Physics of Atomic Clusters by Arun

8/7/2019 Physics of Atomic Clusters by Arun

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PhysicsofAtomicClustersEarliestreferenceofclustersmadebyRobertBoyleaslongas1661AD

By:Arunkumar V

(RollNo2010413002)

M.Tech (Nanoscience &Technology) 1st Year


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Agroupofatomsboundtogetherbyinteratomicforcesiscalledanatomiccluster.

Aggregateofacountablenumberrangesrom to

Clusters span a wide range of particle sizes,,

to the microcrystalline.

(nanoparticles) which may have properties,which are distinct from those of either

discrete molecules or bulk matter.

Example:

ma c us erso a erromagne cma er a aresuper

paramagneticratherthanferromagnetic.


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PhysicsofAtomic&MolecularClusters

DifferenttypesofClusters:

VanderWaalsclusters,

Metallicclusters,

Fullerenes,

Molecularclusters,

Semiconductorclusters,

Mixedclusters,etc.,

Structureofphosphinechloride andphosphinethiolate

rotected39 and11atom oldclusters. a 39atom old

cluster;(b)39atomgoldclustercore;(c)11atomgold

cluster;and(d)11atomgoldcluster.


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Im ortanceofClusters

Metallic Cluster

of Au atoms

Molecular structure of

Ge14[Ge(SiMe3)3]5Li3(thf)6

Van der Waals ClustersFullerene C60


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Im ortanceofClusters

Importantquestion:

What determines the difference in properties between Bulk and Clusters of

same material. How large must a cluster be before its properties resemble

those of the bulk element?

ImportantParameters:

SizeEffect&

Percenta e o atoms on Sur ace


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VariationofClusterPro ertieswithSize

SphericalClusterApproximation(SCA),anNatomclusterismodeledbyasphere.

Thisbecomesabetterapproximationastheclustergetslarger

,

Theradiusofatoms(Ra),surfaceareaofatoms(Sa)andvolume ofatom(Va)

Manypropertiesofclustersdependonthefractionofatoms(Fs)whichlie

onthesurfaceofthecluster


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VariationofClusterPro ertieswithSize

Fraction of surface atoms (Fs) plotted against

N1/3 for icosahedral geometric shell clusters.

The dashed line represents the prediction of

the Spherical Cluster Approximation.

The figure shows that the fraction of surface

atoms approaches the limiting value (4N1/3)

(given by Equation on previous slide) as the

cluster size increases.


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. ,

the diameter (for a cluster of sodium atoms) and Fs is the fraction of

surface atoms.

It is apparent that clusters with as many as 10,000 atoms still have nearly

20% of their atoms on the surface. In fact, Fs only drops below 0.01 (i.e. less. ,

corresponds to a diameter of approximately 0.16 m for sodium clusters


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ClusterSizeEffectsSize

Dependent Melting

Meltingtemperaturesforthesmallestnanoclusters turnedouttobeaslowas300K

significantlylowerthanthemeltingpoint(approximately1336K)ofbulkelementalgold.

The melting temperature (Tm) of gold clusters as a function of radius R. The points represent

experimental data, the solid line is interpolation and the dashed line indicates the bulk melting

temperature.

Themeltingtemperaturesofgoldclustershavebeenfoundtodecreasewithdecreasingclustersize,followinga1/Rtrend.


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Inthelargeclusterregime,manyGenericclusterproperties(G)showaregularvariation

withclustersize.Thekeyclusterpropertiesare:

, , . . . .

SpecificHeat(C) Generallyreducesw.r.t.bulk.

Meltingtemperature Tm Generallyreducesw.r.t.bulk.

, , .,


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A spherical cluster model, in which the Natom cluster is approximated by a

sphere ofradius R, this smooth CSE behavior can be described by simple scaling

laws.

.

dependontheratioofsurfacetobulk(volume)atomsinacluster,andsince,

theexponentsinequationsaregenerallya=1


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TheionizationenergyofpotassiumclustersasafunctionofclustersizeN.Thepoints

representexperimentaldata,thesolidlineistakenfromtheinterpolationformula

andthedashedlineindicatesthebulkworkfunction.


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ImportantPropertiesofClusters

ClusterMagic Numbers

A significant difference between clusters and bulk matter is the variability of the

properties of clusters with the number of their constituent particles called magic

numbers.

The cluster geometry is an important feature of clusters, influencing their stability

and stability itself is a function of magic numbers.

The stability of clusters and their transformations is a crucial importance for

tom c uster systems an s c ose y connecte to t e pro em o c uster mag c

numbers.

cluster's electronic and ionic structure. Understanding the magic numbers of a

cluster is equivalent to understanding its electronic and ionic structure.


