Dynamics and stability of icosahedral Fe-Pt nanoparticles

0.43 MB·English

by  Paweł T. Jochym

Dynamics and stability of icosahedral Fe-Pt nanoparticles
PawełT.Jochym,∗a JanŁaz˙ewski,a MałgorzataSternika andPrzemysławPiekarza
The structure, dynamics and stabilityof Fe-Pt nanoparticles have been investigated using DFT-based techniques: total energy
calculationsandDFTmoleculardynamics. Theinvestigatedsystemsincludedmulti-shellanddisorderednanoparticlesofiron
5and platinum. The study is concerned with icosahedral particles with magic number of atoms (55): iron-terminated Fe Pt ,
43 12
1platinum-terminatedFe Pt ,anddisorderedFe Pt .Additionally,theFe Pt clusterhasbeeninvestigatedtoprobebehaviour
0 12 43 27 28 6 7
ofextremelysmallFe-Ptparticles. MoleculardynamicssimulationshavebeenperformedforafewtemperaturesbetweenT =
2
150−1000 K. The calculations revealed high structural instability of the Fe-terminated nanoparticles and a strong stabilising

b
effectofthePt-terminationintheshell-typeicosahedralparticles. Theplatinumterminationpreventeddisorderingoftheparticle
e
evenatT =1000KindicatingveryhighmeltingtemperaturesoftheseFe-Pticosahedralstructures. Theanalysisofevolutionof
F
theradialdistributionfunctionhasshownsignificanttendencyofPtatomstomovetotheoutsidelayeroftheparticles–evenin
5
theplatinumdeficientcases.
1

]1 Introduction calapplications.18
l
l
a Due to small sizes, standard diffraction techniques cannot
Nanoalloysarebi-ormulti-componentmetallicnanoparticles
h be applied for NPs and most information about their struc-
-(NPs), withthecomplexstructuresandproperties, whichde-
spendontheirsize,structure,andcomposition.1–5 Thesizeof turalpropertiescomesfromhigh-resolutiontransmissionelec-
e tron microscopy.19–21 Relevant information about structural
mnanoalloys(1–100nm)placesthembetweensmallmolecules
stability and electronic properties of the Fe-Pt nanoclusters
andbulkcrystals. Theycanbeconsideredastheintermediate
. have been obtained by the theoretical studies based on ei-
tphase sharing common properties of atoms and solid materi-
a thersemiempiricalpotentialsorabinitiotechniques.22–27The
mals. By adjusting the size, geometry and chemical composi-
Monte Carlo simulations showed that a continuous transfor-
tion, nanoalloys can be optimised for various applications in
- mation between the ordered structure L1 (tP4) and a dis-
dcatalysis,6 nanomedicine,7 optics,8 data recording9 and en- 0
nergystorage.10 ordered phase in Fe-Pt NPs occures at temperatures lower
o than the bulk melting temperature (1572 K).23,24 Disorder-
Iron-platinum (Fe-Pt) nanoalloys consist of two metallic
c ing processes in nanoalloys are enhanced due to finite-size
[components with significant ratios (Pt/Fe) of masses (195.1
and surface effects, e.g. strong surface segregation tendency
/ 55.8 in amu), bulk moduli (230 / 170 in GPa) and atomic
2 ofPtatoms.25,26 Thestructuralorderandmagneticproperties
radii (1.46 / 1.30 in A˚) which result in very interesting, not
v ofFe-Pt nanoalloyswithvariousmorphologies andchemical
3only geometrical, features. They belong to the most studied
composition have been studied previously within the large-
4systemsduetoanextremelyhighuniaxialmagnetocrystalline
scaleDensityFunctionalTheory(DFT)calculations.27 Inthe
1anisotropy(K =7×106J/m3),whichmakesFe-Ptapromis-
7 u present study, we focus on icosahedral Fe-Pt NPs, which
ing material for applications in ultra-dense magnetic record-
0 are energetically favoured over the L1 phase for small par-
ingmedia.9Asevidencedbymanystudies,Fe-Ptsystemsex- 0
. ticles.19,20,27 Application of DFT-based methods, including
1hibitenhancedcatalyticalproperties,comparingtopureplat-
0 DFT molecular dynamics, provides additional, independent
inum surfaces. Fe-Pt nanoalloys may be used as a power-
5 informationonthebehaviourofFe-PtNPs,whichsupplement
ful catalyst for the electro-oxidation of formic acid in fuel
1 the published studies based mainly on semiempirical poten-
:cells11–13andashighlyefficientoxidationcatalystsfordegra-
v tialsandsuppliesavaluableconsistencycheckonthealready
dation of organic pollutants.14 Fe-Pt NPs are also promising
i establishedmodelsofthesesystems.
