Atomic-scale structure of nanosized objects (nanoparticles)

Valeri Petkov Department of Physics, Central Michigan University,

Mt. Pleasant, MI 48859petkov@phy.cmich.edu

Structure of bulk objects (crystals)

Atoms in crystals sit on the vertices of 3D periodic lattices…

Diamond

“Crystal Structure” = Lattice type and symmetryUnit cell parameters:

a, b, c, α, β, γAtomic positions inside the unit cell: (x,y,z)…..

Allow to compute and predict properties of crystals..

How it is characterized ?

Structure of bulk objects (non crystals)

Atoms in non crystals do not sit on the vertices of 3D periodic lattices…

What about nanosized objects ?

Large-size, non-periodic models giving a statistical description of the atomic-scale structure.. (here is indeed where atomic PDFs were applied first)

Crystals

Bragg peaks only Both Bragg peaks and diffuse scattering

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120014001600

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nsity

(a.u

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Bragg angle, 2θ

Disordered/nanocrystals

Simulated

2d patterns

1d patterns

Diffraction patterns of bulk crystals show many well-defined Bragg peaks. Diffraction patterns of nanosized objects show both Bragg-like peaks (not so many, not so sharp) and diffuse scattering (that may not be neglected). Diffraction patterns of bulk non-crystals (glasses, polymers, liquids) show diffuse scattering only.

Glasses, liquidsLimited (~ nm) but measurable order Short-range ( sub-nano) order only

Diffuse scattering only

Simulated

2d patterns

Long-range (~mm), periodic order

1d patterns

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, a.u

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Q (Å-1)

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nsity

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Diffraction patterns from materials with different degrees of structural coherence/size/periodicity

So, what do we do: Atomic Pair Distribution Function Analysis (PDF)

Q=4πsin(θ)/λ=1.0135sin(θ)E[keV]

S(Q)=1+ [ ] [ ]22. )(/)()( QfcQfcQI iiiiel ∑∑−

G(r) = (2/π) ∫=

−max

,)sin(]1)([Q

oQ

dQQrQSQ

G(r) = 4πr[ρ(r) - ρo]ρ(r) is the local andρo the average atomic density

Diffraction experiment

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Inte

nsity

(a.u

.)

B ra g g a n g l e , 2 θ

The atomic PDF peaks at characteristic interatomic distances reflecting the 3D structureof materials. It does not imply periodicity.

CdSe and CdTe nanoparticles

Oleic acid-caped CdSe Thiol-caped CdTeIs there a core-shell “sub-structure” ?

Metallic/semiconductor nanoparticles = Quantum Dots

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Nano CdTe

Red

uced

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ctur

e fa

ctor

Q[S

(Q)-1

]

Wave vector Q(Å-1)

Bulk CdTe

Nano CdTe

Bulk CdTe

Nice properties….Not so nice XRD patterns…

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Rwp

= 15 %

Ato

mic

PD

F G

(r)

Interatomic distance r(Å)

Bulk CdTe

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r(Å)

Nano CdTe

Rwp

= 35 %

CdTe and CdSe nanoparticles

Wurtzite Zinc-blende

Cd-Te Cd-S

Thiol-caped CdTe quantum dots are:i) of zinc-blende type ii) core(CdTe)-shell(CdS) sub-structure

Message one: Nanoparticlesmay be with the periodic structure of their bulk counterpart

Wurtzite Zinc-blende

Acetate-caped CdSe nanopartciles are:i) of good crystallinityii) zinc-blende type structureii) note bulk CdSe is of wurtzite type

Pradhan et. al; J. Appl. Phys. 102 (2007) 044304.

Message two: Nanoparticlesmay not exhibit the 3D structure of their bulk counterpart but a closely related, still periodic one.

CdSe Nanoparticles

BaTiO3

Below 183 K BaTiO3has rhombohedralsymmetry.

When 278K < T < 393K the material possesses a

tetragonal-type structure.

Between 183 K and 278 K the structure is

orthorhombic.

At high temperature BaTiO3has a centrosymmetriccubic structure and is paraelectric.

Although the tetragonal polymorph is the thermodynamically stable form at room temperature, most low-temperature synthesis routes often result in the formation of the “cubic” polymorph, and a high-temperature treatment at around 1000 °C followed by cooling is necessary to induce a phase transformation to the tetragonal one.

BaTiO3 nanoparticles

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R=21 %

R=24 %

BaTiO3 - cubic

BaTiO3 - tetragonal

Ato

mic

PD

F G

(Å-2)

Radial distance r (Å)

R=28 %

R=19 %BaTiO3 - tetragonal

BaTiO3 - cubic

PDF fit in the range 1-14 Å

PDF simulation using the parameters obtained from the fit at short distances

Message three: Nanoparticles may show the periodic structure (e.g. cubic) of the bulk material on average but show local deviations (e.g. tetragonal) from it.

