontopofaC
atomingraphene,whileitonlybindstothehollowsiteofNp
Inthesecondpart,weattempttouseatransition-metaldimer
tofixbotharomaticringsofnaphthaleneinsteadofonlyonelikein
thepreviouscases.InthecaseofCrdimer,onlyonestable
configu-rationcanbefound,inwhichtwoCratomsoccupythehollowsites
intwoadjacenthexagonalhoneycombunitsinbothgrapheneand
naphthalene,asshowninFigure1d.IntheG–Fe2–Npcase,thereare
twostableconfigurationsgivenbystructuraloptimizations;one
structure(Figure1f)issimilartotheCrdimercase,whiletheother
ismuchdistinctivebecauseoneFeatomaccommodatesatthe
hol-lowsiteandanotherlocatesontopofacarbonatom(Figure1e)
Interestinglyenough,thedifferentarrangementsofFeatomsin
G–Fe–NpandG–Fe2–Npresultindifferentmagneticbehaviorsas
willbediscussedinalaterpartofthisLetter.Intotal,wereport
sixconfigurationsinthisstudy:G–Cr–Np,G–Fe–Np(1),G–Fe–Np(2),
G–Cr2–Np,G–Fe2–Np(1),andG–Fe2–Np(2)(seeFigure1)
In the first structure (G–Cr–Np), it can be seen clearly that
Crconnectstosix C atomsin both naphthaleneand graphene;
however, the plane containing naphthalene is not parallel to
graphene.Indeed,theligandishighlydistortedasweobserve
vari-ousCr–C(Np)bondlengths(2.14–2.23 ˚A),whiletheCr–C(graphene)
bondsarealmostidentical(2.20 ˚A).Intermsofbonding,the
inter-actingbehaviorofnaphthaleneasaligandisdistinguishedfrom
thatofbenzeneasseeninapreviousstudy,wherebenzenewas
symmetricallyaligned[19].Asa ligand,C60evenbehavesmore
differentlybecausethegeometryofC60allowsitselftorotateand
achievemoststablestatesbyassemblinghighgeometrydistortions
[31]
Thestructuralstabilityofastructurecanbeevaluatedby
calcu-latingtwodifferentbindingenergies:
Table 1
Binding energies and magnetizations of the investigated nanostructures (the values given by PBE calculations with D2 dispersion corrections are shown in parentheses).
Binding energy (eV)
M T
( B /cell)
M A
( B /cell)
E(a)binding E(b)binding
(2.90)
1.80 (2.82)
0.11 (0.11)
0.20 (0.19) G–Fe–Np (1) 1.27
(2.24)
1.85 (2.69)
1.89 (1.06)
2.39 (1.52) G–Fe–Np (2) 1.62
(2.08)
2.25 (3.03)
2.00 (2.00)
3.27 (3.23) G–Cr 2 –Np 2.71
(4.04)
3.34 (4.48)
2.47 (2.44)
3.36 (3.24) G–Fe 2 –Np (1) 1.62
(2.99)
2.10 (3.42)
1.03 (0.94)
2.36 (2.01) G–Fe 2 –Np (2) 1.42
(2.82)
2.43 (3.51)
1.34 (1.32)
1.88 (1.77)
whereEgraphene,Egraphene–M,ENp,andENp–Mrepresentthetotal ener-giesofpuregraphene,graphenedecoratedwithmetalatom/dimer,
C10H8,andmetal–C10H8,respectively,whileEstructuredenotesthe totalenergyoftheoptimizedcomplex.Thepositivebindingenergy valueisindicativeofastablestructure.Thetwo bindingenergy quantitiesabovecriticallydemonstratetherelativestabilitywith respect toexperimental synthesizing methods In experiments, the synthesis of G–M–Np/G–M2–Np can beachieved by either attachingtheC10H8–metalcomplexonapuregraphenesurface (expressed byE(a)binding)orattachingC10H8 onametal–graphene surface(expressedbyE(b)binding).Thefavorabilityofasynthesizing methodinexperimentalrealitycanbeevaluatedbymakingdirect comparisonsofthetwobindingenergies
