Methodische Aspekte der Strukturcharakterisierung ... · Methodische Aspekte der...

Methodische Aspekte der Strukturcharakterisierung nanokristalliner Materie

Reinhard B. Neder

Institut für MineralogieUniversität Würzburg

reinhard.neder@mail.uni-wuerzburg.de

Nanoparticles

● Extended clusters ~1 nm to 300 nm

● Properties intermediate between molecule and crystal

● Optical properties depend on size

Open topics for nanoparticles

� TEM: preparation; core/shell; statistics� XRD: Debye-Scherrer invalid: size + disorder� Exciton: depends on bulk theory� small angle: available edges

Zanchet et al. J. Phys. Chem B (2000),104,11013

Au particlesscale = 5nm

determination of size

Open topics for nanoparticles

16 Å

32 Å

Dhkl = 0.94 λ

β sin Θ

Open topics for nanoparticles

� TEM: preparation; core/shell; statistics� XRD: Debye-Scherrer invalid: size + disorder� Exciton: depends on bulk theory� small angle: available edges

determination of size

Open topics for Nanoparticles

● structure

small crystal <=> glass <=> unique structure

core = rim ? surface relaxation ?

homogeneous structure ⇔ heterogeneous structure

Open topics for Nanoparticles

● structure� TEM: lattice planes ==> well ordered� XRD: too few, broad peaks� EXAFS: local order only

Zanchet et al. J. Phys. Chem B (2000),104,11013

thiol passivated Au nanoparticles

Open topics for Nanoparticles

● structure� TEM: lattice planes ==> well ordered� XRD: too few, broad peaks� EXAFS: local order only

Wu et al. J. Phys. Chem B (2000), 106, 4569

CeO2

Open topics for Nanoparticles

● structure� TEM: lattice planes ==> well ordered� XRD: too few, broad peaks� EXAFS: local order only

Wu et al. J. Phys. Chem B (2000), 106, 4569

CeO2

Open topics for Nanoparticles

● structure� TEM: lattice planes ==> well ordered� XRD: too few, broad peaks ==> no direct structure� EXAFS: local order only

Characterisation techniquesTEM

Powder diffraction

Pair distribution function PDF

Absorption spectroscopy

Small angle scattering

standard / anomalous

real space refinement

complementary to PDF,chemically selective

chemically sensitive viaanomalous small angle

CdS-Glutathione

contradictory size information 15 to 30 Å

Cd

S

Bond length Cd-S- within core- to Glutathione molecule

Structure

Data Collection

BW5, HASYLAB

λ=0.088 ÅE=140 keVT=15 Ksealed capillaryQmax = 30 Å-1

Experimental Data

Only three broad maxima

Inset corresonds toexperiment with Cu-Kα

Normalized Structure Factor

Experimental PDF

narrow first maximum at 2.525 Å

broad, asymmetric second maximum at 4.11 Å

Experimental PDF

longest distance

broad maxima

Experimental PDF

weak maxima at ~1.5 Å

Analysis of first Maximum

R = 2.525 Å; σ = 0.063 ÅN = 3.4

ONE Cd-S distance

Cd-Sinorganic

Cd-Sorganic

Analysis of second Maximum

R = 4.13 Å; σ = 0.15 Å N = 5.8 R = 3.85 Å; σ = 0.12 Å N = 2.7

TWO Cd-Cd distances=> two Cd-S-Cd angles

Cd-Sorganic -Cd = 100 ° Cd-Sinorganic -Cd = 109 °

Summary of direct Interpretation

Chem. analysis Cd1 S0.5 Glutathione0.5

RAMAN spectroscopy No H-S modes ==> Glutathione bound to Cd

PDF 1. peak Cd-S = 2.525 Å; σ = 0.063 Å

2. peak Cd-Sinorganic-S = 109(5)°Cd-Sorganic -S = 100(4)°

PDF longer distances highly disordered

PDF longest distances Diameter ~ 18 Å

ZnO Nanoparticles

012

110010

002011

013

Rietveld refinement

R wp 18 %Wurtzite

size 9.5 nmFWHM 60 = 1.0

anisotropicline widths

ZnO Nanoparticles

012110

Rietveld refinement

R wp 7 %Wurtzite

size 3.2 nmFWHM 60 = 3.0

deviations at 012 and 110

textureanisotropic shapestacking faults

ZnO Nanoparticles

012

110103

Single line fit

hkl FWHM Size

012 3.75 2.42

110 2.72 3.45

103 2.68 3.60

textureanisotropic shapestacking faults

ZnO Nanoparticles Fitting by Debye

Sum over all atom pairsno restrictions on sample structure

Debye formula :

< | F(h) |2 > = Σ j fj2 + Σ i Σ j,j ≠ i fi fj sin ( 2π h rij) / (2π h rij)

open to finite particle with any shapedefects like stacking faults etc.