Xcandidates for biomedical in vivo applications (e.g. for cel-
rlular magnetic resonance imaging15) because of their high Our study of Fe-Pt NPs has been divided into two main
astability in the presence of oxygen.16 By coating with inor- parts. The first part is a set of total energy calculations and
ganic molecules, the core-shell Fe-Pt nanoparticles become structural optimisations, designed to establish static stability
opticallydetectable17andcanbefunctionalisedforthehyper- propertiesoftheinvestigatedsystems.Themethodsemployed
thermia treatment of cancer and advanced radiopharmaceuti- inthispartaredescribedinsection2.1andtheresultsinsec-
tion 3.1. The second part of the work concerns the investi-
aDepartmentofComputationalMaterialScience,InstituteofNuclearPhysics gationofdynamicalstabilityofthesystemsusingDFT-based
PAN,Cracow,Poland;E-mail:[email protected] molecular dynamics (MD). Description of the methods em-
1–8 |1
ployedforthispartoftheworkisincludedinsection2.2and of the system. Furthermore, additional energy pumped into
theresultsarediscussedinsection3.2. Section4containsthe the system by this noise is cancelled out by the action of the
resultsoftheinvestigationofdynamicalstabilityofthedisor- thermostat. The actual molecular dynamics used the VASP
deredFe Pt andFe Pt particles. Theconcludingsection5 implementation of the Nose thermostat MD algorithm with
6 7 27 28
summarizesthekeyresultsofthepaper. 10 fs time step, which was determined by convergence test-
ing. Theuseofthisfairlylargetimestepwaspossiblethanks
tolargemassesofatomsinthesystem. Thestartingconfigu-
2 Methods
rationscorrespondtoperfecticosahedralgeometrieswiththe
multi-shellordisorderedstructures. Incaseofthedisordered
A common denominator of the methods used in the present
structure the atomic sites were assigned randomly to one of
workistheDensityFunctionalTheory.28,29 Bothpartsofour
thespeciesbydrawingfromthepre-determinedsetofatoms
analysisusethesameDFTcodeasimplementedinViennaAb
– 6 Fe and 7 Pt or 27 Fe and 28 Pt, respectively. The result-
initio Simulation Package (VASP)30,31 and the same atomic
ingstructureswerepre-optimised,bystandardstaticmethods
datasetsprovidedwiththispackage. Forthepreparationand
(seesec.2.1)toavoidlargeinter-atomicforcesatthestartof
analysis of the molecular dynamics runs and control of the
the MD run. For the same reasons we have used the results
DFTcomputations,wehaveusedstandard,python-basedsoft-
of the static structural optimisation (sec. 3.1) for the starting
warestack32–36. Thedetailsofthecomputationalsetupsused
configurationoforderedparticles.
fortheworkaredescribedbelow–separatelyforeachpartof
theanalysis.
Fe Pt Fe Pt
102 12 43 43 12 102
2.1 Structuraloptimisation
101 101
y
The static, zero Kelvin temperature calculations were per- nsit 100 100
e
formed using the full-potential projector-augmented wave d
method37,38withintheGGAapproachinPAW-PBEform.39,40 bility 10-1 10-1
Thefollowingvalencebaseconfigurationswereincluded: Fe ba10-2 Fit T=155K Fit T=154K 10-2
o
3d74s1andPt6s15d9. Theintegrationsinthereciprocalspace Pr Fit T=314K Fit T=315K
10-3 Fit T=518K Fit T=525K 10-3
was reduced to the single k-point Γ and the energy cut-off Fit T=1032K Fit T=1043K
fortheplanewavesexpansionwasequalto320eV.Thecrys- 10-140-3 10-2 10-1 100 10-3 10-2 10-1 10010-4
talstructurewasoptimisedusingtheconjugategradienttech- E (eV) E (eV)
k k
nique with the energy convergence criteria set at 10−7 and
10−5eVfortheelectronicandioniciterations,respectively.In Fig. 1Distributionofparticlekineticenergyintheicosahedral-shell
order to prevent interactions between system images created system(dots)andMaxwell-Boltzmanndistributionfitsforeachdata
set(lines).Thebest-fittemperatureforeachdatasetisincludedin
due to the periodic boundary conditions used in VASP, each
thelegend.
nanoparticlewasplacedinthebig20A˚×20A˚×20A˚ boxcon-
tainingabout10A˚ widevacuum. Thislimitedforceconstants
between neighbouring images below 0.3% of the strongest Thecalculationprocedureinvolvedathermalisationrunof
forceconstantinthesystem. the system with kinetic energies assigned to atoms accord-
ing to the Maxwell distribution. To assess the level of ther-
malisation of the system we calculated a distribution of ki-
2.2 Moleculardynamics
netic energies in each step for all the atoms and for an en-
The molecular dynamics simulations were carried out in the sembleconfigurationsinthe0.1psslidingwindow(10steps).
same DFT framework as the static calculations described The average energies in each step were compared with the
aboveandwiththesetofmethodsandtoolsusedinourprevi- value expected for the perfect Maxwell distribution. When
ous work on minerals.41 We used the PAW-PBE atomic data thesystematicdriftofthecomputedaveragevaluetransitioned
setsandthespin-polarisedVASPcalculationfortheDFTpart. intorandom-lookingfluctuations,weperformedanadditional
Tolowerthecomputationalcostweadjustedtheaccuracypa- checkforgoodthermalisationofthesystembycomputingthe
rametersofthecalculation–sincetheMDdoesnotneedex- fulldistributionofkineticenergiesintheensemblebuiltfrom
tremely precise inter-atomic forces. The precision parameter the configurations in the 1 ps window (100 steps) and com-
ofthecalculationwassettoNormal,thecut-offenergywasre- paringitwiththeMaxwelldistribution. Thecomparisonwas
ducedto275eVandtheenergeticconvergencethresholdwas performedbyfittingtheMaxwelldistributiontothehistogram
set at 10−6 eV. A small numerical noise added by lowering of the kinetic energy in the ensemble and comparing the ob-
accuracy of the calculation is drowned by the thermal noise tainedtemperaturewiththeexpectedvalue. Wealsochecked
2| 1–8
Small Large Fe and Pt shells exhibit very high structural stability.21 The
stability of Ih NPs results from the low energy of the close-
101 101
packed (111) surfaces, whichcompensates the internal stress
y
sit 100 100 existing in the particle core. The present study focuses on
n
de twotypesoficosahedralparticles: particleswithperfectshell
y 10-1 10-1
bilit structures (terminated with Pt or Fe atoms) and disordered
ba10-2 10-2 NPs with approximately equal number of Fe and Pt atoms.