By applying Eqs (1) and (2) for the G–Cr–Np case, E(a)binding
results indicate that the resulted structure is highly stable; also,it is demonstrated that thedirect adsorption of C10H8 on metal–graphene surface is somewhat more favorable In other words,thebondbetweenCradatomandC10H8seemstobequite stronger thanthebondbetweenCrandthegraphene.For con-venience,we summarizeE(a)binding andE(b)binding oftheinvestigated nanostructures in Table 1 The updated binding energies with empirical dispersion corrections are raised by 0.78–1.40eV, as listedinTable1(showninparentheses).ItcanbeseeninTable1
thatsolelyforG–Cr–Np,Ebinding(a) (2.90eV)isquitehigherthanthe correspondingEbinding(b) (2.82eV)whenvanderWaalscorrectionsare introduced
Besides studying structural stability, we also evaluate spin polarization,whichhavemuchinfluenceonthemagneticproperty
Byinterpretingdensityofstates(DOS)fromelectronicstructure data,thetotal(MT)andabsolute(MA)magnetizations(alsolisted
inTable1)arederivedandreportedforeachstructure.The estima-tionoftotalmagnetizationinG–Cr–Npshowsthatthestructure exhibitsaweakmagneticmomentof0.11B/cell,whilethe abso-lutemagneticmomentis0.20B/cell.Infact,theabsolutemagnetic momentindicatesasignificantanti-ferromagneticamountwithin thestructure.Fortheelectronicstructureanalysis,weonly exam-inedatafromthePBEcalculationswithoutdispersioncorrections
ByexaminingthetotalDOSofG–Cr–Np(Figure2a),weobservethat theweakspinpolarizationmainlyoccurspriortotheFermilevel (highest-occupiedbands).WhileCrappearstocontributea posi-tivemagneticmoment(0.15B),Catoms(frombothgrapheneand naphthalene)tendtocontributearesistingamount,whichcauses anti-ferromagneticeffectswithinthestructure.Interestingly,the spinpolarizationofCr3dorbitalscontributestheferromagnetism
Trang 3Figure 1. Side and top views of six optimized nanostructures using PBE calculations without dispersion corrections: (a) G–Cr–Np, (b) G–Fe–Np (1) , (c) G–Fe–Np (2) , (d) G–Cr 2 –Np, (e) G–Fe 2 –Np (1) , and (f) G–Fe 2 –Np (2) Teal is used for graphene.
Figure 2.Total DOS of (a) G–Cr–Np, (c) G–Fe–Np (1) , (e) G–Fe–Np (2) and PDOS of 3d
orbitals of (b) G–Cr–Np, (d) G–Fe–Np (1) , (f) G–Fe–Np (2) The Fermi level is positioned
at 0.
(asmuchas98%).Subsequently,wecalculatethedegreeofspin
polarizationineach3dsubshellbyanalyzingthepartialDOS(PDOS)
of3dorbitals.Comparedtotheother3dorbitals,the3dz2subshell
ismostpolarizedasshowninFigure2b.Thespinpolarizationterms
ofmetal3dorbitalsinallinvestigatedstructuresaresummarized
inTable2
Themoststableformof G–Fe–Np(1) (showninFigure1b)is
0.11eVlowerinenergycomparedtoG–Fe–Np(2)(Figure1c).The
Table 2
Spin polarization terms ( B ) of G, Np, and 3d orbitals of each metal atom.