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CaseStudiesonFewClusters

Deviationsfromre ularclusterbehaviorsoffewHomo eneousClusters

*Sodium *GalliumandTin

*Aluminium *Gold

Theexperimentalobservations

1. Strongnonmonotonicvariationinmeltingtemperatureof SODIUMClusters.

2. TIN

&

GALLIUM have HighermeltingpointthanBulk.

3. Disproportionatesizesensitivity. Ga andAl:NaandGoldClusters

4. TheGroundStateGeometry:TheKey


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CaseStudiesonFewClustures

= , , , , , ,

While,MeltingTemperature (Tm)ofclustersgenerallyreducesw.r.t.bulk,incaseofNa(Sodium)itwasobserved:

Large&irregularfluctuationsinthemeltingtemperature (sizes55 afewhundred)

Allsimulations/calculations(mainlyusinginteratomic potentials)yieldTm 100Kbelow

experimentalresult.T epea sint e eatcapacity onotcorre atewit eit ergeometricore ectronics e

closing..


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ExperimentallymeasuredTm ofNan+ clusters


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Geometrical StructureofNan (n=3962)

Deformationparameter


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SpecificheatofSodium clusters

= :pea e

N=50:flat

N=55:verysharp

N=58: eakedbutbroad


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HigherThanBulkMeltingPoint ofTin(Sn)Clusters

CommonObservation:Tm forclustersislessthanthatofbulk:

Tmelt(R)=Tbulk (1 C/R)

ExperimentsbyJarrold (PRL)etalcontradictthis.

Theyobserved,meltingtemperaturesofTin (Sn)andGallium (Ga)clustersintherangeof1050atomsturnoutto

be

Atleast50KabovebulkforTinand200 300KmoreforGa

AtomicConfigurationZ=50:5p2 ,5p2

Group14 C Si Ge Sn Pb

. . . .

Existsindiamondstructurebelow286K(semiconductor)andinBCTabove(Metal).

Note:SubstantialVariationinthebandGapacrosstheseriesindicatesprogressiveweakeningofsp3

hybridization>>weakestinSn. Failedsemiconductor.Asolidonthevergeofbecomingametal.


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Interesting features of Sn clusters:

roun s a e geome r es o sma n, e, an c us ers are very s m ar(N


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OnemorehigherThanBulkMeltingPoint Gallium(Ga)Clusters

OnemoresystemwithhigherthanbulkTmpoint:

,

Sizesensitive HeatCapacity:N=30VSN=31

Irre ularvariationinTm : Chan esb 350K

Tmbulkis303K

Recentexperimentsinthesizerange3050show:

DramaticsizesensitivityGa30 ..Nopeak,FlatHeatcapacityGa31..Showsanicepeak,welldefinedTm

us usta ewatomsma ea erence


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GoldClusters

Recent re orts revealed Au to be a tetrahedral

structurewithatomic packingclosetothatofbulk gold

FCC *

Au19 is very similar to that of Au20 with one missing

corneratom

These two clusters are speculated to be highly stable

with large HOMOLUMO energy gap

HeatCapacityCurvesofAu19andAu20

Proposedtobehighlycatalyticallyactive

Au20 remains in its ground state untill 700~K

after which it undergoes a dramatic structural

capacity curve


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CaseStudiesConclusions

Na,Ga,Au:showsizesensitivity

Variationinthemeltingtemperature

Variationintheshapeoftheheatcapacitycurve

Ga &Sn have higherthanbulkmeltingtemperature.


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ClustersatfinitetemperaturesbehaveverydifferentlythanBulk

Meltingpointscanbehigherthanbulk

Theshapesofthespecificheatcurvesshowdramaticsizesensitivity.

Thenatureofthegroundstategeometrydictatestheirfinite

temperatureproperties.


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byL.C.Cune,M.Apostol, DepartmentofTheoreticalPhysics,NationalInstituteofPhysicsandNuclearEngineering,Romania

DigestJournalofNanomaterials andBiostructures,Vol.2,No.4,December2007,p.315 333

ATOMICCLUSTERSCIENCE:INTRODUCTORYNOTES

b Andre V. Solov' ov Walter Greiner & JeanPatrick ConneradeVolumeofproceedingsofthe"InternationalSymposiumAtomicClusterCollisions:fission,fusion,electron,ionandphotonimpact"

(a Europhysics Conference)heldinSt.Petersburg,Russia,July1821,2003

LECTURESONCLUSTERSATFINITETEMPERATURE

byD.G.Kanhere ,

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Physics of Atomic Clusters by Arun