o
Pr10-3 Fit T=283K Fit T=310K 10-3 TheorderedFe12Pt43 particlewiththealternatingshellstruc-
ture: 1Pt,12Feand42PtatomsisdisplayedinFig.4(a).
Fit T=486K Fit T=510K
10-4 10-4
10-2 10-1 10-2 10-1
E (eV) E (eV) 3.1 Staticcalculations
k k
Fig. 2Distributionofparticlekineticenergyintherandomsystems The first step, after constructing individual NPs, was to op-
(dots)andMaxwell-Boltzmanndistributionfitsforeachdataset timise the structure at T =0 K, by minimising the total en-
(lines).’Small’system(leftcolumn)isadisorderedFe6Pt7cluster, ergy of the system, keeping Th point group symmetry ele-
while’Large’system(rightcolumn)isadisorderedFe Pt cluster mentsonly,sinceI symmetrywasbrokeninperiodicbound-
27 28 h
(seesec.4).Thebest-fittemperatureforeachdatasetisincludedin ary conditions.∗ The lowering of particle symmetry allows
thelegend. notonlyforvolumechangingbutalsoforsurfaceshellrelax-
ation. In both cases, Fe Pt and Fe Pt , high symmetry
43 12 12 43
configuration with well-defined alternating Fe/Pt shells was
if the size of the residuals is consistent with the size of the
obtained. Thecalculatedradialdistributionfunctionsofopti-
fluctuationsexpectedfortheensemble.
misedstructuresarepresentedinFig.3. Inicosahedrathereis
The combination of all such comparisons is presented in only one non-equivalent position of atoms in the first shell,
Figs1and2. Theprobabilitydistributionspresentedinthese which defines the distance between the centre and the first
figures are based on the whole measurement part of the MD shell, and two different positions in the second shell: at ver-
run–thethermalisationpartwasdiscarded. Verygoodagree- ticesandedgesoftheicosahedron. Interestingly,inbothNPs,
ment of data points with the perfect Maxwell distribution is thedistancesfromthecentralatomtothefirstshell(2.643A˚
slightly broken only at the extreme large energy range in the and 2.587 A˚ for Fe Pt and Fe Pt , respectively) as well
43 12 12 43
case of the Fe-terminated system at the lowest temperature as to vertices in the second shell (5.091 A˚ for Fe Pt and
43 12
(T =150K).NoticethelogarithmicscaleonbothaxisinFigs 5.054 A˚ in Fe Pt case) are quite similar. A larger differ-
12 43
1 and 2, which was chosen to amplify any discrepancy from ence (∼0.1 A˚) is found for the distance between the centre
theexpecteddistribution–onthelinearscalethediscrepancy and edge atoms in the second shell (4.374 A˚ in Fe Pt and
43 12
isinvisible. Thisistherangeofahigh-energytailofthedis- 4.477A˚ inFe Pt case).
12 43
tribution and one can fully expect large relative fluctuations
there, due to the small probability density in this region and Fe Pt Fe Pt
43 12 12 43
thus,smallcountsinthehistogrambins. Furthermore,asthe 8 8
cwahlcicuhlarteiosnusltsreivnedalieffidc,uthlteieFsew43itPht1b2riinsgainqguiittetounesqtaubilliebrsiyusmtemat density675 PFte 567
lgolwe dteismcrpeepraantucryest.oNbeevseirgtnhiefilecsasn,twfoerdtohenoantacloynssisidcearrtrhieisdsoinu-t ability 43 34
b
inthisworkandregardallinvestigatedsystemsasadequately Pro2 2
1 1
thermalised.
0 0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
Radius from c.m. ( ) Radius from c.m. ( )
3 IcosahedralFe-Ptnanoparticles
Fig. 3Radialdistributionofatomicpositionsfromthemasscentre
ofFe Pt (leftpanel)andFe Pt (rightpanel).
43 12 12 43
Icosahedron (Ih) is one of the five Platonic solids and one
of the non-crystallographic structures with fivefold symme- In the surface shell, there are two characteristic nearest
tries.42 It consists of 20 surfaces, 12 vertices and 30 edges, neighbours(NN)distances: fromaverticalatomtothenear-
each surface has close-packed structure with the (111) ori-
entation. The most stable particles are built of closed shells ∗Ihpointgroupincludes5-foldaxes,whicharenotcompatiblewiththetrans-
lationalsymmetryand3Dperiodicboundaryconditionsimposedonsupercell
with the number of atoms N =1,12,42,.... Fe-Pt NPs
shell inVASPpackage. RemainingelementsofIhgroup,formingThpointgroup,
crystallising in the icosahedral geometry with the alternating
wereconsideredinourstaticcalculations.