ZnO Nanoparticles Fitting by Debye

< | F(h) |2 > = Σ j fj2 + Σ i Σ j,j ≠ i fi fj sin ( 2π h rij) / (2π h rij)

= N cJΣ J fJ2 + 2 Σ I Σ J fi fj Σ i Σ j,j > i sin ( 2π h rij) / (2π h rij)

Debye formula :

ZnO Nanoparticles Fitting by Debye< | F(h) |2 > = N cJΣ J fJ

2 + 2 Σ I Σ J fi fj Σ i Σ j,j > i sin ( 2π h rij) / (2π h rij)

for all atom ifor all atoms j > i

compile distance rij into histogram for type IJcompile relative fraction of atoms type I

for all atom pairs IJfor all h

multiply histogram by sin ( 2π h rij) / (2π h rij) (from lookup table) multiply by 2*fi fj

for all atom type Ifor all h

add fi2 * relative amount

creating ZnO Nanoparticles

Calculate powder pattern

Repeat and average

create a large single Wurtzite layer A/B

Stack along c (with faults)

Cut to proper size

{110} and {001}

Repeat with new set of parameter

using a Differential Evolutionary Scheme

Differential Evolution

P1

P2

= trial (d,d)donor

trial (d,p)

trial (p,d)

donor base

parent

choose parent

difference vector

choose difference vector

difference vector * factor

add to donor base to get donorcross-over between parent and donorcompute cost function, keep better of parent/trial

100 * arctan ( | x – 100.23 |

0.05) + noise

Sample for Differential evolution

80.3 * arctan ( | x – 48.188 |

0.87)

Sample for Differential evolution

99.93 * arctan ( | x – 100.23 |

0.049)

Sample for Differential evolution

creating ZnO Nanoparticles

Calculate powder pattern

Repeat and average

create a large single Wurtzite layer A/B

Stack along c (with faults)

Cut to proper size

{110} and {001}

Repeat with new set of parameter

using a Differential Evolutionary Scheme

ZnO Nanoparticles Fitting by DebyeDebye formula

ZnO Wurtzite Structure

acoveral Usize in a-b planesize along cz(oxygen)Stacking probability

R = 8.8 %

ZnO Nanoparticles

Debye formula

Rietveld Rietveld Debyea 3.269 3.256c 5.250 5.224z(O) 0.3876 0.3861B 1.1 1.5

Rietveld Debyesize 3.2 3.6 / 3.8prob --- 0.14

Aspects of PDF Simulation

Finite particle size

Structure more cystal like?more glass like ?complete ?

Proper densityProper coordination distributionProper distance distributions

Best strategy trial and errorRMCevolutionary algorithm

PDF of Nano versus Bulk

Bulk: Number of interatomic pairs increases with r2

4 π ρ0 r

DISCUS uses r !

Nei

ghbo

urs

PDF of Nano versus Bulk

Nanoparticle: A longest vector exists

DISCUS uses r !

4 π ρ0 r tanh(shape(r-diameter)) 4 π ρ0 r

Diameter

Nei

ghbo

urs

Crystal of nanoparticles

Periodic boundary conditions lead to PDF maximawell beyond the particle diameter.

Diameter

Crystal of nanoparticles

Periodic boundary conditions with random orientationdestroy PDF maxima beyond the particle diameter.

Individual nanoparticle

PDF with modified background function

Incomplete structure

Nanoparticle with core and stabilizing molecules

Vectors within core defined by model structure

free molecules

ill defined vectors

scale factor

volume ratio

ZnO Pair Distribution Function

sharp maxima

few stacking faults

Size ~ 9.5 nm

laboratory data

ZnO Pair Distribution Function

laboratory data

simulation based on periodic structure

ZnO Pair Distribution Function

sharp maxima

diameter ~ 5.5 nm

single line fit5.0 nm

dia-

met

er

laboratory data

Rietveld 3.7 nm

ZnO Pair Distribution Function

a 3.256 3.264c 5.238 5.250z(O) 0.3817 0.3836size 38 63

Rietveld PDF

prismatic crystalsno stacking faultsacz(O)Bsize

laboratory data

Size dependent propertiesa and c increase with decreasing particle size Δ vol = 0.7%

smaller particles are less anisotropic in shape

Conclusions

Rietveld/Scherrer equation underestimates particle size

modified Debye formula allows computation of powder pattern for complex nanoparticles

modified PDF calculation allows calculation for finite objects and partially defined objects Differential Evolution is a powerful fitting technique

Acknowledgements

V.I. Korsunskiy

C. Barglik-ChoryG. Mueller

C. KumpfF. NiederdraenkP. Luczak

German Science Foundation SFB410 II-VI Semiconductors

S. DembskiC. GrafC. Ruehl