G Np 3dz2 3d zx 3d zy 3dx2 −y 2 3d xy
G–Fe–Np (2) 0.05 −0.20 0.28 0.57 0.56 0.33 0.31
G–Cr 2 –Np −0.04 −0.19 0.42 0.10 0.18 0.42 0.23
G–Fe 2 –Np (1) 0.01 −0.14 −0.01 −0.10 −0.11 −0.03 −0.05
G–Fe 2 –Np (2) 0.07 −0.01 0.02 0.33 0.18 0.05 0.07
geometricconfigurationofG–Fe–Np(1)issomewhatsimilartothat
ofG–Cr–Np,i.e.Feisboundtotwohoneycombunitsin naphtha-leneandgraphene.Bindingenergycalculations(Table1)suggest thattheFe–naphthaleneinteractionisstrongerthanthe interac-tionbetweenFeandgrapheneinbothG–Fe–Np(1)andG–Fe–Np(2) The metastable configuration, G–Fe–Np(2), hasan odd bonding behavior,inwhichFeonlyestablishesabondtooneCatomfrom graphene,whileitinteractswithsixCatoms fromnaphthalene withdifferentbonddistances.Lowdinchargeanalysis[32]shows thatthechargeofFe(+0.26)inG–Fe–Np(1) isactuallyless posi-tivethanthat(+0.31)inthemetastablestate,G–Fe–Np(2).Indeed, this is explainable because the Fe atom in G–Fe–Np(2) locates
on top of C in graphene, which allows the 2pz orbital of that
Catomtoreceivemorepartialchargefromthemetal.Interms
ofmagneticalignments,G–Fe–Np(1)andG–Fe–Np(2)exhibittotal magnetizationsof1.89B/celland2.00B/cell,respectively Inter-estingly,theabsolutemagnetizationofG–Fe–Np(2) (3.27B/cell)
is 37% higher than the absolute magnetization of G–Fe–Np(1) (2.39B/cell),whichindicateshigheranti-ferromagneticeffectin G–Fe–Np(2)(seeFigure2 andc)
An interesting phenomenon can be observed as we look at thebindingenergiesofG–Fe–Np(1)andG–Fe–Np(2).Eventhough G–Fe–Np(1)isthemoststableconfiguration,itsEbinding(a) andE(b)binding arelowerthanthoseofG–Fe–Np(2).Therefore,theadsorptionof naphthaleneongraphene–Fe(withFesittingontopofaCatom) wouldstabilizethevalenceelectronsofFebetter;asaresult,the bindingenergyforthisprocessbecomeshigher.Whengrapheneis directlydecoratedwiththeFe–naphthalenecomplex,thebinding energyresultssuggestthatFefavortobindontopofC.Overall,the bindingenergyresultssuggestthefavorabilityofC10H8adsorption
ongraphene–Feinactualexperimentalsynthesis
Ingeneral,theuseofmetaldimerenhancesthebondingstrength betweenC10H8andgraphene.WhenaCrdimerisutilizedtobridge
C10H8andgraphene,onlyonestableconfigurationcanbeobserved TwoCratomsarelikelytoestablishbondswiththehoneycomb unitsin both naphthaleneand graphene.Moreover,there isan interactionbetweenthetwoCratomswithadistanceof2.65 ˚A
Inthiscase,twoaromaticringsinC10H8 areheldtightlybythe twometalatoms.Thus,theresultedbindingenergies arelarger thanthepreviouslyreportedcases.Again,weconceivethat cov-eringgraphene–Cr2withC10H8mightbemorefavorable,because
E(b)binding islarger(3.34eV)thanEbinding(a) Whiletheuseofasingle bridgingCratomresultsinasmallmagneticmoment,weobserve that the useof Crdimer raises the total magnetic momentto
Trang 4Figure 3.Total DOS of (a) G–Cr 2 –Np, (c) G–Fe 2 –Np (1) , (e) G–Fe 2 –Np (2) and PDOS
of 3d orbitals of (b) G–Cr 2 –Np, (d) G–Fe 2 –Np (1) , (f) G–Fe 2 –Np (2) The Fermi level is
positioned at 0 The PDOS of the second metal atom are given in dashed lines.
2.47B/cell(MA=3.36B/cell).FromLowdinchargeanalysis,itis
foundthatthespinofoneCratomdonotopposetheother;in
fact,both contributesimilarpositive amounts ofmagnetization
(1.34B), while graphene and naphthalene givenegative
(anti-ferromagnetic)moments(Figure3aandTable2).Amongthe3d
orbitals,3dz2 and3dx2 −y 2 arethemostpolarizedsubshellswith
spinpolarizationtermsof0.42BasshowninFigure3 andTable2
Theother3dsubshellsgivelesssignificantmagneticcontributions
rangingfrom0.10Bto0.23B
Inthelastcase,weinvestigatethepossibilityofattachingC10H8
on graphene using two Fe atoms We observe two distinctive
equilibriumstructures(showninFigure1 andf)asintroduced
previously.Theformerstructure,whichhasoneFeatomlocating
ontopofCingraphene,ismorestableby0.20eVintotalenergy
Thisresult is somewhatcontradicting to theprevious