1–8 |3
estedgeatoms(1–2inFig.4)andbetweentwonearestedge Fe Pt Fe Pt
12 43 43 12
atoms (2–2 in Fig. 4). In Fe Pt , they read 2.704 A˚ and T=150K T=150K 0.8
43 12 8
2.677 A˚, while in Fe Pt – 2.767 A˚ and 2.663 A˚, respec- Pt 0.6
12 43 6 Fe
tively. In the Pt subsurface shell NN distances are equal to 4 0.4
2.778 A˚, while in the Fe one they are 2.720 A˚. For compari- 2 0.2
son,inthebccironstructuresimulatedwiththesameatomic 0 0.0
dataset,43theNNdistanceisequalto2.485A˚ andinfccplat- 60T=3100RKa2dius 3from 4c.m. 5( ) 6 0T=3100RKa2dius 3from 4c.m. 5( ) 6 0.8
inum 2.772 A˚. This means that, contrary to platinum shells, 0.6
4
tohfeFientePr-tatoamnidcsduibstsaunrcfaecseinofbFoethiProtn,sahreellsst,rothneglsyursftarceetchoende ensity 2 00..24
(∼8−43101%2)whichcanbeoneof1t2he4m3ainreasonsoftheiron- bility d 00T=5100K2 3 4 5 6 0T=5100K2 3 4 5 6 0.0
terminated NP instability. The similar influence of strain on ba 4 Radius from c.m. ( ) Radius from c.m. ( ) 1.0
o
ironsurfacestabilitywasobservedpreviouslyintheFemono- Pr
layer on W(110) surface44 and in FeAu and FePt multilay- 2 0.5
ers45,46. In both particles, the NN distances between the Fe
andPtatomslocatedinthefirstandsecondshell(∼2.50A˚) 00T=11000K2 3 4 5 6 0T=11000K2 3 4 5 6 0.0
and between the central atom and the first shell (∼2.60 A˚) 3 Radius from c.m. ( ) Radius from c.m. ( ) 0.6
are reduced comparing to the Fe-Pt distance in the bulk fct 2 0.4
L10 structure (2.70 A˚).47 It causes the internal stress in the 1 0.2
core, which may be the driving force for the amorphisation
0 0.0
0 1 2 3 4 5 6 0 1 2 3 4 5 6
processes and may induce the structural transformation ob-
Radius from c.m. ( ) Radius from c.m. ( )
servedinlargerFe-Ptparticles.
Fig. 5Radialdistributionofatomicpositionsfromthemasscentre
(c.m.)oftheicosahedral-shellsystem.Theresultsforall
3.2 Moleculardynamics
temperaturesarecomparedside-by-sidefortwoinvestigated
The dynamical stability of a nanoparticle is quite different systemsPt-terminated(left)andFe-terminated(right).The
from the static one. The later requires only that the system probabilitiesarenormalisedtounitypereachelement.The
isinthelocalenergyminimum,theformernecessitatesstabil- semitransparentcolouroftheFeplot(orange)isusedtoshowthePt
ity of the structure against finite, even large, thermal fluctua- plot(blue)inthesamerange.
tions. Theamplitudeoffluctuationsisdeterminedbythetem-
peratureofthesystemandthestrengthofinter-atomicbonds
Fig. 4. At the first glance the qualitative difference between
presentinthesystem.Togobeyondthestaticstabilityanalysis
platinum-terminated (a) and iron-terminated (b) particles is
describedabove,weneedtoincludetemperatureinourcalcu-
obvious. All the Fe atoms are in the subsurface in the for-
lations. WeusedtheDFT-MDtechniquedescribedabove(see
mer, nearly perfect structure, while there are many platinum
section2.2). Thesimplewaytoassestheeffectsofsuchcal-
atoms on the surface of the later, strongly distorted structure
culationisbyinspectionoftheevolutionofthestructure.
– despite the fact that this is a Pt-deficient system. What is
more,thepictureisvirtuallyidenticalathighertemperatures.
Even at T =1000 K there is no qualitative visual difference
between Fig. 4 and the corresponding picture at that temper-
ature. This calls for more detailed, quantitative analysis. In
thecrystallinematerialtheradialdistributionfunction(RDF)
wouldbeafirst-linetoolforsuchinvestigation. Here,thesys-
temisfiniteandwecannotusestandardRDFdirectly. Instead
(a) (b)
we have used radial probability distribution p(r) of finding
i
atomofelementiatthedistancerfromthecentreofmassof
Fig. 4Fe Pt (a)andFe Pt (b)structuresatT=150Kafter10
12 43 43 12 thesystem. Theprobabilityiscalculatedovertheensembleof
psthermalisationand20psofMDrun.Thedifferenceinstructural
last10ps(1000steps)ofconfigurationsattheendoftheMD
stabilityisvisibleevenatsuchalowtemperature.Elements:Fe–
dark/brown,Pt–light/grey.1and2denotetwonon-equivalent run. Weperformedthesamecalculationonthemuchsmaller
positionsofatomsinthesurfaceshellofidealicosahedron. ensembles(0.1−1ps)anddeterminedthatthereisnosignif-
icantdifferenceexceptformuchlargerfluctuationspresentin
Thestructuresafterthermalisation(10ps)andequilibration thehistograms(forobviousstatisticalreasons).