Sr/Ba titanate is virtually the most investigatedperovskite material, because of its high dielectricconstant and ferroelectric properties making it

quite useful in electronics applications

More details in V. Petkov et al, Chem. Mater. 18 (2006) 814.

Nanosized objects of complex morphology: V2O5 tubes

Crystalline V2O5 is widely used in application as chemical sensors, catalysts and solid state batteries.The material possesses an outstanding structural versatility and can be manufactured into nanotubes that have many of the useful properties of the parent crystal significantly enhanced.

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tens

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.u.)

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4

V2O5 nanotube

V2O5 crystal

The lack of long range order due to the curvature of the tube walls has a profoundeffect on the diffraction patterns. That of the crystal shows sharp Bragg peaks. The diffraction pattern of the nanotubes has a pronounced diffuse component rendering the traditional techniques for structure determination impossible.

V2O5 nanotubes - search for a structure model

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PDF

G(r

)

xerogel V2O5.nH2O model

Radial distance r(Å)

crystalline K2V3O8 model

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0.25crystalline V2O5 model

crystalline Zn4V21O58 model

Exp. Data – symbolsModel data – solid line

(a)

(b)

(c)

(d)

V2O5 nanotubes – PDF refinement

The well known 16-atom unit cell of crystalline V2O5 (S.G. Pmmn) fits the experimental data well. The agreement documents the fact the atomic PDF provides a reliable basis for structure determination.

Symbols – exp. dataSolid line – calculated data

Best fit to the experimental PDF data for the nanotubes was achieved on a basis of a 46-atom unit cell (S.G.P⎯1). Even a nanocrystal with the complex morphology of V2O5nanotubes possesses an atomic structure very well defined on the nanometer length scale and well described in terms of a unit cell and symmetry.

V2O5 nanotubes – summary

Structure description of V2O5 nanotubes: Double layers of V-O6 octahedral (green)and V-O4 tetrahedral (red) units are undistorted and stacked in perfect registry with the crystal (a). When bent (b) such layers may form nanoscrolls (c) or closed nanotubes (d).Double layers of such complexity may sustain only a limited deformation. As a result, V2O5 nanotubes occur with inner diameters not less than 5 nm. The real-size models shown in (c) and (d) have an inner diameter of approx.10 nm and involve 33,000 atoms.The bending of vanadium oxide layers into nanotubes can be explained by the presence of an anisotropy in the distribution of vanadium 4+ and 5+ ions.

More details in Petkov et al Phys. Rev. B 69 (2004) 085410.

Message four: the structuremay be periodic but the basic structural unit may be very different from that of the bulk counterpart…

Au nanoparticles

water Water + Au clusters

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3 nm

Dendrimer stabilized Au nanoparticles in water

15 nm

Atom

ic P

DF

G(r

)

Radial distance r(Å)

30 nm

Experimental atomic PDFs (symbols) for Au nanosize particles. The x-ray diffraction experiments were carried out at the beamline11IDC at the Advanced Photon Source using x-rays of energy 115 keV.

Au nanoparticles

Larger Au nanoparticles exhibit the fcc-type structure (somewhat distorted) of bulk Au.

What about smaller sizes ?

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dry G6-(Au147)

wet G6-(Au147)

Radial distance (Å)

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mic

PD

F G

(r)

(a)

bulk Au

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nsity

, arb

.u.

Wave vector Q(Å-1)

wet G6-(Au147)

dry G6-(Au147)

bulk Au(b)

Au nanoparticles

Message five: Nanoparticles ( ~ 2nm Au/147 atoms) may exhibit a non-periodic atomic ordering thatshows some signatures (e.g. the local symmetry) of the 3D structure (fcc–type) of the bulk only.

Conclusions:

i) With new technologies moving quickly toward smaller scales nanosized object (“nanoparticles”) of various shapes are produced in increasing numbers.

ii) Nanoparticles have a well defined structure but the structure is not necessarily that of their bulk counterpart.

iii) That is why the structure of nanoparticles has to be determined with care (and not just assumed).

iv) PDFs seem to do a very good job and, for now, the PDF future looks bright….

What would be helpful (from our point of view) ?

1. Improved instrumentation, including in-houseFor now we have:i) Mo/Ag Ka, convenient to use at home but it is very time consuming (there are no detectors optimized for Mo or Ag radiation..). XRD equipment makers: where are you ?(ii) Synchrotron with IPs. Fast but energy not sensitive (more difficult data corrections) iii) Synchrotron with SSD, energy sensitive but is not very fast(easier data corrections)Could we combine the best of (ii) and (iii) ?

2. There is no software to handle models of finite objects (i.e. nanoparticles with free surface). Even RMC assumes bulk-like models with a cell-type periodicity….Scientific software developers: any ideas/developments ?