observa-tionsintheG–Fe–Npcases.RecallthatwhenbridgingofC10H8and
grapheneusingoneFeatom,thestructurewithFelocatedonthe
hollowsitesoftwohoneycombunitsismoreenergeticallystable
Thebindingenergies(E(a)binding andEbinding(b) )ofG–Fe2–Np(1)are
1.62eVand2.10eV,respectively,andthoseofG–Fe2–Np(2)are1.42
and2.43eV,respectively.Atthispoint,thecalculatedbinding
ener-giesallowustoarriveatthefirstconclusionregardingexperimental
synthesis,i.e.attachingtheC10H8grouponametal–graphene
sur-faceshouldbemorefavorableduetothefactthatEbinding(b) ishigher
than the corresponding E(a)binding in most cases Both structures
exhibitsmallermagneticmoments(1.03B/cellfromG–Fe2–Np(1)
and 1.34B/cell from G–Fe2–Np(2)) compared to the single Fe
case(G–Fe–Np).Especially,G–Fe2–Np(1)isthesolecaseinwhich
weobservea smallanti-ferromagnetismfromoneFeatom(see
Table2).ForG–Fe2–Np(2),intermsofbondingandmagnetic
align-ments,therolesoftwoFeatomsarealmostsimilarasillustrated
bythePDOSdistributions(Figure3f)
ItisofparticularinteresttoexaminehowG–Fe–Np(1)couldbe
transformedtoG–Fe–Np(2)andviceversa.Thiscanbeachievedby
performinganudged-elastic-band(NEB)scan[33].Byoptimizing
10intermediatestructures,wehavefoundactivationenergiesof
0.84and0.73eVfortheforwardandbackwarddirections,
respec-tively.Atthetransitionstate,thestructureisfoundtoexhibita
totalmagneticmomentof2.11B,slightlyhigherthanthosefound
inthetwoequilibriumstructures.Moreover,alocalminimumis
alsofoundnearthetransitionstateasshown inFigure4a.The
G–Fe 2 –Np (1) ↔ G–Fe 2 –Np (2) transformations given by NEB scans using PBE calculations without D2 corrections The reaction barriers of both transformations are found to be above 0.8 eV.
sameprocedureisexecutedtofind10intermediatestructuresof theG–Fe2–Np(1)↔G–Fe2–Np(2)transformation;however,dueto energyconvergencedifficulty,aroughresultisreportedherein, whichindicatesabarrierheightof0.88and0.67eVfortheforward andbackwarddirections,respectively(Figure4b).Themagnetic momentfoundatthetransitionstateis 0.71B,which islower thanthoseofthetwoequilibriumstructures.FromtheNEBresults,
wecanmakeasecondconclusion,i.e.themobilityofFeatomson thegraphenesurfaceismoreprohibitedduetostronginteractions betweenFeandnaphthalene
In summary,we have shownin this studythat naphthalene canbeattachedtothegraphenesurfaceviacoordinationbonds withCr/Featomordimerwithgreatstability.Inapreviousstudy, thebinding of transitionmetal dimersongraphene wasfound
tobeweakandhavehighsurfacemobility[12].Withtheuseof naphthalene asa binding ligandonmetal,themetal–graphene bindingisshowntobemorestabilized.Asareferencefor exper-imentalsynthesis,weadoptdifferentbindingenergyevaluation schemes,andtheadsorptionofC10H8moleculeonametal-attached graphenesurface ismore thermodynamicallyfavorable in most cases; in otherwords, themetal–naphthalene bondis stronger thantheinteractionbetweenmetalandgraphene.Theinclusion
ofdispersioncorrectionsfor long-rangeinteractions showsthat theattachmentofNpongraphene–metalisfurtherenhancedby 0.78–1.40eV.WhenFeisutilizedasbridgingatoms,weobserve differentconfigurationsofG–Fe–Np/G–Fe2–Np,whichpossess dif-ferent structure stability and magneticmoments Overall, good structuralstabilityandinterestingmagnetismoftheinvestigated nanostructuresmayelicitpotentialspintronicandelectronic appli-cations
Supplementary material
Theunitcellparametersandatomicpositions(in ˚A)ofthe opti-mizedstructures(withandwithoutD2dispersioncorrections)are giveninonesupplementaryfile
Acknowledgement
WearegratefultothecomputingsupportfromtheUniversity
ofScience,VietnamNationalUniversity.Thisworkisfundedby VietnamNationalUniversityundergrantB2014-18-03
Trang 5Appendix A Supplementary data
Supplementarymaterialrelatedtothisarticlecanbefound,in
theonlineversion,atdoi:10.1016/j.cplett.2014.09.047
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