(20 ps) runs at target temperature T =150 K are depicted in Theprobabilitydensity p(r)plots,normalizedtounityfor
i
4| 1–8
each atomic species, for all investigated icosahedral systems withincreasingtemperatureintherightcolumnofFig.5. In-
andtemperaturesarecollectedinFig.5. Itshouldberemem- terestingly, Featomscanbefoundclosetothecentreonlyat
beredthatthesystemsarestartedintheperfectlyorderedstate low temperatures, while they are systematically replaced by
with temperature-determined kinetic energy distribution. At platinumatomsathighertemperatures.
the start of the simulation p(r) function for all systems re- Theresultsobtainedfortwotypesofparticlescanbeeasily
i
semblestheplotforFe Pt atT =150K(top,leftcornerof understoodifwetakeintoaccountstrongtendencyofPtatoms
12 43
Fig. 5) or the static RDF from Fig. 3. The probability distri- foroccupyingtheouterlayersofNPs. Itpreventsdisordering
butionsintheFig.5arecalculatedattheendoftheequilibra- ofPt-terminatedparticles,whichkeeptheirperfectmulti-shell
tion. Since the relaxation processes may have very different structure even at high temperatures. It agrees with the previ-
timescales,onecannotbesurethatthetrueequilibriumstate oustheoreticalstudies22–27andtheexperimentalobservations
hasbeenreached. Nevertheless,thelackofsystematicdriftin of good thermal stability of icosahedral Fe-Pt particles even
theprobabilitydistributionsattheendofthesimulationperiod withmuchlargersizes.20 Inthethinfilms,thePt-termination
allowsustoconcludethatthesystemsarereasonablycloseto wasdeducedfromtheDFTcalculationsofthephononspectra
equilibrium. andthesurfacesensitivenuclearinelasticscatteringmeasure-
There is a clear difference between final states of the Pt- ment.47 The simulated Fe-terminated surface showed strong
terminated (left column in Fig. 5) and Fe-terminated (right deviationfromthebulkbehaviour.
column in Fig. 5) system. The former, essentially, exhibits The crucial role in the stabilization of multi-twinned
temperature-caused broadening of the distribution peaks, nanoalloys is played by the difference in atomic sizes of the
whilethelatershowsclearsignsofsubstantialreconstruction two elements: larger size mismatch reduces the compression
ofthestructureaswellasmuchstrongerbroadeninganddis- ofthecore. TheMDsimulationsperformedonthepolyicosa-
tortionofthepeaks. hedral core-shell Ag-Cu and Ag-Ni clusters revealed much
highermeltingtemperaturesthanforpureAg,CuandNipar-
Since there is not much happening in the Pt-terminated
ticles.48,49 Even single impurities can stabilize the icosahe-
structure, let us concentrate on the Fe-terminated one. We
dralAgparticles–thesmallerthedopingatom,thehigherthe
candistinguishtwomainphenomenaintheseplots. Thefirst
meltingtemperature.50 Asshowninrecentstudies,thestabil-
one is a significant disordering of the system, shown in very
ityofNi-AuNPsisalsoenhancedinthecore-shellstructure,
broad and irregular peaks – even at low temperatures. The
which has much higher melting temperature than random al-
secondphenomenonisasystematicdriftoftheplatinumdis-
loys.51
tribution to the external shell of the particle. We expect the
TheFe Pt particleisveryunstableduetothemovement
formerprocesstohavefairlyshorttimescaleandlowactiva- 43 12
of Pt atoms towards the surface. This leads to significant
tionbarriers,oppositetotheotheronewhichrequiresglobal,
changes of atomic positions and strong deformation of the
collectivemovementsandthuslargeactivationenergy,andex-
icosahedral geometry. Apart from the segregation processes
hibitsmuchlongertimescale. Consequently, thereconstruc-
resultingfromdifferentsizesofconstituentatoms,otheramor-
tionisprobablyclosetofinishedonlyinthehightemperature
phisationmechanismsmayalsobeofsomeimportancehere.
case (T =1000 K bottom of Fig. 5), is under way for inter-
The previous MD simulations revealed the amorphisation of
mediate temperatures (T =500 K), and is only starting for
mono-atomicPt icosahedralparticlesinvolvingtherosette-
lower temperatures (T =150 K, T =300 K). Nevertheless, 55
likestructuraltransformation,whichformsasixfoldringcen-
even at T =150 K we can see non-vanishing Pt probability
tred around the fivefold vertices and breaks the I symme-
at the outside shell and some migration of Fe atoms towards h
try.52 A preference for low-symmetry amorphous structures
the interior of the particle. This process seems fully consis-
wasfoundalsointheAunanoclusters.53
tentwithourearlierobservationsdrawnfromthestructuresin
Fig.4. ThehightemperatureintheT =1000Kcasehelpsto
overcometheactivationbarriersandspeedsupthereconstruc- 4 DisorderedFe-Ptnanoparticles
tion.Weexpectthatifweleavethelowertemperaturecasesto
evolvelongenoughtheywillreachsimilarshapeofthedistri- Theresultsdescribedaboveconcernedicosahedralmulti-shell
butionasthehightemperaturecase. Unfortunately, thiskind structures. Thesestructuresareinherentlynon-stoichiometric
oftimescaleisprohibitivelylongtoachieve–weestimateit and thus quite different from the fragments of the bulk crys-
willrequireatleastoneyearworthofMDrunforT =150K. tals.Ontheotherhand,suchhighlyorderedsmallparticlesare
Note also that after reconstruction some level of ordering is veryunlikelytoformnaturally,althoughadvancedexperimen-
recoveredinthehightemperaturesystem–thepeaksarebet- taltechniquesmaybewellcapableofproducingjustsuchsys-
ter defined and localised and actually narrower than for the tems. The synthesised icosahedral particles with larger sizes
low-temperature systems. In fact, one can recognise a clear (∼5−6nm)andclosetoequiatomiccompositionsexhibitthe
gradient of decreasing noise and disorder of the distributions shell-periodicstructurewiththeFe/PtcoreandthePtenriched
1–8 |5
outershell.20Forsmallsystemssuchorderedcore-shellstruc- of the MD run) for both sizes of the particles are depicted in
turesmaybeveryunstableandweexpectnaturalprocessesto Fig.6.
form rather disordered particles with the composition of ele-
mentsdeterminedbytheirrelativeconcentrationsintheenvi-
ronmentandotherfactorssuchaschemicalpotentials,surface
Small Large
energies,bondingenergiesetc.
T=300K T=300K
0.8
2
Pt
Fe 0.6
nsity 1 0.4
de 0.2
y
abilit 030T=5001K 2 3 0T=1500K2 3 4 5 6 0.0
b
Pro 0.6
2
(a) (b) (c) 0.4
1
Fig. 6SmalldisorderedparticleatT =300K(a),largerdisordered 0.2
particleatT =300K(b)andatT =500K(c).Allstructuresafter
0 0.0
30psthermalisation.Elements:Fe–dark/brown,Pt–light/grey. 0 1 2 3 0 1 2 3 4 5 6
Distance from c.m. ( ) Distance from c.m. ( )
Asthesimplestmodelwehavedecidedtoselecttwomagic Fig. 7Radialdistributionofatomicpositionsfromthemasscentre
number(i.e. numbersfromthepartialsum: 1+12+42+...) (c.m.)ofthesystem.Theresultsforalltemperaturesarecompared
side-by-sidefortwoinvestigatedsystemssmall(left)andlarge
particles with concentrations close to 50/50 (the magic num-
(right).ThesemitransparentcolouroftheFeplot(orange)isusedto
bers are odd, thus the exact 50% concentration is unattain-
showthePtplot(blue)inthesamerange.
able). TheselectedstructuresareFe Pt andFe Pt –both
6 7 27 28
with slight iron deficiency – as we expect such particles to
bemorestablethantheirplatinum-deficientcounterparts(see
above).Weselectedmagic-numberparticles(13and55atoms Weappliedthesameanalysistechniquesasdescribedabove
respectively) to make it possible for the systems to relax to for icosahedral particles. The resulting radial distribution
closed-shell configurations which one can expect to be ener- functionsareplottedinFig.7.Theresultsforthesmallsystem
geticallyfavourable. indicatethesamepatternweobservedintheicosahedralparti-
Theappliedprocedurewasidenticaltotheoneusedabove cles–theplatinumatomstendtomovetotheexternallayerof
insection2.2. Theonlynotabledifferencewasamuchlonger theparticleandtheironatomsgatherclosertothecentre. The
thermalisation period required for the system to settle down same pattern is less visible in the data for the larger particle
closetotheequilibrium–oftheorderof10ps. Duetoalarge – which is not as close to equilibrium as the small one – but
size of the configuration space of disordered particle and a thesametrendisvisibleanyway. Thereiscleardifferencein
longtimescaleofslowrelaxationprocesses,wedonotexpect theleveloforderingexhibitedbysmallversuslargerparticles,
the system to reach the true equilibrium state. Nevertheless, forthereasonsexplainedabove, butevenforalargersystem
by examining the directions the system configuration drifts there are clear signs of the emerging structure in the form of
after thermalisation, we can determine the direction of these obvious peaks in the RDF function and visible movement of
relaxation processes. This idea can be further cross-checked platinumatomstotheoutsideoftheparticle.Thedetailsofthe
by application to very small particles. Due to much smaller RDFdistributionaresubjecttostandardshort-termstatistical
configuration space and much lower barriers for collective andthermalfluctuations,buttheoverallshapeofthedistribu-
movements,asmallparticlecanreachitsequilibriuminmuch tions proved to be fairy robust and subject only to long time
shortertime. RunningtheMDsimulationuntilfullrelaxation scale relaxation processes. We believe that if the system is
isactuallyfeasibleinthiscase. Weranthisprocedureforthe left to evolve even longer, it will probably reach partially or-
smallest non-trivial, magic cluster: Fe Pt at T =300 K and deredequilibriumwithplatinumatomslocatedmainlyonthe
6 7
T =500 K. The parameters of the simulation were the same surfaceoftheparticle. Unfortunately,theexpectedtimescale
asforlargersystems,exceptthatthetotalsimulationlengthof –measuredatleastinnanoseconds, perhapsevenlonger–is
30 ps was easy and inexpensive to achieve. Simultaneously, prohibitiveforthepureDFTMDtechnique. Thistypeofcal-
the small system stopped to drift in any significant way after culation would require a method which is at least few orders
onlyfewpicosecondsofsimulation–indicatingarrivalatthe ofmagnitudemoreeffectivethanpureDFTMD–e.g. neural
equilibriumconfiguration. Theresultingstructures(attheend networkderived,multi-parametereffectivepotentials.54–56
6| 1–8
5 Conclusions 6 Acknowledgements
This work was partially supported by the COST Ac-
tion MP0903 ”Nanoalloys as Advanced Materials: From
In the presented work we have investigated the stability and
Structure to Properties and Applications” and by the Pol-
dynamics of icosahedral nanoparticles constructed with two
ish National Science Centre (NCN) under Project No.
radicallydifferent(intermsofmass,atomicradius,bulkmod-
2011/01/M/ST3/00738.
ulus, magnetic moment) metals: iron and platinum. The op-
timised icosahedral NPs with perfect layered structures have
References
rather stiff platinum shells with inter-atomic NN distances
wellcorrespondingtothePtbulkvaluesandstronglystretched
1 R.Ferrando,J.JellinekandR.L.Johnston,Chem.Rev.,2008,108,845–
ironshellswithNNdistanceelongatedby8−10%incompar- 910.
isontothebulk. Evenforiron-separatedNPs,withsignificant 2 R.L.JohnstonandR.Ferrando,FaradayDiscuss.,2008,138,9–10.
dominanceofFeatoms,compressionofPtshellsdoesnotoc- 3 M.Alca´ntaraOrtigozaandT.S.Rahman,Phys.Rev.B,2008,77,195404.
curandprovestobeimpossible. Ontheotherhand,unstable 4 M.M.Mariscal,O.A.OviedoandE.P.M.Leiva,MetalClustersand
Nanoalloys: FromModelingtoApplications,SpringerScience&Busi-
ironshellsdrivethesystemtoreconstructionand/orsignificant
nessMedia,2012.
loweringofthemeltingtemperature.
5 S.DuanandR.Wang,ProgressinNaturalScience: MaterialsInterna-
tional,2013,23,113–126.
TheDFTmoleculardynamicscalculationscarriedoutina 6 C.T.Campbell,Nature,2004,432,282–283.
number of temperatures (T =150−1000 K) revealed strong 7 X.Huang,P.K.Jain,I.H.El-SayedandM.A.El-Sayed,Nanomedicine
(Lond),2007,2,681–693.
instabilityoftheiron-terminatedstructureandsignificantten-
8 F.Iskandar,AdvancedPowderTechnology,2009,20,283–292.
dencyforplatinumatomstomigrateintosurfacelayer–even
9 S.Sun,C.B.Murray,D.Weller,L.FolksandA.Moser,Science,2000,
at low temperatures and platinum-deficient particles. The 287,1989–1992.
same tendency was observed in the very small (13 atoms) 10 S.DuanandR.Wang,NPGAsiaMaterials,2014,6,e122.
as well as larger disordered particles (55 atoms) with atomic 11 W.Chen,J.Kim,S.SunandS.Chen,Phys.Chem.Chem.Phys.,2006,8,
concentrationsclosetothe50/50ratio. Furthermore,theplat- 2779.
12 J.Kim,Y.LeeandS.Sun,J.Am.Chem.Soc.,2010,132,4996–4997.
inumcappinglayerseemstoadditionallystabilisetheparticle.
13 S.GuoandS.Sun,J.Am.Chem.Soc.,2012,134,2492–2495.
Inourcalculationstheplatinum-terminatedsystemprovedto
14 S.HsiehandP.-Y.Lin,J.Nanopart.Res.,2012,14,1–10.
be stable up to T = 1000 K. On the other hand, the iron-
15 S. Chen, L. Wang, S. L. Duce, S. Brown, S. Lee, A. Melzer, S. A.
terminated system shows substantial instability – leading to CuschieriandP.Andre´,J.Am.Chem.Soc.,2010,132,15022–15029.
significantreconstructionofthestructureandprobablypartial 16 D.K.Kim,D.Kan,T.Veres,F.Normadin,J.K.Liao,H.H.Kim,S.-H.
meltingevenatalowtemperature(T =150K). Lee,M.ZahnandM.Muhammed,J.Appl.Phys.,2005,97,10Q918.
17 K.SeemannandB.Kuhn,Biomed.Opt.Express,2014,5,2446–2457.
18 K. M. Seemann, M. Luysberg, Z. Re´vay, P. Kudejova, B. Sanz,
Thestabilizingeffectofplatinumatomsseemtoberelated
N.Cassinelli,A.Loidl,K.Ilicic,G.MulthoffandT.E.Schmid,J.Con-
to the geometric aspect of platinum enclosure of the NP. In trolledRelease,2015,197,131–137.
the case of Fe Pt NP, platinum atoms have no significant 19 C.Y.Tan,J.S.Chen,B.H.LiuandG.M.Chow,J.Cryst.Growth,2006,
43 12
influenceonthestabilityoftheNPbecausetheyonlydecorate 293,175–185.
20 R.M.Wang,O.Dmitrieva,M.Farle,G.Dumpich,H.Q.Ye,H.Poppa,
the surface instead of forming complete enclosure. The case
R.KilaasandC.Kisielowski,Phys.Rev.Lett.,2008,100,017205.
of50/50Fe-PtNPsfurtherindicatesthatitisrathergeometry
21 R.Wang,H.Zhang,M.FarleandC.Kisielowski,Nanoscale,2009,1,
thanconcentrationofplatinumatomsthateffectsthestability 276–279.
ofnanoparticles. 22 A.FortunelliandA.M.Velasco,THEOCHEM,1999,487,251–266.
23 R.V.Chepulskii, J.VelevandW.H.Butler, J.Appl.Phys., 2005, 97,
The structural properties of small Fe-Pt NPs and their de- 10J311.
24 R.V.ChepulskiiandW.H.Butler,Phys.Rev.B,2005,72,134205.
pendence on temperature discussed in the present work may
25 M.Mu¨llerandK.Albe,Phys.Rev.B,2005,72,094203.
be important for nano-technological applications. For in-
26 B.Yang,M.Asta,O.N.Mryasov,T.J.KlemmerandR.W.Chantrell,
stance, the catalytic activity of strongly distorted NPs could ActaMater.,2006,54,4201–4211.
beenhancedcomparingtopurePtsurfacesorlargerFe-Ptpar- 27 M.E.Gruner,G.Rollmann,P.EntelandM.Farle,Phys.Rev.Lett.,2008,
ticles. A larger distribution of Fe-Pt bond lengths as well as 100,087203.
the presence of both types of atoms at the surface may lead 28 P.HohenbergandW.Kohn,Phys.Rev.,1964,136,864.
29 W.KohnandL.J.Sham,Phys.Rev.,1965,140,1133.
to selective modification of electronic structure and catalytic
30 G.KresseandJ.Furthmu¨ller,Comput.Mater.Sci.,1996,6,15–50.
activityofPtatoms. ItwasobservedthatadditionalCoatoms
31 G.KresseandJ.Furthmu¨ller,Phys.Rev.B,1996,54,11169–11186.
decoratingthesurfaceofPtnanocrystalsleadtoincreasedse- 32 F.Pe´rezandB.Granger,Comput.Sci.Eng.,2007,9,21–29.
lectivityofhydrogenationreactions.57 33 S.R.BahnandK.W.Jacobsen,Comput.Sci.Eng.,2002,4,56–66.
1–8 |7
34 E.Jones, T.Oliphant, P.Petersonetal., SciPy: Opensourcescientific
toolsforPython,2001–,[Online;http://www.scipy.org/;accessed2015-
01-07].
35 S.vanderWalt,S.ColbertandG.Varoquaux,Comput.Sci.Eng.,2011,
13,22–30.
36 J.Hunter,Comput.Sci.Eng.,2007,9,90–95.
37 P.E.Blo¨chl,Phys.Rev.B,1994,50,17953–17979.
38 G.KresseandD.Joubert,Phys.Rev.B,1999,59,1758–1775.
39 J.P.Perdew,J.A.Chevary,S.H.Vosko,K.A.Jackson,M.R.Pederson,
D.J.SinghandC.Fiolhais,Phys.Rev.B,1992,46,6671–6687.
40 J.P.Perdew,K.BurkeandM.Ernzerhof,Phys.Rev.Lett.,1996,77,3865–
3868.
41 P. T. Jochym, A. M. Oles´, K. Parlinski, J. Łaz˙ewski, P. Piekarz and
M.Sternik,J.Phys.:Condens.Matter,2010,22,445403.
42 A.L.Mackay,ActaCrystallogr.,1962,15,916–918.
43 J.Łaz˙ewski,P.Piekarz,A.Oles´andK.Parlinski,Phys.Rev.B,2006,74,
174304.
44 J.Łaz˙ewski,P.Piekarz,A.Oles´,J.KoreckiandK.Parlinski,Phys.Rev.
B,2007,76,205427.
45 M.Sternik,K.ParlinskiandJ.Korecki,Phys.Rev.B,2006,74,195405.
46 P. T. Jochym, K. Parlinski and A. M. Oles´, Eur. Phys. J. B, 2008, 61,
173–179.
47 S. Couet, M. Sternik, B. Laenens, A. Siegel, K. Parlinski, N. Planck-
aert,F.Gro¨stlinger,A.I.Chumakov,R.Ru¨ffer,B.Sepiol,K.Temstand
A.Vantomme,Phys.Rev.B,2010,82,094109.
48 G.Rossi,A.Rapallo,C.Mottet,A.Fortunelli,F.BalettoandR.Ferrando,
Phys.Rev.Lett.,2004,93,105503.
49 R.Ferrando,A.FortunelliandG.Rossi,Phys.Rev.B,2005,72,085449.
50 C.Mottet,G.Rossi,F.BalettoandR.Ferrando,Phys.Rev.Lett.,2005,
95,035501.
51 B.Li,G.Xing,H.WangandR.Wang,AIPAdvances,2014,4,117132–
1–9.
52 E.Apra`,F.Baletto,R.FerrandoandA.Fortunelli,Phys.Rev.Lett.,2004,
93,065502.
53 I.L.Garzo´n,K.Michaelian,M.R.Beltra´n,A.Posada-Amarillas,P.Or-
dejo´n, E.Artacho, D.Sa´nchez-PortalandJ.M.Soler, Phys.Rev.Lett.,
1998,81,1600.
54 S.Hobday,R.SmithandJ.BelBruno,Nucl.Instrum.MethodsPhys.Res.,
Sect.B,1999,153,247–263.
55 M. Malshe, R. Narulkar, L. M. Raff, M. Hagan, S. Bukkapatnam and
R.Komanduri,J.Chem.Phys.,2008,129,044111.
56 J.Behler,ChemicalModelling,RoyalSocietyofChemistry,Cambridge,
2010,vol.7,pp.1–41.
57 S.C.Tsang,N.Cailuo,W.Oduro,A.T.S.Kong,L.Clifton,K.M.K.Yu,
B.Thiebaut,J.CooksonandP.Bishop,ACSNano,2008,2,2547–2553.
8| 1–8